Critical Thinking: A Concise Guide, 3rd Edition 33505 Thinking

User Manual:

Open the PDF directly: View PDF .
Page Count: 305 [warning: Documents this large are best viewed by clicking the View PDF Link!]

crıtıcal thınkıng

Attempts to persuade us – to believe something, to do something, to buy something –

are everywhere. How can we learn to think critically about such attempts and to

distinguish those that actually provide us with good reasons for being persuaded?

Critical Thinking: A Concise Guide is a much-needed guide to argument analysis and

a clear introduction to thinking clearly and rationally for oneself. Through precise and

accessible discussion, this book equips students with the essential skills required to tell

a good argument from a bad one.

Key features of the book are:

•clear, jargon-free discussion of key concepts in argumentation

•how to avoid common confusions surrounding words such as ‘truth’, ‘knowledge’

and ‘opinion’

•how to identify and evaluate the most common types of argument

•how to spot fallacies in arguments and tell good reasoning from bad

•topical examples from politics, sport, medicine and music; chapter summaries;

glossary and exercises throughout.

This third edition has been revised and updated throughout, with new exercises and

up-to-date topical examples, including: ‘real-world’ arguments; practical reasoning;

understanding quantitative data, statistics, and the rhetoric used about them; scientiﬁc

reasoning; and expanded discussion of conditionals, ambiguity, vagueness, slippery

slope arguments, and arguments by analogy.

The Routledge Critical Thinking companion website features a wealth of further

resources, including examples and case studies, sample questions, practice questions

and answers, and student activities.

Tracy Bowell is senior lecturer in Philosophy at the University of Waikato, New

Zealand.

Gary Kemp is senior lecturer in Philosophy at the University of Glasgow, UK.

Reviews of earlier editions

‘This concise guide offers relevant, rigorous and approachable methods . . . The

authors focus on analysing and assessing arguments in a thoughtfully structured

series of chapters, with clear deﬁnitions, a glossary, plenty of examples and some

useful exercises.’

Will Ord, Times Educational Supplement

‘In my view this book is the most useful textbook on the market for its stated

audience. It provides exceptionally clear explanations, with sufﬁcient technical

detail, but without over-complication. It is my ﬁrst-choice text for teaching critical

thinking to ﬁrst-year undergraduate students.’

Dawn Phillips, University of Southampton

‘. . . written with actual undergraduates, and the standard mistakes and confusions

that they tend to be subject to, clearly borne in mind...’

Helen Beebee,

‘This is the best single text I have seen for addressing the level, presumptions, and

interests of the non-specialist.’

Charles Ess, Drury University

TRACY BOWELL

and

GARY KEMP

crıtıcal

thınkıng

A CONCISE GUIDE

3RD EDITION

First published 2002

This edition published 2010

by Routledge

2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

Simultaneously published in the USA and Canada

by Routledge

270 Madison Ave, New York, NY 10016

Routledge is an imprint of the Taylor & Francis Group, an informa business

reproduced or utilised in any form or by any electronic,

mechanical, or other means, now known or hereafter

invented, including photocopying and recording, or in any

information storage or retrieval system, without permission in

writing from the publishers.

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data

Bowell, Tracy, 1965–

Critical thinking: a concise guide / Tracy Bowell and Gary Kemp. – 3rd ed.

p. cm.

Includes bibliographical references and index.

1. Critical thinking. I. Kemp, Gary, 1960 Oct. 14– II. Title.

B809.2B69 2009-07-10

16—dc22

2009002265

ISBN10: 0–415–47182–6 (hbk)

ISBN10: 0–415–47183–4 (pbk)

ISBN10: 0–203–87413–7 (ebk)

ISBN13: 978–0–415–47182–4 (hbk)

ISBN13: 978–0–415–47183–1 (pbk)

ISBN13: 978–0–203–87413–4 (ebk)

This edition published in the Taylor & Francis e-Library, 2009.

To purchase your own copy of this or any of Taylor & Francis or Routledge’s

collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.

ISBN 0-203-87413-7 Master e-book ISBN

CONTENTS

Preface to the third edition ix

GINTRODUCTION AND PREVIEW 1

1 INTRODUCING ARGUMENTS 3

BEGINNING TO THINK CRITICALLY: RECOGNISING ARGUMENTS 6

ASPECTS OF MEANING 10

STANDARD FORM 12

IDENTIFYING CONCLUSIONS AND PREMISES 14

ARGUMENTS AND EXPLANATIONS 20

INTERMEDIATE CONCLUSIONS 22

CHAPTER SUMMARY 23

EXERCISES 24

2 LANGUAGE AND RHETORIC 27

LINGUISTIC PHENOMENA 27

RHETORICAL PLOYS 40

CHAPTER SUMMARY 50

EXERCISES 51

3 LOGIC: DEDUCTIVE VALIDITY 55

THE PRINCIPLE OF CHARITY 56

TRUTH 60

DEDUCTIVE VALIDITY 62

PRESCRIPTIVE CLAIMS VS DESCRIPTIVE CLAIMS 67

CONDITIONAL PROPOSITIONS 68

THE ANTECEDENT AND CONSEQUENT OF A CONDITIONAL 71

ARGUMENT TREES 73

DEDUCTIVE SOUNDNESS 76

THE CONNECTION TO FORMAL LOGIC 78

CHAPTER SUMMARY 81

EXERCISES 82

4 LOGIC: INDUCTIVE FORCE 89

INDUCTIVE FORCE 90

‘ALL’, ‘MOST’ AND ‘SOME’ 98

SOFT GENERALISATIONS: A REMINDER 99

INDUCTIVE SOUNDNESS 100

PROBABILITY IN THE PREMISES 100

ARGUMENTS WITH MULTIPLE PROBABILISTIC PREMISES 101

INDUCTIVE FORCE IN EXTENDED ARGUMENTS 104

CONDITIONAL PROBABILITY IN THE CONCLUSION 105

EVIDENCE 105

INDUCTIVE INFERENCES 107

A PROGRAMME FOR ASSESSMENT 112

CHAPTER SUMMARY 113

EXERCISES 114

contentsvi

5 THE PRACTICE OF ARGUMENT-RECONSTRUCTION 118

EXTRANEOUS MATERIAL 119

DEFUSING THE RHETORIC 122

LOGICAL STREAMLINING 123

IMPLICIT AND EXPLICIT 125

CONNECTING PREMISES 132

COVERING GENERALISATIONS 133

RELEVANCE 135

AMBIGUITY AND VAGUENESS 138

MORE ON GENERALISATIONS 144

PRACTICAL REASONING 147

BALANCING COSTS, BENEFITS AND PROBABILITIES 150

EXPLANATIONS AS CONCLUSIONS 153

CAUSAL GENERALISATIONS 156

A SHORT-CUT 158

CHAPTER SUMMARY 159

EXERCISES 160

6 ISSUES IN ARGUMENT-ASSESSMENT 169

RATIONAL PERSUASIVENESS 169

SOME STRATEGIES FOR LOGICAL ASSESSMENT 177

REFUTATION BY COUNTEREXAMPLE 180

ENGAGING WITH THE ARGUMENT I: AVOIDING THE ‘WHO IS TO

SAY?’ CRITICISM 183

ENGAGING WITH THE ARGUMENT II: DON’T MERELY LABEL THE

POSITION 184

ARGUMENT COMMENTARY 185

COMPLETE EXAMPLES 188

COMMENTARY ON THE COMMENTARY 195

contents vii

CHAPTER SUMMARY 196

EXERCISES 197

7 PSEUDO-REASONING 202

FALLACIES 202

FAULTY ARGUMENT TECHNIQUES 228

TOO MUCH MATHS! 235

CHAPTER SUMMARY 237

EXERCISES 239

8 TRUTH, KNOWLEDGE AND BELIEF 242

TRUTH AND RELATIVITY 243

TRUE FOR ME, TRUE FOR YOU 248

TRUTH, VALUE AND MORALITY 251

THEORIES 252

BELIEF, JUSTIFICATION AND TRUTH 253

JUSTIFICATION WITHOUT ARGUMENTS 255

KNOWLEDGE 256

JUSTIFICATION FAILURE 257

KNOWLEDGE AND RATIONAL PERSUASIVENESS 259

PHILOSOPHICAL DIRECTIONS 261

CHAPTER SUMMARY 264

EXERCISES 264

Glossary 266

Answers and hints to selected exercises 275

Index 291

contentsviii

PREFACE TO THE THIRD EDITION

Like all authors of texts on critical thinking or critical reasoning, we have tried to write

a book that is genuinely useful. But our conception of what is useful differs somewhat

from that of most of those authors.

On the one hand, we have avoided formal logical methods. Whereas the application of

formal methods is justiﬁed primarily by its value in coping with complex logical structure,

the logical structure of everyday argumentation is very seldom so complex that an argu-

ment’s validity, or lack of it, cannot be revealed to ordinary intuition by a clear statement

of the argument in English. Yet no formal means short of the ﬁrst-order predicate calculus

is sufﬁcient to represent the logic of the majority of everyday arguments. Rather than

compromise by presenting less comprehensive formal methods that are useful only in a

narrow range of cases, we have avoided them entirely.

On the other hand, we have discussed and employed the concepts of logic more

thoroughly than is customary in texts that avoid formal methods. We have deﬁned them

as accurately and in as much detail as we could, without superﬂuous reﬁnement or

inappropriate theoretical elaboration. We have done this for three reasons. First, it is only

by grasping those concepts clearly that the student can achieve a stable and explicit under-

standing of the purposes of presenting and analysing arguments. Second, facility with

those concepts enables the student to think and to talk about arguments in a systematically

precise way; it provides a common currency in terms of which to generalise about

arguments and to compare them. Third, experience, including our teaching experience,

suggests that the concepts of logic themselves, when they explicitly appear in argumenta-

tive contexts, are amongst the most persistent sources of confusion. A symptom of this

is the relativism that is so often encountered and so often lamented. At the root of this,

we assume, are certain equivocations over the word ‘truth’. We have tried to clear these up

in a common-sense and non-dogmatic way, and thereby to clarify further concepts that

depend on the concept of truth, such as validity, probability, inductive force, soundness,

justiﬁcation and knowledge. We hope that clarity about these concepts, and the ability to

use them with conﬁdence in analysing arguments, will be among the most valuable

accomplishments to be acquired by studying this book.

We do not entirely accept the view that examples and exercises in a book on critical

thinking should be real, or even that they should be realistic. Of course, the aim is that

students should be able to deal with real arguments. But, whereas real examples typically

call for the exercise of several strategies and the application of various concepts at once,

those strategies and concepts have to be learned one at a time. Unrealistic, trumped-up

examples and exercises are often much more useful for illustrating and learning isolated

concepts and points of strategy. We have tried to vary the realistic with the artiﬁcial as the

situation recommends.

For work on the ﬁrst edition, we’d like thank Lee Churchman and Damien Cole, both of

whom updated earlier versions of the original text for us in preparation for teaching, and

thereby provided many helpful examples. Thanks also to all those who have provided ideas

either as teaching assistants or students of our Critical Reasoning course at the University

of Waikato during its initial years: especially Paul Flood, Stephanie Gibbons, Andrew

Jorgensen, Dawn Marsh, Alastair Todd, Louis Wilkins and Tim Wilson. We also thank the

Philosophy Department at the University of Waikato for giving Bowell time to stop in

Glasgow to work with Kemp in October 1999.

The second and third editions have beneﬁted enormously from teachers using the book

who have been kind enough to pass along comments and suggestions. The most recent

changes include the split of the material on rhetorical ploys and fallacies into a separate

chapter on fallacies (Chapter 7) and a chapter on linguistic matters generally, including

rhetorical ploys (Chaper 2), a treatment of the vexing issues surrounding the use of the

word ‘theory’ in argumentation, and a simpliﬁcation of the treatment of inductive force.

Along the way, we have streamlined, clariﬁed and reordered in sundry smaller but

sometimes signiﬁcant ways, and updated many examples and exercises. We have many

tutors, teachers and other readers to thank, but we would especially like to single out

Helen Beebee, Jimmy Foulds, Ilan Goldberg, Lawrence Goldstein, Chris Lindsay, Anne

Pittock and Dimitris Platchias. We thank Bre Gordon for all her work on the index.

We also thank the Faculty of Arts and Social Sciences, University of Waikato, for funding

Kemp’s visits to Waikato in spring 2004 and spring 2008, and the study leave granted to

Bowell in autumn 2008 to enable her to visit Glasgow to work on this edition.

Tracy Bowell, University of Waikato

Gary Kemp, University of Glasgow

15 December 2008

preface to the third editionx

introduction and

preview

We are frequently confronted with arguments: these are attempts to persuade us – to

inﬂuence our beliefs and actions – by giving us reasons to believe this or that, or to act in

this way or that. This book will equip you with concepts and techniques used in the

identiﬁcation, analysis and assessment of arguments. The aim is to improve your ability

to tell whether an argument is being given, exactly what the argument is and whether you

ought to be persuaded by it.

Chapter 1 introduces the concept of argument as it should be understood for the purposes

of critical thinking. Argument is distinguished from other linguistic means of getting

people to do and to believe things. We introduce a method for laying out arguments so as

to understand them more clearly.

Chapter 2 begins with a detailed discussion of various ways in which language can

obscure an arguer’s intended meaning. We then return to non-argumentative techniques

of persuasion, introducing rhetorical ploys. Common species of rhetorical ploys are

considered.

Chapter 3 introduces validity and soundness, the main concepts required for the analysis

and assessment of deductive arguments. These are arguments whose premises, if true,

guarantee the truth of the conclusion. We discuss the assessment of validity and sound-

ness, and explain the meaning and use of the principle of charity.

Chapter 4 continues our coverage of the concepts central to this book, this time for the

analysis and assessment of inductive arguments: inductive force and inductive soundness.

We also discuss inductive inferences and degrees of probability.

Chapter 5 covers in more detail the techniques required for reconstructing arguments

and discusses speciﬁc issues that tend to arise in practice. We demonstrate techniques for

deciding which material is relevant to an argument; for dealing with ambiguous and vague

language; for uncovering an argument’s hidden premises; for adding connecting premises;

for dealing with practical reasoning and for dealing with causal arguments.

Chapter 6 is concerned with further concepts and techniques for argument assessment.

We introduce the concept of rational persuasiveness, and introduce further techniques for

assessing arguments and for refuting them. We also include complete worked examples,

applying and illustrating the analytical techniques and concepts developed during the

course of the book.

Chapter 7 is a detailed discussion of fallacies and faulty argument techniques, two species

of what we call ‘pseudo-reasoning’. Common species of each are considered and, using the

concepts and techniques covered in previous chapters, we provide a method for exposing

fallacious reasoning and explaining what is fallacious about it.

Finally, in Chapter 8 we consider some of the philosophical issues underlying the concepts

and techniques used here. We discuss truth and its relationship to belief and knowledge,

and relate these issues to the concept of rational persuasiveness. We sketch some con-

nections to philosophical questions in the theory of knowledge.

Each chapter concludes with a chapter summary and exercises; answers to selected

exercises are at the end of the text. Where appropriate, the reader is encouraged to look

outside the book for further examples to serve as exercises.

introduction and preview2

introducing

arguments

•Beginning to think critically: recognising arguments 6

•Aspects of meaning 10

Rhetorical force • Implicature • Deﬁnitions

•Standard form 12

•Identifying conclusions and premises 14

Identifying conclusions • Several points make the identiﬁcation of

conclusions an easier task • Identifying premises • Extraneous material

•Arguments and explanations 20

•Intermediate conclusions 22

•Chapter summary 23

•Exercises 24

The focus of this book is written and spoken ways of persuading us to do things and to

believe things. Every day we are bombarded with messages apparently telling us what to do

or not to do, what to believe or not to believe: buy this soft drink; eat that breakfast cereal;

vote for Mrs Bloggs; practise safe sex; don’t drink and drive; don’t use drugs; buy free trade

goods; euthanasia is murder; abortion is murder; meat is murder; aliens have visited the

earth; the economy is in danger; capitalism is just; reduce your carbon footprint, etc. Some

messages we just ignore, some we unreﬂectively accept and some we unreﬂectively reject.

Others we might think about and question, asking, ‘why should I do, or refrain from doing

that?’, or ‘why should I believe that, or not believe it?’

When we ask the question ‘why?’ we’re asking for a reason for doing what we are being

enjoined to do, or for believing what we are being enjoined to believe. Why should I vote

for Mrs Bloggs, or eat this particular breakfast cereal? Why should I believe that meat is

murder, or that the economy is in danger? When we ask for a reason in this way we are

asking for a justiﬁcation for taking the action recommended or accepting the belief – not

just a reason, but a good reason – that ought to motivate us to act or believe as we are

recommended to do. We might be told, for example, that Wheetybites are a nutritious,

sugar-free, low-fat breakfast cereal; if this is so, and we want to eat a healthy breakfast, then

we’ve been given a good reason to eat Wheetybites. If, on the other hand, we are given only

state-of-the-art marketing techniques – for example, images of good-looking people

happily eating Wheetybites with bright red strawberries out of fashionable crockery –

then, although an attempt has been made to persuade us to buy Wheetybites, it would not

appear that any attempt has been made to provide good reasons for doing so.

To attempt to persuade by giving good reasons is to give an argument. We encounter many

different types of attempts to persuade.1 Not all of these are arguments, and one of the

tasks we will concentrate on early in this book is how to distinguish attempts to persuade

in which the speaker or writer intends to put forward an argument, from those in which

their intention is to persuade us by some means other than argument. Critical thinkers

should primarily be interested in arguments and whether they succeed in providing us

with good reasons for acting or believing. But we also need to consider non-argumentative

attempts to persuade, as we need to be able to distinguish these from arguments. This is

not always straightforward, particularly as many attempts to persuade involve a mixture

of various argumentative and non-argumentative techniques to get us to accept a point of

view or take a certain course of action.

You may ﬁnd it surprising to think of an ‘argument’ as a term for giving someone a reason

to do or believe something – telling them why they should buy certain products or avoid

illicit drugs for instance. Perhaps in your experience the word ‘argument’ means a dis-

agreement – shouting the odds, slamming doors, insults, sulking, etc. In fact in some of

those situations the participants might actually be advancing what we mean by an argu-

ment, putting forward a well-argued case for putting one’s own dishes in the dishwasher,

for example, but in many cases they will not be arguing in the sense that we have in mind

here.

The sort of argument we have in mind occurs frequently in ordinary, everyday situations.

It is by no means restricted to the works of Plato, Descartes and other scholars famous for

the arguments they put forward. You and your friends or family give each other reasons

for believing something or doing something all the time – why we should expect our

friend to be late for dinner, why we should walk rather than wait for the bus, and so on.

Open a newspaper, and you’ll ﬁnd arguments in the letters section, editorials and various

1 Not all attempts to persuade use language. Often they use images or combine images with language; most

advertising, for instance, involves a combination of images and text or speech aimed to persuade us by non-

argumentative means to buy stuff. Although the persuasive power of images is an interesting issue, here we are

interested only in attempts to persuade that use written or spoken language. But images can also occur in

argumentative attempts to persuade. We see on television, for example, a shot of dead ﬁsh in a dirty pond.

A voice says, ‘This is why we must strengthen the anti-pollution laws’. In this sort of case, we can think of the

image as implicitly stating a premise, in the sense to be described below (p. 19).

introducing arguments4

other discussion pieces. In television and radio broadcasts (especially current affairs shows)

and in internet forums and blogs you’ll ﬁnd people arguing their case (though they may

well also resort to other persuasive techniques, as well). The same thing occurs in a more

elevated form at university and college. Throughout your time as a student you will hear

lecturers and other students arguing for a point of view, and in set readings you will

encounter attempts to persuade you of various claims about all manner of issues. In the

workplace you may ﬁnd yourself having to argue for a particular course of action or argue

on behalf of a client or associate.

If you develop your ability to analyse people’s attempts to persuade so that you can

accurately interpret what they are saying or writing and evaluate whether or not they are

giving a good argument – whether, for example, they are providing you with a good reason

to believe that you should buy Fairtrade goods – then you can begin to liberate yourself

from accepting what others try to persuade you of without knowing whether you actually

have a good reason to be persuaded.2

But then, you may ask, why is it liberating to demand reasons before you are persuaded to

adopt new beliefs or to do something? Isn’t it less trouble to go through life unreﬂectively,

doing more or less as you please and not worrying too much about whether you have good

reason to do or believe something, beyond whether or not you want to? Well, it may often

be easier in the short run, but it might lead to a life dominated by bad decisions and

discontentment. Socrates, the ancient Athenian philosopher, famously argued that ‘the

unexamined life is not worth living’.3 While this may or may not be true, the only way to

ﬁnd out is to approach the issue in a critical and rational manner. Even though you may

not always be able to tell deﬁnitively whether you have been presented with a good

argument, paying due attention to arguments gets you closer to the truth of a matter,

thereby making the world and the people in it easier to comprehend and to deal with.

Even if a desire to discover the truth does not seem a sufﬁciently strong reason for being

concerned about having good reasons to justify your actions and beliefs, there are various

life situations in which the ability to interpret and evaluate a person’s case properly may be

crucial to that person’s well-being, or even to their remaining alive. For example, in a court

trial the jury is instructed to convict an alleged murderer if the prosecution has proved

their guilt beyond reasonable doubt. The jury is being asked to consider the prosecution’s

case (which, ideally, is an argumentative attempt to persuade them of the guilt of the

accused), and the evidence they offer at each step of making that case. It has to consider

2 Although this book emphasises the value of reason and the beneﬁts of using techniques of persuasion that

are rational, we should also bear in mind that what is claimed to be rational is not always rational, and certainly

does not always have positive consequences. Historically, for example, those who wield power have often

granted themselves authority over what counts as ‘rational’, condemning as ‘irrational’ what threatens the status

quo. The correct response to that sort of rhetorical manoeuvre, however, is not to say ‘so much the worse for

rationality, then!’; the correct response is to question whether the charge of irrationality is justiﬁed, or whether

the term is merely being abused or manipulated. Rationality in itself is a neutral force, independent of anyone’s

particular interests or beliefs.

3 Plato, Apology, 38a (Harmondsworth: Penguin, 1969), p. 72.

introducing arguments 5

whether there is good reason to accept the argument or whether some faults in it mean

that there must be some doubt about its truth. The skills of evaluation and interpretation

involved in argument analysis are what we use (or ought to use) in determining the

strength of the prosecution’s case in such situations. In fact in any situation in which we

have to make decisions, be they about our lives or the lives of others, there is no substitute

for the ability to think logically and to detect errors in the thinking of others.

It is a good reﬂection of the importance of the skills you are developing that those in power

sometimes fear the effects of those who can think critically about moral, social, economic

and political issues. The ability to think critically, then, is essential if one is to function

properly in one’s role as a citizen. It is not for nothing that Socrates, the most famous of

critical thinkers, was sometimes referred to as ‘the Gadﬂy’.

BEGINNING TO THINK CRITICALLY: RECOGNISING

ARGUMENTS

We do many things with language – state a fact, ask a question, tell someone to do

something, insult someone, praise someone, promise to do something, swear an oath, make

a threat, tell a story, recite a poem, sing a song, say a character’s lines in a play, cheer on a

football team. In this book we write about ‘attempts to persuade’ – by argument and by

other means. As we’ve mentioned, not all attempts to persuade (using language) are

attempts to persuade by argument. Others are attempts to persuade by means of rhetorical

devices. In Chapter 2 we discuss the most common of these devices in detail. For the time

being we’ll just make some remarks about rhetoric in general. For our purposes rhetoric is

deﬁned as follows:

Rhetoric

Any verbal or written attempt to persuade someone to believe, desire or do

something that does not attempt to give good reasons for the belief, desire or

action, but attempts to motivate that belief, desire or action solely through the

power of the words used.

The crucial thing to understand here is that an attempt to persuade by argument is an

attempt to provide you with reasons for believing a claim, desiring something or doing

something. Arguments appeal to your critical faculties, your reason. Rhetoric, on the other

hand, tends to rely on the persuasive power of certain words and verbal techniques to

inﬂuence your beliefs, desires and actions by appeal to your desires, fears and other

feelings.

Threats and bribes are special cases that may appear to count as rhetoric according to

our deﬁnition. In fact they are closer to argument; for they work by announcing to the

introducing arguments6

recipient that they have a good reason to act as suggested. For example, if Smith attempts

to persuade Jones to lend him her car by threatening to inform the police that she uses

a fake driver’s licence, then he is implicitly giving her a reason to lend him her car – if

she doesn’t do so, the police will ﬁnd out about the driver’s licence; since she doesn’t

want that to happen, she has a reason to lend him the car. Although threats and bribes

may be immoral and may motivate partly by appeal to our fears and desires, among

other feelings, they do motivate through force of reason and for that reason do not count

as rhetoric.

Rhetorical techniques can be manipulative and coercive; their use should generally be

avoided by those who aspire to think critically and to persuade by reason. That is not to

say that rhetoric is always undesirable. Often it is used to great effect for good causes.

Consider this excerpt from Barack Obama’s victory speech to supporters after winning

the 2008 US Presidential election in which he attempts to temper the sense of euphoria at

his success, and to remind Americans that they should not squander the opportunity for

signiﬁcant change and to build a better future for their children. Obama uses some

remarkably effective rhetoric for a good cause, as he had done throughout his campaign,

and he might well be admired as a talented rhetorician. But his speech does not amount to

an attempt to persuade by argument:

America, we have come so far. We have seen so much. But there is so much more to

do. So tonight, let us ask ourselves – if our children should live to see the next

century; if my daughters should be so lucky to live as long as Ann Nixon Cooper,

what change will they see? What progress will we have made? This is our chance

to answer that call. This is our moment. This is our time, to put our people

back to work and open doors of opportunity for our kids; to restore prosperity

and promote the cause of peace; to reclaim the American dream and reafﬁrm that

fundamental truth, that, out of many, we are one; that while we breathe, we hope.

And where we are met with cynicism and doubts and those who tell us that we

can’t, we will respond with that timeless creed that sums up the spirit of a people:

Yes, we can.

Those who try to persuade us of not such good causes might also be effective, persuasive

rhetoricians. European dictators of the last century – Hitler, Mussolini, Franco, Stalin –

provide good examples of this.

Of attempts to persuade that are arguments, not all are good arguments. So when analysing

attempts to persuade we have to perform three tasks:

•The crucial ﬁrst stage involves distinguishing whether an argument is being presented.

We need to identify the issue being discussed, and determine whether or not the writer

or speaker is attempting to persuade by means of argument.

•Once we have established that the writer/speaker is presenting an argument, we can

move to the task of reconstructing the argument so as to express it clearly, and so as to

demonstrate clearly the steps and form of the argument’s reasoning.

introducing arguments 7

•A clear reconstruction makes our third and ﬁnal stage – evaluating the argument,

asking what’s good about it and what’s bad about it – much easier to perform and to

justify.

In subsequent chapters we explain in detail what we mean by reconstruction, and explain

what makes an argument a good one. Our aim is not to help you acquire the basic com-

prehension skills that you need to work out what a passage or speech is about. We assume

that you already have that skill, though working through this book might help you to

hone it more ﬁnely. So we will begin with the ﬁrst step, by considering how to distinguish

arguments from other ways of putting forward opinions and persuading people to act.

When we put forward an argument we are either advancing an opinion (a claim that we

think is true) or recommending an action. In either case we give a number of claims

intended to support the claim or the recommendation. However, these two types of

arguments can be collapsed into one. For we can think of an argument that recommends

an action as advancing a claim to the effect that the hearer or reader should, or ought to, do

such-and-such. For example, an argument whose aim is to get you to buy Wheetybites can

be understood as advancing the claim ‘you ought to buy Wheetybites.’

Thus all arguments can be understood as attempting to provide reasons for thinking that

some claim is true. The nature of truth is a deep and controversial philosophical issue that

we do not need to contemplate here. We are working with an ordinary, non-theoretical

concept of truth – one which says that to label a person’s claim as true is to say that what

it states is how things really are. For example, if a person makes the true claim ‘Moscow

is further from London than Paris is’, then according to our intuitive conception of

truth, it is true just because Moscow is further from London than Paris is. Our working

deﬁnition of truth, then, is as follows:

To say that a claim is true is to say that what is claimed is how things actually are.

A single claim, however, does not constitute an argument. An argument needs more than

one claim: it needs the claim of which the arguer hopes to convince his or her audience,

plus at least one claim offered in support of that claim. To illustrate the difference

between arguments and claims, consider these unsupported claims:

•It’s going to rain later.

•Obama is a better leader than Bush ever was.

•Philosophers are odd, unworldly people.

•The world is facing environmental catastrophe.

The following examples, by contrast, attempt to give some support for these claims.

Whether they provide adequate support is something we will look at later. The important

point is to see the difference between this set and the ﬁrst set:

introducing arguments8

•It’s going to rain later; I know because I heard the weather forecast on the radio

and it’s usually reliable.

•Obama is a better leader than Bush ever was. He already has the support of most

sectors of the population and is well-respected by leaders overseas.

•I’ve met a few philosophers in my time and they’ve always been strange people,

heads in the clouds, not really in touch with the real world. Philosophers are odd,

unworldly people.

•Climate scientists predict that the world is facing environmental catastrophe,

and they are the experts on these issues.

There are special terms for the two parts of arguments: the primary claim, the one we are

trying to get others to accept, is the conclusion. The supporting claims, the ones intended

to give us reasons for accepting the conclusion, are the premises. As with the word

‘argument’, we are using the word ‘premise’ here in a restricted way, not necessarily

corresponding to all the ways in which the word is ordinarily used. People might respond

to an expression of opinion by saying, ‘that’s just your premise, but no one knows that for

sure’; they do so to cast doubt on the truth of the claim being made. That is not the sense

of the word ‘premise’ used in the discussion and analysis of arguments: for this purpose, a

premise is simply any claim put forward as support for the conclusion of an argument,

however certain or uncertain that claim may be.

We can now give a working deﬁnition of argument:

An argument

A set of propositions of which one is a conclusion and the remainder are premises,

intended as support for the conclusion.

And what exactly do we mean by a proposition?

A proposition

The factual content expressed by a declarative sentence on a particular occasion.

The same proposition may be expressed by different sentences. For example, on a

given occasion, ‘The Government has decided to hold a public enquiry into the

affair’ would express the same proposition as ‘It was decided that the Government

would hold a public enquiry into the affair’.

The same proposition can be expressed by different sentences when we change the

personal pronoun. For instance, if Eric says to Pattie, ‘You look wonderful tonight’ and

she replies ‘Yes, I look wonderful tonight’, then they each utter different sentences, but

they express the same proposition, namely that Pattie looks wonderful tonight.

introducing arguments 9

Conversely, the same sentence can express different propositions depending (among

other things) on who utters it. For instance, if Muhammad Ali, John McEnroe and Pele

were each to utter the sentence, ‘I am the greatest sportsman of all time’, they would each

express a different proposition, one about Ali, McEnroe and Pele respectively.

One outcome of this is that different sets of sentences could express the same argument

and a particular sentence within an argument could express more than one proposition.

Which proposition the sentence expresses is usually discernible by careful attention to

context.4

ASPECTS OF MEANING

Depending on how we use a sentence, it may express aspects of meaning additional to its

factual, propositional content.

Rhetorical force

This is the rhetorical aspect of a sentence’s meaning. It is not part of the propositional

content that it expresses; rather, it is the emotive or otherwise suggestive window-dressing

surrounding the proposition, which may be used to persuade us. The sentence in question

can reasonably be taken to express this rhetorical message given the linguistic conventions

according to which the words involved are normally used. The point is best grasped when

we consider sentences that express the same proposition but have different rhetorical

force. The sentence ‘She is bringing up her children on her own’ expresses the same

proposition as the more rhetorically charged ‘She’s a single mum’. But, while the former

merely expresses a fact about the person’s family arrangements, the second, by its use

of the emotive and politically signiﬁcant term ‘single mum’, might function not only to

inform us of a fact, but also to manipulate our sympathies concerning the person in

question (depending upon our beliefs and feelings about parenthood).

Implicature

Implicature is meaning, which is not stated, but which one can reasonably take to be

intended, given the context in which the sentence is written or uttered (it is known more

generally in linguistics as conversational implicature). Unlike rhetorical force, implicature

cannot typically be interpreted according to conventions covering our ordinary use of the

words in the sentence used. In order to recognise implicature, if there is any, we need

to know the context in which a statement is made. Contextual factors include who the

speaker is, who she is addressing and the circumstances surrounding the particular use of

4 The examples provided here involve words called indexicals. The meaning of an indexical changes relative to

its context of use or the person to whom it refers, as the term ‘I’ does in the example about sportsmen. We deal

with indexicals in more detail in Chapter 8.

introducing arguments10

the sentence. Suppose, for example, that a student’s parent asks one of her lecturers how

she is progressing in her studies and he replies, ‘well, she hasn’t been thrown out for

missing classes.’ The lecturer doesn’t actually state ‘she’s not doing very well’, but the

implicature is that she’s not. Implicature can serve as a source of rhetorical power when

the unsaid, implied aspect of a sentence’s meaning is employed to stimulate responses

motivated by emotion or prejudice (we discuss this rhetorical ploy on p. 48). It is also a way

of communicating something without incurring the full responsibility of having explicitly

said it. Note that a statement cannot implicate something merely because the speaker

intends to convey it. A statement implicates a given proposition only if a listener who is

fully aware of the relevant context would reasonably take that proposition to have been

intended. For the same reason, something can be implicated even when the speaker

does not intend it. If a given proposition is indeed what a fully informed listener would

reasonably take to have been implicitly intended by a statement, then that proposition is

implicated even if the speaker did not intend it. Thus our responsibility for what we say –

our responsibility to choose the right words – goes beyond what we explicitly state.

Deﬁnitions

Deﬁnitions tell us what it takes for something to qualify as a particular type of thing. The

kind of deﬁnition with which you are most familiar is probably a dictionary deﬁnition. A

dictionary deﬁnition of a word explains the normal use of a word by providing synonyms

for its various uses. For example, a dictionary deﬁnition of ‘house’ (taken as a noun) is

‘a building made for people to live in, a home’.5 You will have noticed that we provide

deﬁnitions of key terms used throughout this book (the deﬁnitions appear in boxes). These

deﬁnitions are not dictionary deﬁnitions; rather they set out what it takes for something to

count as the type of thing to which the term deﬁned applies. For example, our deﬁnition of

an argument sets out what it is for something to count as an argument. This kind of

deﬁnition of some thing or phenomenon tells us the necessary and sufﬁcient conditions

for counting as that kind of thing. The necessary conditions for being some thing or some

phenomenon X are the conditions that a thing must satisfy if it is to count as an X.

NB X functions here a placeholder, it stands for ‘some object or feature’. The sufﬁcient

conditions for being some thing or some phenomenon X are the conditions such that if

something meets them, that is enough for it to count as an X. Here are some examples.

1. Something is a ewe if and only if it is a) a sheep and b) female

A ewe must be female and a sheep, and its being female and a sheep is enough to make it

a ewe. It may have wool, it may say ‘bah’, it may eat grass, but these are neither necessary

nor sufﬁcient conditions of its being a ewe. (The discussion of primary and secondary

connotation in Chapter 2 provides insight into the role of these non-essential features in

determining the meanings of terms.)

5 Cf. Oxford Paperback Dictionary (Oxford: OUP, 1994) p. 386.

introducing arguments 11

2. Something is square if and only if it is a planar ﬁgure with a) four sides of equal

length and b) four equal angles adding up to 360°

A ﬂat, two-dimensional ﬁgure must have four equal sides and four equal angles totalling

360°, and its having four equal sides and four equal angles is enough to make it square. It

may be 2cm2, it may be 100m2, it may be red, green, purple with orange spots, but these

are neither necessary nor sufﬁcient conditions of its being square.

When devising such deﬁnitions we start with some plausible candidate(s) for necessary

and sufﬁcient conditions. We then test them by seeing if there are any counterexamples to

them. In this context a counterexample is either something that ﬁts the deﬁnition, but that

we strongly believe isn’t an example of whatever is being deﬁned, or something that we

strongly believe is an example of whatever is being deﬁned, but which fails to meet the

conditions suggested as necessary and sufﬁcient. When faced with a counterexample, we

either alter the deﬁnition to accommodate something(s) we strongly believe should count

as cases of the X in question or accept the deﬁnition and admit that the thing in question

does not count as a case of X. For example, suppose we start off deﬁning square as ‘a planar

ﬁgure with four equal sides’. We would soon realise that such a deﬁnition is not strict

enough – it would allow diamonds to count as square. Being a planar ﬁgure with four sides is

clearly a necessary condition of being a square, but it isn’t a sufﬁcient condition; our putative

deﬁnition needs reﬁning in order to include the sufﬁcient conditions for being square.

STANDARD FORM

An argument may be about any subject and have any number of premises, but it will

always have only one ﬁnal conclusion. This argument has just one premise:

Bart has two sisters.

Therefore, Bart is not an only child.

This has two:

Helping someone to commit suicide is the same as murder.

Murder is wrong.

Therefore, helping someone to commit suicide is wrong.

And this one has three:

Car use is seriously damaging the environment.

Reducing car journeys would reduce damage to the environment.

introducing arguments12

We should do what we can to protect the environment.

Therefore, we should use cars less.

As you can see, arguments for analysis are set out in a particular style, with the premises

listed in the order that they occur in the reasoning process and the conclusion appearing at

the bottom. We can reﬁne this style and further clarify the argument by numbering the

premises P1, P2 and so on, and drawing a line between the last premise and the conclusion,

which we mark with a ‘C’. The line between premises and conclusion is called an inference

bar, and its purpose is to distinguish steps in reasoning. The bar should be read as standing

for ‘therefore’. This style of setting out arguments is called standard form. The purpose

of setting out arguments in this manner is to maximise clarity. Using this method helps

us to see the stages of reasoning clearly and to make comparisons between arguments of

similar form. When dealing with arguments as they are ordinarily presented, distinguish-

ing the exact conclusion from the premises, the premises from each other, and the

premises and conclusion from other, irrelevant, material can be difﬁcult. Writing the

argument in standard form provides us with the most comprehensive and clearest possible

view of it, ensuring that while discussing the argument and attempting to evaluate it we

do not lose track of exactly what the argument is.

A number of the exercises included in this book require you to set out arguments in

standard form. To do this is to reconstruct the argument, and the end product – the

argument set out in standard form – is called a reconstruction of the argument, or an

argument-reconstruction. In reconstructing arguments you should follow the example

below by taking these steps:

•Identify the conclusion.

•Identify the premises.

•Number the premises and write them out in order.

•Draw in the inference bar.

•Write out the conclusion, placing ‘C)’ in front of it.

Thus the previous example looks thus in standard form:

P1) Car use is seriously damaging the environment.

P2) Reducing car journeys would reduce damage to the environment.

P3) We should do what we can to protect the environment.

C) We should use cars less.

introducing arguments 13

IDENTIFYING CONCLUSIONS AND PREMISES

The question of whether a passage or speech contains an argument is the question of

whether the speaker or writer is attempting, by means of that passage or speech, to

persuade her audience of some conclusion by offering premises in support of it. This is a

question about the intentions of the writer or speaker – ‘What does this person intend to

do with these words here?’ – that cannot always be answered unless we know something of

the context – the circumstances in which the passage or speech appeared or took place.

But even when we’ve determined that an argument is being advanced, its premises and

conclusion are often buried deep among the other elements of a speech or text, and there

are no hard-and-fast rules for distinguishing the propositions that form an argument from

those that perform some other function in a text or speech. Identifying arguments is

largely a matter of determining what the author or speaker intends by interpreting her

words (spoken or written), and this comes with practice. Often writers and speakers leave

some of their premises unstated because they assume that readers or listeners will know

what they have in mind. So in reconstructing arguments we often have to add premises to

make their structure and content complete. Further, people do not always express their

arguments in very clear language, so we have to clarify each proposition before we can

command a clear view of the argument as a whole (we look at difﬁculties with linguistic

meaning later in Chapter 2).

Identifying conclusions

Once you have determined that a text or speech contains an attempt to persuade by

argument, it is easiest to proceed by identifying its conclusion. Determining whether a

passage contains an attempt to persuade by argument and identifying the conclusion of

that argument do not always occur independently, however. Sometimes you will identify

the conclusion in the process of working out that a passage does indeed contain an

argument. On other occasions you may have already worked out that a passage contains

an argument by paying careful attention to the writing style and the context without yet

having identiﬁed the conclusion. We will, in any case, treat these processes as independent

steps in argument analysis.

The conclusions of the following examples are probably clear from the ﬁrst reading:

Since Jo Bloggs is a politician and politicians are always corrupt, I guess Jo Bloggs is

corrupt.

I’m anti-hunting because I believe that hunting animals is wrong. After all, it’s

wrong to kill simply for pleasure and hunting involves the killing of innocent

animals for pleasure.

Before moving on, make sure that you can identify the conclusions in each of these

examples.

introducing arguments14

Several points make the identiﬁcation of conclusions an easier task

1 Once you have decided that a passage or speech contains an attempt to persuade by

argument, try to see what the main point of the passage or speech is. Ask what point

the speaker or author is trying to establish; that point will be the conclusion. Once

you come to reconstruct an argument for analysis, paraphrasing the main point as one

simple proposition will make the argument easier to handle. Bear in mind that a

writer or speaker may make the same point in a number of different ways, so you

may have to settle upon one particular way of expressing it.

2 Any proposition on any topic can be a conclusion. It is possible to attempt to argue

for any claim, from the highly theoretical to the most mundane. So the type of

subject-matter of a proposition – religion, morality, science, the weather, politics,

sport – is not in itself a guide to identifying whether or not that proposition is

intended as the conclusion of a passage’s argument. The premises and conclusions of

arguments should ideally be expressed in declarative sentences, but in real-life argu-

ments they may be expressed otherwise. When reconstructing arguments, we may

need to rewrite premises and conclusions as declarative sentences in order to clarify

the propositions expressed. For example, the apparent question ‘Aren’t all socialists

idealists?’ might be used to express a premise that all socialists are idealists. The types

of linguistic phenomena that need to be rewritten for clarity’s sake are discussed in

detail in Chapter 2.

3 A single text or speech may contain several arguments for several different but

connected conclusions. Sometimes we argue for one point, then a second, and then

use those conclusions as premises in an argument for a third and ﬁnal conclusion.

These chains of arguments are known as extended arguments and we look at them in

more detail shortly.

4 A helpful guide to recognising arguments are words that usually indicate that a writer

or speaker is putting forward an argument. For example, if someone says, ‘Given the

facts that A, B and C, it follows that D’, you can be sure that D is the conclusion

of the intended argument (and that A, B and C are the premises). Other common

conclusion indicators are:

•Therefore...

•Hence...

•Thus...

•It can be concluded that...

•So...

Usually (though not always) these words or phrases follow the sentences that express

an argument’s premises. Another way of expressing an argument is to include the

premises and conclusion in a single sentence with an indicator word separating them.

For example, in the sentence ‘The fact that John Plunkett is a politician proves that

he has a very big ego’, the conclusion that Mr Plunkett has a very big ego is separated

from the premise that states that he is a politician by the indicator ‘proves’. Other

words that serve the same function are:

introducing arguments 15

•. . . implies...

•. . . establishes...

•. . . shows...

Commonly, a writer or speaker will state the conclusion of their argument before

stating the premises. There are indicator words that are typically placed after the

conclusion in these cases. For example, in the sentence ‘Joe Biden must be a very

important man since he is Vice-President of the USA’, the conclusion that Mr Biden

must be a very important man is separated from the premise stating that he is Vice-

President of the USA by the indicator word ‘since’. Other words and phrases that

serve the same function are:

•. . . because...

•...for...

•. . . follows from the fact that...

•. . . is established by...

•. . . is implied by...

These indicators are not foolproof and should not be treated as a substitute for

careful identiﬁcation and interpretation of attempts to persuade by argument. Not all

arguers will help the critical thinker out by making use of indicator words. The fact

that a text or speech does not include an indicator word is not a reliable reason for

thinking that it does not express an argument. If a passage does not appear to have

any conclusion indicators then an alternative way of identifying the conclusion is to

try inserting conclusion indicators at appropriate places in sentences that appear to be

good candidates for the conclusion. Then see if the passage or speech still reads or is

heard smoothly and if its meaning is unchanged. There are no conclusion indicators

in the following speech, but it is still an attempt to argue:

I think that Dinnah should sue the local council. They have admitted that

they were negligent in not mending the cracked pavement that she

tripped over when she broke her ankle and that’s sufﬁcient grounds for

compensation.

Here if we try placing the conclusion indicator ‘therefore’ at the beginning of the

second sentence (‘They have admitted that they were negligent . . .’), it becomes clear

that it is not the conclusion of the intended argument. Inserting ‘because’ between

the ﬁrst and second sentence (and thereby joining them to make one sentence), on

the other hand, leaves the meaning intact and makes it clear that the conclusion – the

claim that the speaker wants us to accept – appears at the beginning of the speech.

Of course, when we write out the argument in standard form we change the order of

the sentences and place the conclusion at the end preceded by the inference bar.

Notice that the second sentence contains two premises so that in standard form the

argument would be written thus:

introducing arguments16

P1) The local council has admitted negligence.

P2) An admission of negligence is sufﬁcient grounds for compensating an

injured party.

C) The local council should compensate Dinnah.

5Indicator words are not parts of the propositions that the argument comprises; rather

they introduce or frame the conclusion and premises. So when we write arguments in

standard form so as to reconstruct them, we omit the conclusion indicator words

from our reconstruction.

6 So far we have only discussed explicit conclusions in which a writer or speaker

expresses her conclusion directly and more or less clearly. However, conclusions

sometimes remain unexpressed. These are implicit conclusions. They are only

implied or suggested by the actual text or speech content, not explicitly expressed

by it. This usually happens when the speaker or writer thinks that the context is

sufﬁcient to make the conclusion obvious so that it literally ‘goes without saying’.

This is often a bad idea, as the conclusion is not always as obvious to those

whom one is trying to persuade as it is to the persuader. It can also be a way of

concealing one’s uncertainty as to exactly what one is arguing for. In the name

of clarity and explicitness, try to avoid implicit conclusions in your own writing

and speech. It isn’t clear, for example, what (if any) conclusion is implicit in the

following:

There’s so much pornography available via the internet these days and young

people are so easily inﬂuenced, it’s bound to result in a social collapse into an

orgy of rape, abuse and indecency.

Identifying premises

As you go through the process of identifying an argument’s conclusion, it is likely that

you will also spot some or all of its premises. Thus the stages of identiﬁcation are not

entirely separate in practice. The identiﬁcation of an argument’s premises is a search for

reasons given by the writer or speaker to think that their conclusion is true. Like the

identiﬁcation of conclusions, much of the process of identifying premises amounts to close

and charitable reading of what a writer or speaker says, but again there are some helpful

guides:

1 Ask yourself what the writer’s or speaker’s reasons for believing their conclusion are.

What evidence does the writer or speaker give to think that the conclusion is true?

The propositions that you come up with in response to these questions are likely to

be the premises of the intended argument.

2 Like conclusions, premises can have any subject-matter whatsoever. It does not

matter whether a proposition is controversial or unanimously agreed, it can still be a

premise.

introducing arguments 17

3 In most real examples of writing and speech, arguments are embedded within other

language that is not intended as part of the argument itself, although some of this

language may be used rhetorically (we discuss such uses in Chapter 2). Again, it helps

to work out the overall structure of the passage when trying to identify the premises.

Consider the following:

I really think the Government should reconsider its policies on the environ-

ment. The environment is such a complicated topic, and their policies are just

more poll-driven nonsense; Brown and his cronies are so business-oriented with

their corporate-looking suits and so on, they invite business types to advise

on policy and behave as if they too were chief executives of multi-national

corporations, just out to make money for their friends really.

In this example the speaker gets sidetracked into commenting upon the Prime

Minister’s suits and policy advisors and fails, beyond the vague charge that the

Government’s policies are ‘poll-driven nonsense’, to offer a substantive criticism.

Most of what is said is at best only obliquely relevant to the issue.

4 As with conclusions, there are certain words that usually (but not always) indicate

the presence of premises – premise indicators. We have already seen some of these

because they mark the speaker or writer’s move from premises to conclusion or from

conclusion to premises (‘since’, ‘because’, ‘is implied by’ and so on). There are other

words and phrases that introduce sentences stating a premise or premises. A speaker

or writer might state their conclusion and then begin the next proposition with such

phrases as:

•My reason is...

•My evidence for this is...

•This is so because...

For example:

I put it to you that Ms White killed Colonel Mustard in the ballroom with the

candlestick. The reason I make this claim is that on the night of Colonel

Mustard’s death Lady Scarlet saw Ms White in the ballroom beating Colonel

Mustard over the head with the very candlestick that was later found to have

Ms White’s ﬁngerprints and Colonel Mustard’s blood on it.

Other premise indicators may occur at the beginning of a sentence containing both

the premise and the conclusion. For example:

On the basis of the fact that they have promised big tax cuts, I conclude that

the Conservative Party will probably win the next general election in Great

Britain.

introducing arguments18

5 Again, when writing out the premises of an argument in standard form, take care not

to include the indicator words, as they are not part of the propositions that make up

the argument. When indicator words such as ‘since’ and ‘because’ are not functioning

to indicate premises or conclusions, however, but are used within an argument’s

propositions, then they should be included in the reconstruction. This is particularly

important when ‘because’ is used in a proposition used to express an explanation. See

the section later in this chapter, discussing the distinction between arguments and

explanations.

6 Again, as with conclusions, a text or speech may not include speciﬁc premise indica-

tors. Context is the best means of identifying premises in such cases. It may also help

to try adding premise indicators to propositions to see if the passage or speech still

runs smoothly.

7 Ordinary language can make identifying arguments more difﬁcult than it might

otherwise be, because people do not always express all of their premises explicitly.

Thus many attempts to persuade by argument rely on implicit premises: these are

propositions assumed or intended by the arguer as reasons in support of the conclu-

sion, but which are not actually expressed by any sentence provided by the arguer.

Sometimes this happens out of oversight; and other times because the arguer assumes

that, in the given context, the premise may already be taken for granted. In Chapter 5

we will discuss the interpretation of hidden premises and the reconstruction of

arguments to include them.

Extraneous material

As you try to identify arguments’ conclusions and premises, you will notice that much

of what people say or write when putting forward an argument plays no role in the

argument itself. It is there as stage-setting, for emphasis, for rhetorical effect, or has some

purpose other than that of expressing the propositions that constitute the argument.

Before identifying those propositions – the argument’s conclusion and the premises given

as support for it – we often have to identify and hive off this material, which has no role to

play in the reconstruction of the argument. Here’s an example. We’ve given each sentence

a number in order to facilitate discussion.

These days we live on an overabundant supply of news and comment, and everyone

seems to get involved. 1

One day people phone in or email or write in about global warming, the next day

about scandals and sleaze in the government, the next day about child abuse and

social services, the next day about taxes, and the next day about who knows what

else. 2

It’s enough to make your head spin! 3

But one issue is so obvious and maddening that it makes me want to speak up

myself. 4

introducing arguments 19

Is it true that the exposure of uranium to neutrons inside a nuclear reactor is not

responsible for large outputs of greenhouse gases; but it does create plutonium, the

material for nuclear weapons. 5

No one has any idea what to do with this dangerous waste, and the economic impact

of this will be seriously signiﬁcant. 6

Our generation must not bequeath a lethal legacy to our children, their children and

their children’s children. 7

Mr. Jeremy Dayton

Bournemouth

In sentences 1–4 Dayton is merely providing some commentary on an unrelated issue,

complaining of the non-stop news media that is ‘enough to make your head spin!’; this has

to do with the general circumstances in which he writes but not the issue he is concerned

to write about. This is not part of the argument he is advancing and should be omitted

from a reconstruction of the argument.

Sentences 5 and 6 express claims about the effects of nuclear power generation, our lack

of knowledge about how to deal with them and their economic implications. These claims

form the premises of Drayton’s argument. This conclusion appears in sentence 7 where

the writer expresses the main point, but the proposition being expressed is obscured by the

rhetorical ﬂourish provided by the phrase ‘lethal legacy’. This rhetorical element should be

omitted from the argument reconstruction.

ARGUMENTS AND EXPLANATIONS

Words that function as indicator words can be used for other purposes. The sentence,

‘Since 2007 I have been a student at the University of Anytown’ contains the word ‘since’;

but in this case the word merely designates the beginning of a period of time, and does not

indicate a premise of an argument.

A trickier case is the use of words such as ‘since’ and ‘because’ – especially ‘because’ – in

explanations. The distinction between arguments and explanations is important, but

not always easy to make because arguments and explanation often have a very similar

structure. In some cases we have to think hard about the context in order to determine

which is intended. We need to work out whether they are telling us that such and such

event occurred as a result of some other event – that is, whether they intend to assert a

relation of cause and effect. For in that case, ‘because’ is being used to introduce an

explanation, not an argument.

introducing arguments20

The best way to appreciate the distinction between arguments and explanations is to

consider an example. Consider this proposition:

The tap is leaking.

Someone might advance an explanation for this by saying something like:

The tap is leaking because it needs a new washer.

On the other hand, we can imagine someone advancing an argument for that very same

proposition, reasoning as follows:

There is a sound of dripping water coming from the bathroom.

Therefore, the tap is leaking.

What exactly is the difference? The difference is that, when giving the explanation, the

speaker assumes that his or her audience already accepts the proposition that the tap is

leaking, or at least that the speaker has no need to persuade the audience of this fact.

Given this fact, the speaker is asserting that the cause of that fact is the faulty or

worn-out washer. By contrast, when giving an argument, the speaker does not assume

that the audience accepts or will accept that the tap is leaking outright; the arguer

intends to persuade the audience that this is so by giving the audience a good reason to

believe it.

This example of an explanation uses the word ‘because’ – the word here indicates a

causal relationship instead of a logical connection between premise and conclusion. As

demonstrated by the following examples, ‘since’, ‘therefore’, ‘thus’ and ‘so’ may also be

used in explanations that are not intended to provide reasons for acting or believing

something:6

•Since we forgot to add yeast, the bread didn’t rise.

•We forgot to add yeast, therefore the bread didn’t rise.

•We forgot to add yeast, thus the bread didn’t rise.

•We forgot to add yeast, so the bread didn’t rise.

The distinction between arguments and explanations can be confusing where the

explanation of actions is concerned (that is, things that people do). This confusion arises

because, in the case of actions, reasons are causes! That is, the explanation of an action

normally involves specifying the reason for it: a person does something because he or she

had a certain reason. Thus, in asking about reasons for actions – asking, ‘Why are you

doing that?’ – we are sometimes looking for a justiﬁcation – that is, we want the person to

6 While reading this book you may also have noticed a further use of ‘thus’. ‘Thus’ can be used to mean ‘in

this way’ and often precedes an example or a quotation.

introducing arguments 21

give us an argument for why the action is reasonable or acceptable – and other times we

simply want an explanation, in the sense of wanting to know the cause. Nevertheless, the

distinction between arguments and explanations still holds.

Suppose you are driving fast and your passenger asks, ‘Why are you driving so fast?’. You

assume your passenger is not in any way suggesting that you shouldn’t drive so fast.

You think they don’t mind in the slightest. You assume they are merely curious as to why

you’re driving fast – whether it’s because you’re late, being chased by the police or perhaps

testing the limits of your new car. Your reply, however, is simply, ‘Because I enjoy it.’ This

would be an explanation: you are telling your passenger why you’re driving fast, not trying

to persuade them of anything.

But suppose, when your passenger asked, ‘Why are you driving so fast?’, you think maybe

they do mind. So you take the question as demanding a justiﬁcation for your driving so

fast. If you now say, ‘Because I enjoy it’, then you would be arguing, roughly, that it is all

right to drive at such a speed on the grounds that you have a right to do what you like. In

that case ‘Because I enjoy it’ would be a premise of an argument, which might initially be

expressed thus:

It’s OK for me to drive as fast as I like, because I like driving fast.

I think we should be free to do anything that we enjoy.

It might be rewritten thus in standard form:

P1) I enjoy driving fast.

P2) It is acceptable for me to do anything I enjoy.

C) It is acceptable for me to drive fast.

In such a case, your enjoying it might be both a reason for driving fast and a cause of it.

INTERMEDIATE CONCLUSIONS

The conclusion of one argument may serve as a premise of a subsequent argument. The

conclusion of that argument may itself serve as a premise for another argument and so on.

A simple illustration:

Fido is a dog. All dogs are mammals, so Fido is a mammal. And since all mammals

are warm-blooded, it follows that Fido is warm blooded.

In this argument, an intermediate conclusion – that Fido is a mammal – is used as a

premise for a further argument, whose conclusion is that Fido is warm-blooded. We

represent extended arguments of this kind like this:

introducing arguments22

P1) Fido is a dog.

P2) All dogs are mammals.

C1) Fido is a mammal.

P3) All mammals are warm-blooded.

C2) Fido is warm-blooded.

We give the two conclusions numbers: C1 is the conclusion of an argument whose

premises are P1 and P2; C2 is the conclusion of an argument whose premises are C1 and

P3. So C1 is both the conclusion of one argument and the premise of another.

Normally, in such cases, the last conclusion reached (the one with the highest number) is

the proposition that the arguer is most concerned to establish. It is the ultimate target. So

we call this simply the conclusion of the argument, whereas any other conclusions, reached

as steps along the way, are called intermediate conclusions.

We sometimes want to concentrate for a moment on a particular part of an extended

argument. In the above case, for example, we might be particularly interested either in the

ﬁrst part of the argument, or in the second. We will sometimes speak of the argument

from P1 and P2 to C1, or of the argument from C1 and P3 to C2. We can also speak of the

inference from P1 and P2 to C1, and the inference from C1 and P3 to C2.

The use of the word ‘inference’ in logic and critical thinking is another case where a word

is used in a somewhat restricted sense in comparison with ordinary language. All reasoning

consists of inferences. In the logician’s sense of the word, each step of reasoning, each

move from premise or premises to conclusion, is an inference. Contrary to the way the

word is often ordinarily employed, there need be nothing doubtful about an inference.

We sometimes say, ‘but that’s just an inference’, meaning to cast doubt upon whether a

given proposition should really be accepted on the basis of others. But in our sense of the

word, an inference may be completely certain, not subject to doubt. For example, it is an

inference, in our sense, to go from ‘John is a classical musician’ to ‘John is a musician’ –

despite the fact that there can be no doubt that if the ﬁrst proposition is true, then so is the

second (in the terminology to be introduced in Chapter 3, it is a valid inference).

CHAPTER SUMMARY

Critical thinking enables us to ensure that we have good reasons to believe or do that

which people attempt to persuade us to do or to believe. Attempts to persuade may be

argumentative or non-argumentative. Most of the latter count as rhetoric, which is any

attempt to persuade that does not attempt to give good reasons for the belief, desire or

action in question, but attempts to motivate that belief, desire or action solely through the

power of the words used. The former, on the other hand, persuade us by giving reasons for

us to accept a claim or take the action suggested. Not all arguments are good arguments.

Good arguments are those that provide us with good reasons to act or to accept a claim.

introducing arguments 23

An argument consists of a set of propositions. The proposition expressed by a statement is

its factual content, and should as far as possible be distinguished from the rhetorical force

of the sentence. Propositions may implicated by an utterance without being explicitly

stated: a proposition is implicated by an utterance when it would reasonably be taken to

have been intended. Among the propositions that constitute an argument, one is its

conclusion – the proposition argued for – and the rest are its premises – the reasons given

to accept the conclusion. Once we have determined that a text or a speech contains an

argument, we must work out which sentence is intended to express the argument’s con-

clusion and which are intended to express its premises. Words that serve as conclusion

indicators and premise indicators offer a helpful (but not foolproof ) guide to doing so

successfully. We should also pay close attention to the context of the text or speech

and be careful to exclude any extraneous material from our argument reconstruction.

Setting out arguments in standard form is a ﬁve-stage process that enables us to see the

form of arguments better and, hence, to compare, analyse and assess them more easily.

Arguments must be distinguished sharply from explanations: arguments attempt to

provide reasons for believing a proposition whose truth is not assumed already to be

accepted; explanations assume a certain proposition is already accepted as fact, and

attempt to specify the cause.

EXERCISES

1 Decide whether each of the following cases contains an argument. If it does not,

write ‘N/A’. If it does, identify its premises and conclusion by underlining the

appropriate propositions and writing ‘C’ under the conclusion and ‘P’ and the

appropriate number under the premises. Remember that premise and conclusion

indicators are not part of those propositions:

Example

Bob is a dog and all dogs are black. So Bob is black.

✎P1 P2 C

Notice that we have not underlined the words that connect or introduce the

propositions, only the propositions themselves.

a You should tidy up after yourself since nobody likes to use this room after

you.

b The room is messy because John Campbell was in here earlier, and he is a

messy person.

c Is the dollar over-valued?

d Isn’t it obvious that the dollar is over-valued?

e Jimmy thinks the dollar is over-valued.

f Jimmy thinks the NZ dollar is over-valued, so the NZ dollar is over-valued.

introducing arguments24

g Ilan is the lecturer for Critical Thinking. Falafel is yummy. So Ilan must like

falafel.

h Eat your greens!

i Students should not have to pay any fees for tertiary education. A well-

educated population beneﬁts the country and the country should be

prepared to pay for those beneﬁts.

j In order to think critically about a particular subject you need to have

enough knowledge about that subject.

k In order to think critically about a particular subject you need to have

enough knowledge about that subject. So you should look for deﬁciencies in

your beliefs.

l Studying critical thinking can help you clarify your thinking, and

make better choices in belief and action. Everyone should study critical

thinking.

m If you put an effort into your studies, and if you apply the material to other

courses, then a critical thinking course can help to improve your academic

skills.

n Doing one critical thinking course will not automatically make you think any

better.

o Morality is culturally relative, so female circumcision is okay and we should

not criticise it.

p I’m late because there was an unexpected trafﬁc jam that I couldn’t

avoid.

q I’m in a trafﬁc jam, so I’m probably going to be late.

r He’s been on crutches since he was injured in the accident.

s The biscuit tin is empty because the children ate all the biscuits.

t If the children ate all the biscuits, the biscuit tin will be empty. The children

ate all the biscuits, so the biscuit tin is empty.

2 Write out the following arguments in standard form. You need not supply missing

premises or change the words used unless it is absolutely necessary to retain the sense

of a sentence, but you should omit indicator words:

Example

The Government should regulate the sale of spray paint. Spray paint can be

used for tagging and tagging causes damage to private property. The sale of

anything that causes damage to private property should be regulated.

✎P1) Spray paint can be used for tagging.

P2) Tagging causes damage to private property.

P3) The sale of anything that causes damage to private property should be

regulated.

C) The Government should regulate the sale of spray paint.

introducing arguments 25

a Mrs Brown says it’s acceptable for parents to smack their kids. Mrs Brown

raised eight kids successfully. It’s acceptable for parents to smack their kids.

b If we want to know if it’s okay to believe or do something, we need to know

if the arguments in support of it are good enough. Argument analysis helps

us to ascertain the quality of arguments. So argument analysis can help us

make better decisions.

c Most people believe that the invasion of Iraq was morally wrong. What

the majority believe is probably true. So the invasion of Iraq was morally

wrong.

d Almost everyone eats meat. What the majority does is okay to do. Eating

meat, then, is not morally wrong.

e If Manchester United win against Arsenal, Chelsea will go to the top of the

Premier League. Manchester United have beaten Arsenal, so Chelsea will be

top of the league.

f History will show President Bush to have been a successful president after

all. The reason is that he managed to maintain the USA’s reputation as

a superpower and that’s the most important criterion by which to judge a

US president.

3 Without looking back at the relevant section of the chapter, explain the difference

between arguments and explanations. Use examples to illustrate your answer.

4 Without looking back at the relevant section of the chapter, explain what necessary

and sufﬁcient conditions are.

5 What are the necessary and sufﬁcient conditions for the following?

Example

✎Being square: something is square if and only if it is a planar ﬁgure that a) has

four sides of equal length and b) four angles, each measuring 90°.

a Being a car?

b Being a mammal?

c Being an oak tree?

d Being milk?

e Being water?

introducing arguments26

language and

rhetoric

•Linguistic phenomena 27

Ambiguity • Vagueness • Primary and secondary connotation • Rhetorical

questions • Irony • Implicitly relative sentences • Problems with quantiﬁers •

Quantiﬁers and generalisations

•Rhetorical ploys 40

Appeals to speciﬁc feelings • Appeal to novelty • Appeal to popularity •

Appeal to compassion, pity or guilt • Appeal to cuteness • Appeal to

sexiness • Appeal to wealth, status, power, hipness, coolness, etc. • Appeal to

fear (also known as scare tactics) • Appeal to ridicule • The direct attack and

hard sell • Buzzwords • Scare quotes • Trading on an equivocation • Trading

on implicature • Many questions (aka leading question or complex question) •

Smokescreen (changing the subject) • Spin

•Chapter summary 50

•Exercises 51

LINGUISTIC PHENOMENA

As we’ve seen, once we’ve determined that a text or a speech contains an attempt to

persuade by argument, the remainder of argument-reconstruction is largely a matter of

interpreting the speech or text as accurately as possible. Here we are trying to work out

what the speaker or writer intends readers or listeners to understand, and consequently

do or believe, on hearing or reading their words. Phenomena in ordinary language some-

times make this task more difﬁcult because they obscure speakers’ and writers’ intended

meanings and therefore make it hard to tell which proposition their sentences are

supposed to convey. So aspirant critical thinkers need to be aware of the ways in which

language can work to hide writers’ and speakers’ meanings and must practise spotting

potentially problematic sentences. We begin this chapter by examining some of these

problematic phenomena and explaining how they work. At this stage you should aim to be

able to recognise these sentences and to be able to give the possible interpretations of

them; that is, the propositions that they could be used to convey. In the second part of the

chapter, we continue our focus on language by considering rhetorical ploys; that is, various

ways in which the power of words is used to persuade us to do or believe things in the

absence of giving us reasons in the way that an argument does.

Ambiguity

A sentence is ambiguous in a given context when there is more than one possible way of

interpreting it in that context – that is, if there is more than one proposition it could

plausibly be taken to express in that context. There are two types of ambiguity.

Lexical ambiguity

This is a property of individual words and phrases that occurs when the word or phrase

has more than one meaning. The set or group of things to which an expression applies

is called its extension (it helps to think of an extension as all the things over which the

word or phrase extends or spreads itself). Thus the extension of the word ‘student’ is the

set of all students. An ambiguous word or phrase, then, has two or more separate and

different extensions – it picks out two or more different sets of things. Ambiguous words

and phrases can bring their ambiguity into sentences, making those sentences capable of

having more than one possible interpretation. The word ‘match’ is one such word. The

sentence ‘He is looking for a match’ could be intended to mean any of the following

propositions:

•He is looking for a small stick of wood with an inﬂammable tip.

•He is looking for another one the same [as this one].

•He is looking for [wants] a game of tennis (or some such).

Words that are potentially lexically ambiguous are not necessarily ambiguous in every

context. Suppose you know that the person ‘looking for a match’ in the example above is

trying to light a ﬁre, then there would be little reason to interpret him as looking for

anything other than a small stick of wood with an inﬂammable tip. Notice that it is not

only nouns that can be lexically ambiguous. Suppose you are going to meet someone for

the ﬁrst time and all you’ve been told about them is what a friend has told you – ‘She’s a

hard woman’. This could mean: She’s a difﬁcult person; She’s an aggressive person; She has

a very well-toned muscular body. Whichever interpretation you adopt will have an

important effect on your expectations of the woman in question. When interpreting

sentences that are lexically ambiguous, we have to focus on the context in which they are

written or said and the consequent probability of each of the possible interpretations being

the correct one. For instance the sentence ‘A visitor to the zoo was attacked by the

language and rhetoric28

penguins’ is lexically ambiguous because the preposition ‘by’ has two possible meanings in

this context. The sentence could express either of the following propositions:

•The penguins attacked a visitor.

•A visitor was attacked beside the penguins’ enclosure.

However, in the absence of any information about a vicious penguin, and given what we

know about the usually non-aggressive behaviour of penguins towards zoo visitors, it

would probably be reasonable to interpret the sentence as intended to express the second

proposition.

There are a few words that are not really ambiguous but may seem so when we hear them,

though not when we see them written. This is because the words, though spelled dif-

ferently, sound the same. For example, when heard, as opposed to read, the question ‘Are

you a mussel (muscle) man?’ could be either an enquiry as to a person’s taste in seafood or

as to his physique. Of course, once we see the question written, we are in no doubt as to its

meaning.

The examples considered so far are relatively simple to understand because the alternative

meanings of words such as ‘match’ and ‘hard’ are very different. However, instances of

lexical ambiguity also occur when a word has alternative meanings that are much closer

together. Such cases are much harder to interpret and we need to pay a lot of attention to

the context in which the word is being used and to the probability of the speaker or

writer’s intending one interpretation rather than the other.

Suppose someone reports that ‘The average mortgage has doubled in six years’. The

speaker or writer might mean to say that the average existing mortgage has doubled its

value in the past six years, so people with mortgages owe twice as much now as they did

six years ago, which would be a pretty worrying situation because so many people would

have increased their debts in such a short space of time. On the other hand, the speaker or

writer might have intended to claim that the average mortgage taken out now is twice as

big as the average mortgage taken out six years ago, which would simply be a reﬂection of

increasing property prices.

Syntactic ambiguity

This occurs when the arrangement of words in a sentence is such that the sentence

could be understood in more than one way (as expressing more than one proposition).

You will probably be familiar with examples of syntactic ambiguity as it is often the basis

of jokes and newspaper headlines that appear odd. For example, ‘33-year old Mrs Jones

admitted to dangerous driving in Leeds Crown Court yesterday’ could mean either of the

following:

•In Leeds Crown Court yesterday Mrs Jones admitted to dangerous driving.

•Yesterday Mrs Jones admitted to driving dangerously inside Leeds Crown Court

itself.

language and rhetoric 29

The sentence is syntactically ambiguous because it could, consistent with English

grammar, be used to express either proposition. But since the second interpretation

is extremely implausible, it is unlikely that an actual use of this sentence would be

ambiguous. But consider this case:

US President Obama has cancelled a trip to Canada to attend a peace summit.

We can easily imagine a real context in which this sentence is ambiguous as to whether the

purpose of the cancelled trip was to attend a peace summit or whether the trip was

cancelled so that the President could attend a peace summit (elsewhere than Canada).

Once we decide the most likely interpretation, we should always rewrite the ambiguous

sentence so as to eliminate the ambiguity. For example, we might rewrite the above

sentence thus:

In order for him to attend a peace summit, US President Obama’s trip to Canada has

been cancelled.

Notice that in cases such as this we have to change the sentence quite radically to rid it of

the syntactic ambiguity and clarify its meaning. Consider a further example:

The Government will announce that the electricity supply is to be cut off tomorrow.

The sentence leaves ambiguous the question of when the announcement will be made and

when the electricity supply is to be cut off:

•Tomorrow, the Government will announce that the electricity supply is to be cut

off. (The announcement will be made tomorrow.)

•The Government is going to announce that, tomorrow, the electricity supply will

be cut off. (The announcement will be made now, the electricity will be cut off

tomorrow.)

Syntactic ambiguities are sometimes more difﬁcult to interpret on the basis of context

than lexical ones are. Also, the possible interpretations of a sentence may be closely related

so that there may not appear to be a very wide difference in meaning. Often we assume

that one interpretation is intended without giving any consideration to alternatives. But

such differences can be very signiﬁcant indeed. Suppose someone were to claim:

We should not tolerate those homeless people living on our streets.

They might be saying that we should be intolerant of homeless people themselves. Or they

might be saying that the people who do live on the streets should not be allowed to live on

the street. On the other hand, the intended proposition might be that we should not

tolerate the fact that there are homeless people living on our streets. That is to say, the view

expressed might be critical of a society in which people are forced to live on the streets

rather than critical of such people themselves.

language and rhetoric30

Vagueness

Vagueness is a property of words and phrases. It is not the same as ambiguity, but it is

often mistaken for it. For instance, when former world leaders US President George W.

Bush and British Prime Minister Tony Blair used the alleged threat of ‘weapons of mass

destruction’ as a reason to form a coalition of willing nations (a group that was to become

known as the ‘Coalition of the Willing’) to invade Iraq and overthrow its government, they

traded on the vagueness of the phrase – a weapon of mass destruction could be any

weapon capable of killing large numbers of people, but it needn’t be a weapon that has

a particularly long range – they were able effectively to appeal to the US and British

populations’ fear of annihilation even though the weapons they were talking about were

probably only capable of killing or maiming a large number of Iraqi people. As we saw

when considering lexical ambiguity, a word is ambiguous when it has two or more possible

and different meanings – thus two or more separate extensions. The particular meanings

might themselves be perfectly clear and precise. The vagueness of a word, on the other

hand, is really a feature of its meaning: the meaning of a word or expression is vague if it is

indeﬁnite or uncertain what is conveyed by the word. Thus a word may be ambiguous

without being vague – as in ‘ball’ (round plaything, formal dancing-party) – or vague

without being ambiguous, as in ‘weapons of mass destruction’ (what exactly counts as such

a weapon – hundreds of people can be killed in a train or plane crash; does that make

trains and planes weapons of mass destruction?).

Sometimes, someone aware of the weakness of their own position will deliberately leave

their meaning vague in order to camouﬂage that weakness and to evoke strong feelings

of approval or disapproval in their readers or listeners. Many highly charged words that

wield rhetorical power in public discourse are used vaguely. Examples include ‘rights’,

‘liberal’, ‘harassment’, ‘racism’, ‘sexism’. It is hard to discern one perfectly exact meaning

for each of these words and it would be unrealistic to expect them to have such a meaning.

Their extensions tend to include a cluster of objects, beliefs or actions that are not

necessarily uniﬁed in any precise way. Take ‘left-wing’, for instance. This word conveys

various characteristics including:

•belief in a permissive society

•pro-trade union

•socialist

•communist

•pro-feminist

•anti-war

•environmenalist

•activist

•radical

•protester

•progressive

•Marxist.

language and rhetoric 31

One might be aligned with the political left and not hold all of these beliefs or have

all of these characteristics. Indeed, a person might have some or even many of them and

not be left-wing. Here is a whole passage infected with vagueness of the kind we have

in mind:

Make no mistake, the researchers involved in the highly controversial project to

map the human genome are involved in a radical project of unprecedented gravity

and spiritual signiﬁcance. Do they venture there with appropriate caution and

humility? What they are doing is not even comparable to the research that made the

atomic bomb possible, for it goes right to the essence of what we are as human

beings. Like Dr Frankenstein, they are tinkering with life; they are travelling into

unknown and sacred regions as no scientist previously has ever dared. The secret

wellsprings of life, of our very being as homo sapiens, have ever remained shut up,

concealed by aeons of either blind but cunning and ultimately unfathomable

natural processes, or, as some continue to believe despite the showy displays of

science and technology, concealed by the very hand of its Author, the Author

of Nature Himself.

What is the writer of this rather over-excited dose of hyperbole trying to argue? Clearly

they think that there is something dangerous or otherwise ill-advised about the project to

map the human genome. But they have not begun to make it clear what the danger is. The

research is distinguished from atomic research by its concern speciﬁcally with life, but

nothing is said as to why this is peculiarly dangerous beyond the use of extremely vague

verbiage such as ‘sacred’, ‘radical’, ‘gravity’, ‘spiritual signiﬁcance’ and so on. In a context

such as this, with so much at stake, we need to have precise reasons why, despite the

promise of medical beneﬁts, the project is dangerous.

Words can also be vague in another, more philosophically technical respect. Philosophers

of language use the term ‘vague’ to apply to words that have a clear meaning, but which

have an indeﬁnitely demarcated extension. Obvious cases are colour words like ‘orange’:

there is no precise division between orange things and yellow things, for example. Things

can often be precisely compared with respect to such attributes, however. For example, X

may be more bald, or fatter, sleepier, taller or faster than Y, even if it is not deﬁnite

whether or not X is bald, fat, sleepy, tall or fast. Borderline cases can also arise in the case of

nouns. In fact vagueness occurs in many more cases than we might at ﬁrst think. Take

‘city’: York is normally said to be a city, but is it really? Is it not merely a town? What about

Doncaster? Lancaster? Harrogate? Carlisle?

To a great extent, we take these sorts of vagueness in our stride, having become used to

interpreting these phenomena unreﬂectively in ordinary language. But even the simplest

cases can cause misunderstandings. Suppose your boss promises that you’re going to

receive a ‘big pay rise’ this year. When you receive the pay increase, you discover that the

rise is only 10p an hour. When you complain, your boss defends their promise by saying

that the rise is bigger than last year’s and therefore big in comparison (see the section

on implicit relativity, pp. 35–36, for further discussion of such cases). These examples

language and rhetoric32

demonstrate how widespread and common ambiguity and vagueness are and the extent to

which they frustrate our attempts clearly to understand others and to communicate clearly

ourselves.

Primary and secondary connotation

The rich secondary connotation of some words provides a further source of vagueness.

Every ordinary noun and every adjective – ‘elephant’, ‘immoral’, ‘company’, ‘stupid’ – has

a range of things to which it applies: the extension of the term. The set of all bananas

constitutes the extension of ‘banana’; the set of all square things constitutes the extension

of ‘square’. A given thing falls within a word’s extension if, and only if, it ﬁts a certain rule

associated with the use of that word. For example, the rule for the noun ‘ram’ is ‘male

sheep’. This rule is called the primary connotation of the term. This will be some set of

characteristics, in this case being male and being a sheep which, by deﬁnition, everything

to which the word applies must have. All of a term’s primary connotation must apply to an

object for that term to apply to it. The notion of a female ram, for example, is a logical

impossibility, a contradiction. If you know the primary connotation of a term, then you at

least know the necessary and sufﬁcient conditions for something to count as part of that

term’s extension. Thus when we are told that something is a B, for some general term B,

we know that the thing must exemplify the primary connotation of the term and, hence,

that it satisﬁes the necessary and sufﬁcient conditions for counting as a B; if we’re told it’s a

ram, then we know it’s a male sheep.

However, when we are told that something is a ram, we tend to assume other things about

that thing that are not included in the primary connotation: that it is woolly, has horns,

lives on a mountainside or in a ﬁeld, eats grass . . . So if you know that something is a

ram, it is reasonable to suppose that it has these additional characteristics. These further

characteristics that the term ‘ram’ also conveys make up its secondary connotation. Things

that fall under the term will generally exhibit these characteristics, but there is no logical

contradiction in supposing there to be a thing that falls under the term but lacks a

characteristic included under the secondary connotation. For instance, there is no logical

contradiction in supposing that a thing might count as a ram – that is, fulﬁl the demands

of the primary connotation – yet lack some or, indeed, all of these characteristics. It is not

logically impossible that there could be a bald, hornless male sheep that lives in a barn and

whose diet consists of potatoes.

Why should critical thinkers be interested in the distinction between primary and

secondary connotation? The most immediate relevance was demonstrated in our exami-

nation of vagueness. It is difﬁcult to pin down the precise meaning of a word such as

‘left-wing’ because, on the one hand, its primary connotation is very difﬁcult to pin down

and, on the other, its secondary connotation is so rich. In fact, in the case of vague words,

the distinction between primary and secondary connotation tends to break down, or be

difﬁcult to draw. Take a look back at the list given earlier of characteristics conveyed by

‘left-wing’: it is difﬁcult to say which are part of its primary connotation, and which are

only part of its secondary connotation.

language and rhetoric 33

A further reason for us to concern ourselves with this distinction is that it is the secondary

connotation of many words that gives the sentences in which they occur their rhetorical

force. Consider the noun ‘feminist’. Its primary connotation is difﬁcult to pin down and it

is full of secondary connotations that can be used to the rhetorical advantage of both those

who support and those who oppose feminism. Here are just some of the characteristics our

critical thinking students have come up with when asked what the word ‘feminist’ conveys

to them:

When interpreting speakers and writers we should also be aware of the role of secondary

connotation in metaphorical uses of language. Metaphors often function by bringing

only the secondary connotation of a word into play. In most cases the primary connotation

is in fact false of the object or person in question. When someone insults another person

by calling them a ‘pig’, the claim is literally false, but they are attempting to ascribe some

of the characteristics of the secondary connotation of ‘pig’ – the way it eats, the way it

smells, its penchant for mud, for instance. In the course of interpretation, we should take

care not to treat metaphors as literal claims and not to confuse a metaphorical use of a

word with an ambiguous one. When Shakespeare’s Romeo attempts to express the beauty

of his lover, Juliet, he says, ‘My love is a rose’; this is intended as a metaphor that ascribes

some of the characteristics of the secondary connotation of ‘rose’ to her – its beauty,

fragility and sweetness – and is not ambiguous between literal and metaphorical meanings

of ‘rose’.

Rhetorical questions

Rhetorical questions take the form of a question but indirectly assert a proposition

(whereas a declarative sentence directly asserts a proposition). That is, they are not really

used to ask a question, but to make a point in an indirect way. Speakers and writers often

use rhetorical questions when they’re making a point they assume to be obvious, so the

answer to the question ‘goes without saying’. However, in many cases the point is neither

obvious nor universally agreed. Rhetorical questions obfuscate speakers’ and writers’

intended meanings because they make it more difﬁcult to interpret whether or not a

speaker/writer really does support a given claim. Rhetorical questions are common in

polemical newspaper articles and in contributions to internet discussion forums. If you

encounter rhetorical questions in texts and speech that you are analysing, try to rewrite the

question as a declarative sentence. For instance, if someone were to write:

Should my right to freedom of speech be limited just because you disagree with me?

•Man-hating •Fighter

•Lesbian •Staunch

•Dungarees •Left-wing

•Unshaven •Pro-abortion

•Strong •Pro-women

•Political

language and rhetoric34

they probably wish to convey the proposition that their freedom should not be so cur-

tailed, so they are not genuinely asking a question. They expect that the reader’s response

will be an automatic ‘No, of course not’. To convey the proposition that seems to be

intended, we could rewrite the rhetorical question as a declarative sentence:

My right to freedom of speech should not be limited just because you disagree with

me.

You should resist the temptation to employ rhetorical questions in your own arguments.

Irony

Speakers and writers sometimes express their claims using irony. This takes the form of

language that, taken literally, would convey the opposite of what they wish to convey,

or something otherwise very different from it. Consider the following instance:

It is pouring with rain, very windy and cold. Mr I. Ronic says, ‘Mmm, lovely weather

today’.

Mr Ronic is probably being ironic, and intends to comment that the weather is lousy.

It is important to be aware of the possibility of irony. In order to ridicule a position they

are opposed to, speakers and writers sometimes sarcastically pretend to espouse that

position; but it isn’t always obvious that they are doing so.

Implicitly relative sentences

Consider the following examples:

•She earns an above average salary.

•It is the best of its kind.

•Great Uncle Eddie is a fast runner.

•Taxes are high.

•The rent on our ﬂat is low.

Sentences such as these represent another potential problem for the critical thinker

striving to work out exactly what a speaker or writer intends to convey by their words. The

sentences are implicitly relative. They make a comparison with some group of things, but

that comparison is not explicitly mentioned. For instance, to understand what it is for a

person to earn an ‘above average salary’, we need to know of what group the average to

which it is compared is. Or consider the one about Uncle Eddie? Does the speaker intend

to convey that Great Uncle Eddie is a fast runner such that he runs at world-record pace or

that he is a fast runner for a man of his age? Or something in between, such as that he is

faster than the average person? If such sentences are interpreted without the recognition of

their implicit relativity, then there is the possibility that they will be interpreted as making

language and rhetoric 35

a comparison with a group other than that intended by the writer or speaker. Great Uncle

Eddie is not a fast runner when compared with Usain Bolt and thus interpreted the claim

would be false. But when compared with other 94-year-olds, many of whom haven’t

broken into a run for many years, he is a fast runner and the claim is true. Once we

recognise such claims as implicitly relative and interpret them accordingly, they are more

likely to have a deﬁnite truth-value. But not always. Implicit relativity is often com-

pounded by other sources of vagueness. For example, even if we do know what comparison

class is being invoked in the case of Uncle Eddie, it is by no means clear just how much

faster a person must be than the average person of that class in order to be fast relative to it.

Problems with quantiﬁers

Quantiﬁers are words that tell us how many/much of something there are/is, or how often

something happens. As you will see, not all quantiﬁers specify an exact quantity of the

thing; rather they provide a rough guide. In the following examples the quantiﬁers are

underlined (this is not an exhaustive list of quantiﬁers):

•All men drive too fast.

•Politicians are often self-serving.

•Few doctors support health reform.

•Nearly all the students passed the course.

•She likes hardly any of her fellow students.

•No examiner should take bribes.

•Lots of computers develop faults.

•Nine hospitals will close at the end of this year.

•She never closes the door behind her.

•There are adequate computing facilities in fewer than half of the country’s

schools.

•He always writes his own speeches.

•Most women would choose to stay at home with their children if they could

afford to.

There are three potential problems with quantiﬁers:

1 Speakers and writers don’t always use quantiﬁers with sufﬁcient precision, so that the

proposition they intend to convey is unclear and open to misinterpretation and

rhetorical abuse. Suppose your friend says: ‘Premiership footballers all earn massive

payments from sponsorship deals.’ You don’t agree and you mention an exception –

Fergie Footballer receives only his (admittedly relatively generous) footballer’s salary,

with no extra money from endorsing sports shoes or shirts. Suppose your friend

defends her claim by saying that she didn’t really mean that every single player in the

Premiership earns big money from endorsements and sponsorship, but only that

most or nearly all of them supplement their earnings in this way. Now that her claim

is clear, you see that it is one with which you are more likely to agree.

language and rhetoric36

2 Some quantiﬁer-words are themselves vague. Suppose, for instance, that someone

claims:

Some doctors support the decriminalisation of cannabis use.

What does ‘some’ mean here? It could mean that only a handful hold the view

described, it could mean that a larger minority of members hold that view. Without a

more precise understanding of how many doctors are intended to be conveyed by

‘some’, it is difﬁcult to know how to respond to the claim. Moreover, the claim is

open to abuse from people who hold views on both sides of such a debate. Advocates

of decriminalisation can use it in support of their cause; their opponents can use it to

back up their anti-decriminalisation stance (the latter might say, ‘Only some doctors

support . . .’).

3 Often people simply omit quantiﬁers. For instance, someone might protest:

Lecturers don’t give students a chance to complain.

At face value this might appear to convey the proposition that:

No lecturer (ever) gives a student a chance to complain.

Yet it is likely that what the speaker really wants to say is something like:

Most of the lecturers I’ve encountered haven’t given students enough chance

to complain.

Notice that once the appropriate quantiﬁer is made explicit, the claim applies to a

much smaller group of lecturers than one might have supposed when the quantiﬁer

remained implicit.

Consider another example:

Today’s students are dedicated to their studies.

If we interpret this as expressing this proposition:

All of today’s students are dedicated to their studies.

we are likely to want to challenge the claim as we will be able to cite exceptions to the

generalisation. If, however, we interpret the claim as it is more likely to be intended, then

the quantiﬁer that we make explicit should be ‘most’ or ‘almost all’, thereby exposing

the proposition really intended as:

Most of today’s students are dedicated to their studies.

language and rhetoric 37

and this proposition has a greater likelihood of being true. Cases that we use to challenge

the truth of a generalising claim are known as counterexamples. You will notice that this is

a slightly different, but related, use of the notion of a counterexample from that intro-

duced in the discussion of deﬁnitions in Chapter 1. In both cases, however, the notion

encompasses the idea of an exception to a claim or to a suggested rule. (The process

discussed here should not be confused with that of refuting a complete argument by

counterexample, which is dealt with in Chapter 6.)

Quantiﬁers and generalisations

It is a commonplace for people to say that you can never really generalise. However, this is

certainly not true just as it stands. When someone says this they might be understood as

claiming, ‘all generalisations are false’. But this is itself a generalisation; so if the claim is

true, the claim is false! So that can’t be what it means. In any case, it is obvious that some

generalisations are true (even if they are not very interesting ones). That is, there are

counterexamples to the claim that all generalisations are false. For example, ‘All cities

in the UK have a bus service’ is obviously true and no case could really be raised to

undermine its truth.

What exactly is a generalisation? In fact, the ordinary term ‘generalisation’ is a bit vague; it

means, roughly, ‘a statement about a category of things’. A generalisation is not simply any

statement that includes quantiﬁers, since ‘there are ﬁve eggs in the refrigerator’ contains

the quantiﬁer-phrase ‘there are ﬁve’, but is not a generalisation. But we need not be too

precise about this. For our purposes we will reserve the term for ‘categorical’ statements

involving quantiﬁers such as ‘all’, ‘every’, ‘always’, ‘no’, ‘never’ and so on, but also ‘most’,

‘usually’ and the like.

To get a better grasp of which types of generalisations may cause problems during the

analysis and assessment of arguments, the main thing we need is to distinguish between

hard and soft generalisations. Consider the following generalisations (note that few of

them have explicit quantiﬁers):

•Girls’ schools attain better examination results than boys’ schools.

•Trafﬁc congestion is bad in Glasgow.

•Regular exercise beneﬁts your health.

•Left-leaning voters support a ban on SUVs in cities.

•People play less sport when they get older.

No doubt the counterexample fanatic will be able to provide us with plenty of exceptions

– congestion-free short cuts across Glasgow; voters who vote for left-of-centre candidates

but don’t support a ban on urban SUVs; the person who had a heart attack while doing

their regular workout at the gym. And they can cite this as a reason to accept the claim that

all generalisations are false because one can always ﬁnd an exception to them. However, to

do so would be to misinterpret what people usually intend to convey when they say or

write such things. It’s rare for someone to mean that these sorts of generalisations are true

language and rhetoric38

without exception. The quantiﬁer they intend to imply is probably one that is not syn-

onymous with ‘all’ or ‘every’, but one such as ‘in most cases’, ‘usually’, or ‘almost all’. These

generalisations are soft generalisations. We use soft generalisations when we want to

express the idea that such and such is true of certain things normally, typically, generally,

usually, on average, for the most part.1 In the examples above, the speaker/writer could

make her intended meaning much clearer by adding one of these words or phrases; for

example:

Girls’ schools generally attain better examination results than boys’ schools.

On the other hand, someone using a hard generalisation does intend it to apply without

exception. Such a generalisation is rightly conveyed by a quantiﬁer such as ‘all’, ‘every’,

‘no’, ‘always’, ‘never’. For example:

•Every passenger must hold a valid passport.

•No doctor who helps a patient to die should consider themselves to be above the

law.

If someone makes a claim that is intended as a hard generalisation and we can ﬁnd a

counterexample to it, then we have refuted their claim. But quantiﬁer-free generalisations

are not typically intended as hard generalisations. If the fanatical anti-generaliser does have

a point, we believe, it is a point about rhetoric, not truth. What the anti-generaliser is

justiﬁably worried about are generalisations about groups deﬁned by race, ethnicity,

nationality, gender, class and sexuality. Suppose that there are two social classes amongst

Martians: the Zormons and the Ringons. And suppose the generalisation ‘Ringons are

more violent than Zormons’ is true when taken as a soft generalisation, but false when

taken as a hard generalisation. A Ringon anti-generaliser might object to someone’s saying

this. But we’ve seen that the point cannot be that the generalisation is not true, in spite of

the fact that not every Ringon is more violent than every Zormon. This generalisation is, it

must be admitted, true when taken as a soft generalisation.

However, it might be argued, it is rhetorically dangerous. There are two reasons. The ﬁrst

reason is that many people are not very clear about the possible ambiguities of such a

statement. It might wrongly be taken as a hard generalisation, and furthermore it might

wrongly be taken as asserting something about the innate or genetic qualities of Ringons.

In itself, it does not do this. So unless these possible misinterpretations are deﬂected by

making the exact intended meaning perfectly explicit, this generalisation will remain very

provocative and a likely cause of ill-feeling. The second reason is the brute fact that, even if

1 Care should be taken interpreting and using ‘usually’ to express soft generalisations because it is ambiguous

in some contexts. For instance, the sentence, ‘British universities usually have a mathematics department’ could

be intended to mean that most or almost all British universities have a mathematics department, or that they

have them most or almost all of the time, but at some times they have no such department. If ‘usually’ could be

ambiguous in a context, it is better to use ‘typically’ or ‘generally’ instead.

language and rhetoric 39

these ambiguities are resolved, generalisations (even soft ones) about groups of people

do often cause people to take offence. There are times when people take offence at a

generalisation about a group and are simply irrational in doing so; no amount of explaining

the difference between a soft generalisation and a hard one, or the difference between a

generalisation about actual facts and one about alleged genetic qualities, will change this.

Like many kinds of irrationality, this is a natural kind of irrationality that cannot easily be

overcome. No matter how factually true a generalisation may be, it is natural to feel that

there is something dehumanising about it. So we cannot reasonably expect that people will

always be able to overcome that feeling. Morality requires us to consider the consequences

of our actions and, since speech and writing are types of action, natural (though irrational)

responses to what we say and write must sometimes be taken into account in deciding

what we ought to say. We should not say what is false, but that a proposition is true is

not always enough to justify expressing it. This, we believe, is the grain of truth in the

anti-generaliser’s position.

RHETORICAL PLOYS

Sometimes we are moved to accept or reject claims when we have been given no good

grounds for doing so. Often this is because speakers or writers attempt to persuade us in

ways that appear to provide motivation for doing or believing something, but do not give

us good reasons to do or believe that thing. These attempts to persuade fall into two

categories: rhetorical ploys and fallacies. Neither rhetorical ploys nor fallacies provide us

with good reasons to do or believe that of which they attempt to persuade us. Fallacies are

argumentative, but they constitute bad reasoning. Later, in Chapter 7, we refer to them as

‘pseudo-reasoning’. That is, they are still arguments in the sense that ﬁts our deﬁnition of a

set of propositions, some of which are premises, one of which is a conclusion, the latter

intended to follow from the former. But in one way or another, they are bad arguments.

Rhetorical ploys, on the other hand, are non-argumentative: some of these persuasive

devices may pretend to provide reasons for accepting a claim, but their real persuasive

capacity depends on something non-argumentative. It is important to learn to distinguish

between rhetorical ploys and fallacies, as the latter can be dealt with using techniques of

argument analysis and assessment. Here we aim to familiarise you with various common

types of rhetorical ploys. Later, in Chapter 7, we focus on common types of fallacies. Recall

our earlier deﬁnition of rhetoric as:

Rhetoric

Any verbal or written attempt to persuade someone to believe, desire or do

something that does not attempt to give good reasons for the belief, desire or

action, but attempts to motivate that belief, desire or action solely through the

power of the words used.

language and rhetoric40

As we saw in Chapter 1, politicians, advertisers and newspaper columnists tend to be

experts when it comes to using rhetorical ploys. Rhetorical ploys typically make a more or

less direct appeal to feeling and emotion rather than to reason, which is the domain of

argument.

The detection of rhetorical ploys is an exercise of psychology: we consider ways in which

our desires, fears, beliefs and actions could be non-rationally inﬂuenced by uses of language

that are intended to persuade us to hold beliefs and perform actions. As critical thinkers,

we aim to become adept at distinguishing and identifying these different types of

rhetorical ploy. We want to understand how they work, and how to avoid being taken in

by them. In the next sections, we consider speciﬁc types of rhetorical ploy and examples

thereof.

Appeals to speciﬁc feelings

There is a range of rhetorical ploys that attempt to tap into speciﬁc feelings in order to

inﬂuence our behaviour and opinions (especially our consumer behaviour). Here we dis-

cuss a number of the most common. Some of them are not strictly or speciﬁcally linguistic

ploys, but this will not affect the points we need to make.

Appeal to novelty

Here someone attempts to persuade us to try or buy something because the item is new

and, by implication, different from and better than existing related items. Often this ploy

appeals to our desire not to miss out on a new trend, or arouses our fear of appearing

outdated in our tastes. Sometimes it appeals to our (vain) sense of ourselves as ﬂexible and

willing to try out new experiences. It may also persuade us that, because the product is

new, it must be an improved version of the existing product. Familiar examples of the

appeal to novelty include advertising that attempts to persuade us to upgrade to allegedly

new and improved versions of existing products such as computer software and new

cars. The appeal to novelty may also be employed to persuade us to adopt new ideas or

beliefs. Again, this appeals to our desire not to appear inﬂexible or stick-in-the-mud. Thus

we might be enjoined to give up a belief in the value of trade union participation on the

grounds that trade unionism is ‘old-fashioned’ and ‘has no place in the workplace of the

twenty-ﬁrst century’. Notice that we have been given no reason to reject trade unionism;

we are just told that it is ‘old-fashioned’ and thus, by implication, something undesirable

that we wouldn’t want to be involved with if we care about our image as progressive and

in touch.

Appeal to popularity

Like the appeal to novelty, this ploy appeals to our desire to run with the crowd, not to

appear different from the norm and not to miss out on what others have. Again, it is

commonly used to persuade us to buy things, but also occurs frequently as a means to

language and rhetoric 41

persuade us to adopt a belief or to follow a certain course of action. Consider the following

attempt to persuade students to buy a computer software package:

Get Hotstuff! – the best-selling comprehensive software package among today’s

students – and turn your assignments into hot stuff.

Such an advertisement can work in various ways. It makes a straightforward appeal to our

desire to have what others have and not to miss out on the beneﬁts enjoyed by those who

already use the package in question. But, in addition, it tends to lead us to make some

unjustiﬁed assumptions about why the product is the most popular (‘best-selling’). If we

take insufﬁcient care, we are inclined to think that the most popular product must be the

most effective, but its popularity might stem purely from its competitive price or the

success of the marketing campaign. The fact that the software package is the best-selling

does not give us a compelling reason either to buy the product or to conclude that it must

be the most suitable software package for student-use.

Like many rhetorical ploys, the appeal to popularity can sometimes be construed as pre-

senting an argument – in this case, as presenting a reason to buy something. As we can

see from the following reconstruction, the reason given is not typically a good one (so the

argument is fallacious):

P1) The software package that sells best among students must be the best

software package for students.

P2) The software package that sells best among students is Hotstuff.

C1) Hotstuff is the best software package for students.

This argument would be valid but almost certainly not sound because the assumption

made explicit in P1 is not plausible; it is not the case in general that the best-selling product

of a given kind is the best of that kind (see the discussion of the fallacy of majority belief in

Chapter 7). Certainly if you were a student intending to invest in an expensive software

package, you would want much stronger evidence that Hotstuff is the best (and further-

more, you might well think that, since different students have different needs, the claim

that a given software package is the best for students in general must be pretty vague, and

without any direct implication for you, with your particular needs; we will discuss this

kind of vagueness in more detail on pp. 47–48).

Appeal to compassion, pity or guilt

This common rhetorical ploy operates by attempting to move us to do something purely

by evoking a feeling of compassion towards the recipients of the suggested act or belief, or

a feeling of guilt about their plight. The feeling alone does not provide a good reason for

us to perform the act in question. Examples of this ploy are myriad. Charity appeals and

advertising provide plenty of instances. Pictures of hungry children, suffering animals and

so forth, accompanied by simple slogans, are designed to tweak our feelings of compassion,

language and rhetoric42

pity and guilt about the situation of the people or animals featured. Remember that

the primary purpose of our examination of rhetorical ploys is a critical one; that is, we

encourage critical thinkers not to be persuaded by rhetoric and to avoid rhetoric in their

own attempts rationally to persuade others.

As we pointed out in Chapter 1, however, rhetoric can play a useful role when put to good

ends. In the case of the appeal to compassion, it serves a positive role by pricking our

conscience and opening us up to rational argument regarding how we should act in the

given situation. Feelings of compassion can prompt us to look for arguments that do

provide good reasons for the course of action recommended by the rhetorical ploy.

Suppose, for example, you read a charity advertisement that appeals to your sense of

compassion toward hungry children. You may go on to reason that if one can do something

to alleviate hardship, one should; and if you are in a position to do so then you should

make a donation to the charity. Such an argument might look thus when reconstructed

and rendered in standard form:

P1) A donation to the Worldwide Fund for Children would probably help to alleviate

the suffering of children from extreme hunger.

P2) I should try to alleviate extreme suffering where it’s possible for me to do so.

P3) It is possible for me to make a donation to the WWFC.

C) Probably, I should make a donation to the WWFC.

Notice that the argument is inductively forceful, its premises make it probable that I

should act in the way prescribed. It is certainly not implausible to say that this argument is

sound. Suppose, then, that you were moved to donate to the WWFC by a message simply

stating that many children throughout the world suffer from extreme hunger, along with

instructions on how to donate to the WWFC. The message certainly does not present the

above argument, nor any other. But it might have moved you to act by causing you to

think of the argument yourself.

Appeal to cuteness

This rhetorical technique supplements its words with images of children, animals or

animated characters to deliver a message. The product that we are urged to buy or the

action we are urged to take is made to seem attractive by its association with the cute

character that urges us to buy it or take it. The appeal can also work by helping us

to remember a product (what advertisers would call making us brand-aware) via its

association with the cute ﬁgure delivering the sales pitch.

Appeal to sexiness

This is similar to the appeal to cuteness, except that it uses a different type of image. It also

has a further dimension. To those who would desire the sexy person depicted in the

language and rhetoric 43

advertisement, the product is made to seem desirable by its association with the sexy

person. But it is also made to seem desirable to those who would like to think of

themselves as sexy in the way that the sexy person is. The ad seeks to ﬂatter us. It may

even invite us to reason, fallaciously: all sexy people buy or do this; therefore, if I buy or

do this, I’m sexy. This would be the fallacy of afﬁrming the consequent, discussed in

Chapter 7.

Appeal to wealth, status, power, hipness, coolness, etc.

You can easily work out what these are by analogy with the appeals to cuteness and

sexiness.

Appeal to fear (also known as scare tactics)

This is the tactic of trying to elicit a fear in one’s readers or listeners in order to inﬂuence

their behaviour or attitudes. A frequent example of the appeal to fear occurs in discussions

about immigration into wealthy countries. Many politicians and other opinion-formers use

the tactic of eliciting citizens’ fears of economic destitution and cultural demise by con-

structing deliberately exaggerated images of ‘waves of immigrants’2 entering a country

illegally and generally living a life better than that they deserve; taking jobs, education,

health care and state beneﬁts to which they have no rightful entitlement and thereby

making Mr and Ms Average Citizen worse off. This familiar scare tactic (that almost

certainly also makes appeal to some people’s racist attitudes) is often used by politicians to

persuade people to support draconian immigration policies and infringements of people’s

civil rights, and to demonstrate that support by voting for them at election time. But no

reason has been given for the belief that disaster would result if such extreme policies were

not enacted. Instead, it is hoped that describing these disastrous scenarios will alarm

people so severely as to disturb their reason, prompting the confused supposition that

the disastrousness of the worst possible scenario should be matched by the severity of the

preventive measures taken.

The appeal to fear should be distinguished from genuine warnings. In instances of the

former, there is no warranted connection between the fear elicited and taking the sug-

gested course of action or accepting the claim, whereas in the case of a warning, we are

given a good reason to act. This is usually because the circumstances of the warning are

themselves such as to warrant the belief that the warning is well-founded. For example, the

warning ‘Don’t touch the dog, it may look cute and friendly but it bites!’ would normally

be given only by someone who knows that the dog bites; since such warnings are very

seldom given insincerely or with a deceitful motive, the fact that such a warning has been

given is good reason to heed it. Such an inference, needless to say, would be much more

doubtful in the realm of advertising or political discourse.

2 Notice the rhetorical power of the phrase ‘waves of immigrants’, connoting as it does a ﬂood that will sweep

people away.

language and rhetoric44

Appeal to ridicule

This ploy occurs when a speaker/writer attacks their opponent’s position or claim by

casting it in a light that will make it seem ridiculous to their audience. For example, during

the 2008 US Presidential Campaign, the Republicans frequently labelled President

Obama’s policies as ‘socialist’. This can be understood as an appeal to fear – invoking

voters’ fears of the types of policies enacted by the ‘socialist’ dictatorships of the mid-

twentieth century – and the use of a buzzword (see below). In response, Obama said,

‘Next they’ll be calling me a communist because I shared my toys in kindergarten’. Pushing

the ‘socialist’ label to an extreme makes it appear silly and neutralises its appeal to fear. In

addition, by invoking mental images of Obama as a small boy who shared his toys, the

remark also makes an implicit appeal to cuteness, thereby casting the inclination towards

sharing and community in a good light.

These are just the most common instances of rhetorical ploys intended to manipulate

speciﬁc feelings and thereby to inﬂuence our attitudes and behaviour, but there are others

that occur frequently. Try to think of some and ﬁnd some examples of your own.

The direct attack and hard sell

The direct attack is the simplest of all rhetorical ploys. It occurs most frequently in

advertising, though it also appears in political campaigning. It often takes the form of a

very simple slogan. For instance, ‘Say no to tuition fees!’, ‘Drink cola!’ Notice that we are

given no reason to say ‘no’ or to drink cola. The belief of those who employ the direct

attack is that the more we hear or read these commands and internalise them, the more

likely we are to do as they advocate, despite having been given no reason to do so. We often

talk about ‘giving someone the hard sell’. The hard sell is simply the direct attack repeated

persistently. Children are notably effective with it. The persuader just keeps it up until the

subject of their attack gives in and does as they want, the persuader thereby having

inﬂuenced their target by verbal means without giving reasons for doing as they command.

Buzzwords

This is the technique of using fashionable or otherwise currently ‘hot’ words or phrases

that are loaded with rhetorical power due to their rich secondary connotation. (If you

don’t feel familiar with the concept of secondary connotation, have another look at the

relevant section of this chapter.) Buzzwords can be enormously provocative and therefore

hard to tame, and this makes them especially problematic for the critical thinker. If we

want to make an objective analysis of a passage or speech act, we should rephrase what is

said or written in such a way as to eliminate the buzzwords, and then embark on the

analysis. For example, in the 2008 US Presidential campaign the word ‘change’ became a

buzzword. Tuning in to voters’ desire for new policies and a new approach to governance,

the Democratic campaign constructed their candidate as the candidate of ‘change’. In the

context of voters’ desire for a different approach, the term, which in other contexts may

language and rhetoric 45

have had negative connotations and invoked fear of the future, took on a positive

rhetorical import. It is notable that the nature of the promised change wasn’t frequently

spelled out, the positive rhetorical pull of the term ‘change’ was sufﬁcient to attract voters’

support.

Scare quotes

This tactic is a means of inﬂuencing opinion against a view that one opposes. The speaker/

writer takes key words in terms of which their opponent expresses their views and

attempts to discredit those views by making them appear ridiculous or suspicious

through the use of scare quotes. No reason is given for rejecting the view; we are simply

manipulated into rejecting it because it has been made to appear ridiculous or suspicious.

Suppose someone makes the following claim about people trying to settle in a new country

for reasons of political asylum:

Almost all asylum seekers are economic migrants.

Now consider the effect of using scare quotes around the term ‘asylum seekers’ so that the

claim becomes:

Almost all ‘asylum seekers’ are economic migrants.

As you can see, the addition of scare quotes has the same rhetorical effect as putting

the phrase ‘so-called’ before the crucial term or phrase. The claim becomes much more

explicitly negative in respect of its questioning of the legitimacy of people’s claims for

asylum. Indeed, it has virtually the same effect as the rhetorically explosive phrase ‘bogus

asylum seekers’.

This tactic can also be used more subtly, but to similar effect. In such cases an opponent’s

opinion is made to seem dubious by placing scare quotes around words used to describe

what would be perfectly normal, acceptable facts about them. This can turn a perfectly

innocuous statement into one that casts doubt on someone’s credibility. Compare:

My opponent does of course have his reasons for what he believes to be right.

with the scare-quoted:

My opponent does of course have his ‘reasons’ for what he believes to be right.

While the ﬁrst sentence suggests disagreement with the opponent’s view, the use of scare

quotes in the second lends it increased rhetorical power, not only expressing disagreement

with the opinion in question, but also casting doubt on the legitimacy of the justiﬁcation

provided for those views.

Care should be taken not to confuse the rhetorical ploy of scare quoting with the legitim-

ate use of quotation marks to demarcate a direct citation of what someone has said or

language and rhetoric46

written. Sometimes we use quotation marks in this way even if the view we are quoting is

one with which we disagree. For instance, in responding to a letter one has read in a

newspaper, one might write:

Ms Long is simply mistaken when she claims that ‘men are better critical thinkers

than women’.

Here the writer is simply using quotation marks to show that she is using the original

writer’s words verbatim. Sometimes we do use citations of what people actually say or

write to rhetorical effect and we use quotation marks to demarcate their actual words, but

this is not the same as the tactic of scare quoting. A good example of this latter technique is

the use of someone else’s words taken out of context in order to give rhetorical support to

one’s own opinions.

Trading on an equivocation

This ploy deliberately exploits the ambiguity, and in some cases the vagueness, of a word

or phrase in the given context. Although nothing false is claimed, the speaker or writer

manages to inﬂuence our actions or beliefs by misleading us. It is generally used when

someone is attempting to persuade us of the beneﬁts and virtues of their product or

policy; hence it is common in advertising. So imagine we come across the following

Petrol consumption zero, the new Barolla and Chav4 diesels are here.

To equivocate is misleadingly to use the same word in more than one sense; the ploy is to

get us to interpret a message in a way that favours the product or view being advanced. In

this case, the word ‘petrol’ is used vaguely to give the initial impression that the vehicles

in question consume no petro-chemical fuels at all. Reading the smaller print, however, we

see that the advertisement attempts to persuade us to buy a vehicle that runs on diesel.

The advertisement equivocates by treating the word ‘petrol’ as meaning something

imprecise such as ‘fuel for cars’ rather than a speciﬁc type of reﬁned oil product. Of course,

the vehicle consumes fuel – but diesel, not petrol (gasoline) in the speciﬁc sense. So, while

it is true that it does not consume petrol in this speciﬁc sense, it is not true that it doesn’t

consume any fuel in the less precise sense denoted in the use of ‘petrol’ in the advertise-

ment’s initial slogan.

Another common instance of equivocation occurs when the ambiguity and vagueness of

the phrase ‘links to’ is used rhetorically to imply that someone is involved in some kind

of illegal or immoral activity (and is therefore a bad person). Suppose you read a newspaper

article which reports that:

Mr Smith, who is believed to have links to terrorist organisations, was seen boarding

a ﬂight at Heathrow Airport.

language and rhetoric 47

You may well be inclined to think that Mr Smith is a terrorist. But all that you have been

told is that someone believes he has ‘links to’ terrorist organisations. These ‘links’ could

amount to nothing more than his having visited premises belonging to such organisations,

or he may have attended a meeting, or bought propaganda material, or done business with

members of such an organisation, or simply have a relation who is involved in such an

organisation. The ploy is also commonly employed using the phrase ‘associated with’, as in

‘Mr Smith is believed to be associated with Al Qaeda’.3

The ploy of equivocation also occurs when someone attempts to mislead with statistics

by saying something that is true, but which they expect their audience to understand

according to an interpretation that is false. The following example of attempting to

mislead with statistics, which comes from a speech by George W. Bush, also includes an

equivocation on the meaning of ‘average’:

These tax reductions will bring real and immediate beneﬁts to middle-income

Americans. Ninety-two million Americans will keep an average of $1,083 more of

their own money.

This claim sounds like the average American will get a little over $1,000. But hang

on. Ninety-two million is the number of Americans who pay income tax. One might

understand Bush, as his speechwriters intend one to, as saying that the tax bill of the

average American will reduce by $1,083. But if ‘average American’ means ‘American with

average income’, then Bush’s claim is false. What is true is that $1,083 is the average tax

reduction under the new plan. But that’s because the highest earners save hundreds of

thousands (similarly, if Bill Gates is in the room along with ten call-centre workers, then

the average net worth is still in the billions). The American with average income still only

gets a few hundred dollars relief.

Trading on implicature

This is the tactic of using a statement’s implicature to mislead the audience (if you are

not clear on what implicature is, revisit the discussion in Chapter 1, pp. 10–11). Since the

proposition implicated is not actually stated by the speaker, the speaker can hope to avoid

responsibility for having misled the audience. This is common in political discussion. For

instance, suppose an opposition politician says:

If the Government increases income tax, it will be a further burden on working

families.

3 Notice that the word ‘terrorism’ is itself vague in that the boundaries of what counts as terrorism are ﬂuid

and the meaning of the term remains contested. Public discourse about terrorism often involves trading on

equivocation about the meaning of ‘terrorism’. As the cliché goes, one person’s terrorist is another’s freedom

ﬁghter.

language and rhetoric48

Suppose the politician knows that the Government is not actually considering the tax

increase. Still, the audience is led to believe that the Government is considering it – for

why else would the politician think it relevant to specify the negative consequence of a tax

increase? In using implicature in his way, the speaker or writer intends their audience to

interpret their words in this misleading way and to be emotionally moved as a result. Yet,

if accused of having misled the audience, the politician can say that he did not actually say

anything false, since he did not assert that the Government is considering a tax increase.

Many questions (aka leading question or complex question)

This is another ploy used knowingly to mislead one’s audience. It is the tactic of posing a

question that appears to seek an explanation for some proposition, p, thereby misleadingly

implying that p is true (if you feel unsure about how explanations work, review the section

on explanation and argument on pp. 20–22). For example, when we are asked, ‘Why do

cats paint?’, we are asked for an explanation of the proposition ‘cats paint’ and don’t

question whether they do paint; we assume it is true. A familiar instance of this misleading

use of questions is ‘Are you still beating your wife?’, the effect of which is to imply that the

proposition ‘x beats his wife’ is true. The many questions ploy is often treated as a fallacy.

We believe this to be misleading as it is not an attempt to argue; rather it is an attempt to

mislead an audience into accepting a proposition by embedding it in a question.

Smokescreen (changing the subject)

This is the tactic of avoiding discussion of an issue or acknowledgement of a point through

diverting or distracting one’s opponent from the issue at hand by addressing a different

(possibly related) issue. The issue irrelevant to the discussion thereby acts like a smoke-

screen by obscuring our view of the real issue. The more subtle the smokescreen, the

more effective at distracting the listener or reader it tends to be. Consider, for instance, a

government minister trying to defend her government’s proposed changes to legislation of

some kind. The proposals have come to light because a civil servant has leaked some

classiﬁed documents. In defending the proposals, the minister responds to questions by

launching into a speech about how the leak constitutes a dreadful dereliction of duty and

breach of trust. Instead of addressing the issue at hand – whether or not the proposed

legislative changes are good ones – the minister is attempting to distract attention from it

by obscuring it in the rhetoric of her speech about duty, responsibility and trust, a speech

that is rhetorically powerful because duty, responsibility and trust are the sorts of things

that right-minded people are supposed to uphold and admire.

The smokescreen tactic is very similar to the red herring fallacy, discussed in more detail

below (pp. 230–231). The crucial difference is that, while the smokescreen works via its

rhetorical power, the red herring is still an attempt to persuade by argument: it gives

reasons for accepting a claim, just not good reasons. When we are trying to distinguish the

smokescreen ploy from the red herring fallacy, we must ﬁrst work out whether or not the

writer or speaker is attempting to persuade by argument.

language and rhetoric 49

Spin

You will often hear talk of ‘spin’ and ‘spin-doctors’, particularly in the context of political

discourse. Essentially, the term ‘spin’ is a way of referring to techniques that employ

rhetorical ploy to good effect in inﬂuencing people’s (potential voters, opponents, the

media) opinions. Consider, for example, the language employed to describe various

governments’ attempts to rescue or support banks that might otherwise go bankrupt or do

not have sufﬁcient funds to lend to businesses. When large amounts of money are pro-

vided to those banks, governments are not simply ‘giving them money’; rather they are

‘injecting liquidity’. The use of this buzz phrase enables the project of giving public

funds to support banks to be ‘spun’ as something positive that anyone with a proper

understanding of ﬁnance would advocate. Employing the phrase ‘injecting liquidity’, then,

makes it seem like something that we should approve of, something highly technical that

takes ﬁnancial expertise to understand. If we don’t really understand the phrase, then the

spin will also have done the job of obfuscating the truth about what is going on between

governments and banks, thereby making us less likely to understand and to oppose it.

CHAPTER SUMMARY

There are various linguistic phenomena that can make the task of identifying and

interpreting arguments more difﬁcult. In the case of ambiguity, vagueness, metaphor,

rhetorical questions and irony, these can be problematic because they obscure speakers’

and writers’ intended meanings. In the case of implicitly relative sentences and sentences

that use quantiﬁers inappropriately, they can be problematic because they fail to convey

speakers’ and writers’ intended meanings in their entirety. Quantifying sentences can

also cause problems for the interpretation of arguments when they are used to express

generalisations inaccurately. There are two types of generalisation: hard and soft. Hard

generalisations are true only if they are true without exception. To avoid misinterpretation

they should be expressed in sentences that use quantiﬁers such as all, every, no, none,

always, never. Soft generalisations are only true of the majority of the class that is the

subject of the generalisation. They should be expressed in sentences that use quantiﬁers

such as most, almost all, in most cases, generally, typically, usually. In all cases linguistic

phenomena prevent the intended meaning from being explicit, we should pay careful

attention to context in order to render the most plausible interpretation of the attempt to

persuade. Where appropriate we should rewrite sentences to make their meaning explicit.

Rhetorical ploys seek to persuade by non-argumentative means. Insofar as we aim to be

rational, and to appeal to the rationality of others, we should avoid using rhetorical ploys

and fallacies in our own attempts to persuade and should take care not to be persuaded by

others’ rhetorical attempts to persuade us to do and believe things. The best way of doing

so is to familiarise ourselves with various common rhetorical ploys.

Many rhetorical ploys are appeals to speciﬁc feelings or desires; these include the appeals to

novelty, popularity, compassion, pity, guilt, fear, cuteness, sexiness, hipness, coolness,

language and rhetoric50

wealth, power, ridicule and many others. Typically a position or consumer item is repre-

sented in association with some object of the speciﬁc feeling or desire, in order that the

feeling or desire should be directed upon the position or consumer item. The direct attack

involves the bold assertion of a position or command; the hard sell is the direct attack

repeated. The use of buzzwords is the use of words with high emotive or otherwise

rhetorical charge to manipulate the passions of an audience. Scare quotes are used

mockingly to make an opponent’s position or other phenomenon look ridiculous or

dubious. Trading on an equivocation occurs when someone knowingly makes an ambigu-

ous or vague statement that may be true when interpreted in a certain way, but when

interpreted in another way may be false, but also more favourable to the position being

advanced or to the product being advertised. Smokescreen occurs when one talks about

some highly controversial, compelling or otherwise arresting issue or object, in an effort to

divert the audience momentarily from the issue under discussion. A successful smoke-

screen causes the audience to overlook the fact that the issue has not been addressed.

EXERCISES

1 Without looking back at the relevant section, write a paragraph explaining the

difference between lexical and syntactic ambiguity, then give a plausible example of

each and explain their possible interpretations.

2 In the following sentences indicate the words or phrases that are lexically ambiguous

and explain their possible meanings:

a The last time I saw them they were sitting beside the court.

b Happiness is the end of life.

c Archbishop of Canterbury praises organ donor for his humanity.

d Museum visitor attacked by mummy.

e Stolen car found by statue.

f British left wafﬂes on Ireland.

g Iraqi head seeks arms.

h An intense depression swept over the Midwest today.

i Obama leans further to the right.

j Finance Minister wins on budget, but more lies ahead.

3 The following sentences are syntactically ambiguous. Rewrite them so as to give the

most plausible interpretation. If two or more interpretations are equally plausible,

give them all. You may need to rearrange the word order and/or add words:

Example

A former professional dancer was accused of assaulting a 33-year old woman

with her daughter.

✎A former professional dancer and her daughter were accused of assaulting a

33-year old woman.

language and rhetoric 51

a The two suspects ﬂed the area before the ofﬁcers’ arrival in a red Ford Escort

driven by a woman in black.

b I was invited to go to the movies yesterday.

c Mary left her friends depressed.

d People who use cocaine often die early.

e Smith had a pair of boots and a pair of slippers that he borrowed from

Jones.

f Wanted: a bay mare, suitable for a novice with white socks.

g Jones left the company in a better state.

h Glasgow’s ﬁrst commercial sperm bank opened last Friday with semen

samples from twenty men frozen in a stainless steel tank.

i They were exposed to someone who was infected with the virus a week

ago.

j The police would like to speak to two women and a van driver who ﬂed the

scene of the accident.

4 Without looking back at the relevant sections, write a paragraph explaining the

difference between vagueness and ambiguity. Give examples to illustrate your

explanation.

5 For each of the following, identify the quantiﬁer and say whether the generalisation is

soft or hard:

Example

Almost all students have contemplated cheating in an examination.

✎Almost all soft generalisation

a No one may leave the room until the culprit owns up.

b Few of the applicants are sufﬁciently qualiﬁed for the job.

c Most politicians are committed to the people they represent.

d A majority of our members are prepared to go out on strike in support of

their pay claim.

e All passengers must fasten their seatbelts for take-off and landing.

f Generally birds can ﬂy.

g Almost all of the patients are ready to be discharged.

h Hardly any of the people surveyed were in favour of the proposed law

change.

i Every doctor must abide by the Hippocratic Oath.

j Almost none of the candidates have the charisma to succeed in politics.

6 Each of the following sentences expresses a generalisation, but its quantiﬁer is

missing. For each sentence, if it is true as a hard generalisation, add an appropriate

quantiﬁer to make it a hard generalisation. If it could only be true as a soft generalisa-

tion, add an appropriate quantiﬁer to make it a soft generalisation:

language and rhetoric52

Example

Passengers must hold a valid ticket before boarding the train.

✎All passengers must hold a valid ticket before boarding the train.

a Cats have tails.

b Children like to eat ice cream.

c Voters voted for Democratic Party candidates in the 2008 US election.

d Owls are mammals.

e Cars run on petrol or diesel.

f Citizens of a democratic country should be free to come and go as they

please.

g Members of Parliament are male.

h UK universities have an English Department.

i People care enough about climate change to change their lifestyles.

j Americans can speak a language other than English.

7 Name the following rhetorical ploys.

Example

If we allow the development of nuclear power plants, we are leaving our

children and our children’s children open to the threat of environmental

catastrophe.

✎Appeal to fear/scare tactics.

a The ‘relationships’ of homosexuals cannot be compared to that of marriage:

marriage is something that involves a man and a woman united through the

word of God.

b Take a look at the latest hatchback from Fraud: the all new Ego.

c Successfully applied knowledge management is now impacting on organisa-

tions in terms of both direct competitive advantage, and in building a

learning culture that identiﬁes itself through a shared vision and common

purpose.

d More pet owners feed their puppies First Choice puppy food than any other.

If you want to give the little fella a head start, shouldn’t you too?

e These people say we have a moral duty to honour our United Nations com-

mitments and provide refugees with a safe haven. I say to you: look at all

these people arriving here and then claiming state beneﬁts, they are sucking

the taxpayer dry.

f Fatbusters – the most successful weight loss programme on the market today!

g Imagine yourself, or worse, your daughter, alone beside your broken-down

car on a remote country road in the middle of the night. Few people pass by,

no one stops to help and your cell phone has no signal. Don’t get caught like

that – don’t get caught without the super 3GM digital phone, offering the

widest coverage available.

language and rhetoric 53

h By scheduling the broadcast at 1 am, the TV company is committing an act

of censorship.

i Hair unmanageable and dull? Try Goldie Glow from Bella. The latest in hair

management technology.

j Have you stopped smoking those dreadful cigars?

8 Give an example of each of the following rhetorical ploys. Try to make your examples

appreciably different from those already provided. Explain how, in your example, the

ploy functions to persuade us to do or believe something.

a Appeal to ridicule

b Many questions

c Trading on an equivocation

d Buzzwords

e Scare quote.

9 Try to ﬁnd an example of spin that appears in the media, either print or digital.

i) Explain why it exempliﬁes the phenomenon of spin.

ii) Identify the rhetorical ploys it employs.

iii) Analyse how they inﬂuence our feelings and beliefs in favour or against the

idea or person in question.

language and rhetoric54

logic: deductive

validity

•The principle of charity 56

•Truth 60

•Deductive validity 62

How to judge validity • Further examples

•Prescriptive claims vs descriptive claims 67

•Conditional propositions 68

•The antecedent and consequent of a conditional 71

Conditionals vs arguments

•Argument trees 73

•Deductive soundness 76

•The connection to formal logic 78

•Chapter summary 81

•Exercises 82

We hope that you are now a little better than you were at distinguishing rhetorical pseudo-

reasoning from arguments. You have got more tools for identifying and characterising

the former; your defences are keener and more nimble. Now we want to improve your

capacity to understand and reason about the latter.

Our attempts to engage in critical thinking are sometimes frustrating. Often, even when

we feel certain that there is something wrong with an argument, we ﬁnd it hard to explain

exactly what it is that’s wrong with it. Sometimes this is frustration with ourselves; but it

can easily look like frustration with the person giving the argument (it can certainly be

interpreted as such by that person!). One of the primary aims of training in critical

thinking is to learn concepts and techniques that will help us to express clearly what is

wrong with an argument, thereby dispelling that frustration. By helping us to assess

arguments more efﬁciently, this helps us in the pursuit of truth. But also, by becoming

more articulate in our criticisms, we become less frustrated, and thereby less bad-

tempered. This can help to smooth out our relationships with other people.

This frustration derives from two sources. First, confronted with an argument, we ﬁnd it

hard to hold the whole thing clearly before our mind’s eye; we ﬁnd it hard to say exactly

what the argument is. Second, even when we do succeed in laying the argument out before

us clearly, we ﬁnd it hard to describe or explain what is wrong with it:

•The ﬁrst issue is addressed by techniques and strategies for argument-reconstruction:

the representation of arguments in standard form, so as to give us a clear and com-

prehensive view of them.

•The second issue is addressed by techniques and concepts of argument assessment: the

determination of whether or not arguments provide good reasons for accepting their

conclusions.

We discuss practical details of argument-reconstruction in Chapter 5. This chapter and the

next are mostly concerned with argument assessment. Ordinarily, we speak of arguments

as being good or bad, strong or weak, valid or invalid, sound or unsound, persuasive or

unpersuasive, intelligent or stupid, without having a clear idea of what we mean by these

terms, and without clearly distinguishing their meanings. So not only are we vague when

we use one of these terms to criticise the argument; our attempts to explain ourselves by

means of the others are still vague. Thus our primary task in this chapter and the next is to

explain the basic logical concepts in terms of which assessment is carried out – validity,

soundness and inductive force.

You may be surprised that detailed discussion of argument assessment precedes the

detailed discussion of argument-reconstruction in Chapter 5; surely you have to

reconstruct an argument before you can assess it? In fact, it is slightly less straightforward

than that: although the ﬁnal assessment of an argument must await its reconstruction,

good reconstruction practice must be informed by a good grasp of the concepts used in

assessment. The purpose of the next section is to explain this important point.

THE PRINCIPLE OF CHARITY

An argument is a system of propositions: a set of premises advanced in support of a

conclusion. People succeed in expressing the propositions they have in mind with varying

degrees of clarity. In addition, an argument may depend upon premises that the arguer

does not state at all, but which he or she is implicitly assuming.

For example, if someone argues: ‘Sally is an artist; so I’ll bet she has some paintbrushes’, the

arguer is probably using the rather vague term ‘artist’ in the narrow sense of ‘painter’. In

logic: deductive validity56

the wider sense of ‘artist’ that includes sculptors and even pop and rock musicians, this

would obviously be a bad argument. Furthermore, the arguer is assuming, without

explicitly stating, that someone’s being a painter is reason to think they have paintbrushes.

So two sorts of thing are left implicit in this argument: ﬁrst, the arguer assumes a more

precise meaning than is explicitly expressed by the word ‘artist’; second, the arguer fails to

make explicit all the facts from which he or she infers the conclusion. A premise is left

implicit.

Since the purpose of argument-reconstruction is to determine exactly what argument

has been given, part of the task of argument-reconstruction is to clarify what the

arguer actually said, and to supplement what the arguer actually said (to make explicit

what was merely implicit in the arguer’s statements). That is, we try to represent the

argument in such a way as to create a perfect match between the propositions that actually

constitute the argument and the sentences which represent the argument in standard

form.

Two important consequences follow from this:

•The sentences we use in a reconstruction of the argument need not be the very same

sentences used by the arguer in giving their argument. We may employ sentences that

more clearly or precisely express the propositions that constitute the argument.

•Our reconstructed version of the argument may contain premises that are not

expressed by any of the sentences actually used by the arguer.

Argument-reconstruction is essentially a task of interpretation. What we are trying to

reconstruct, to represent as clearly as we can, is a certain train of thought, of reasoning –

however well or badly the arguer may have succeeded in expressing it. This cannot be an

exact science. It cannot be mechanical or foolproof. It calls for judgement, a critical but

sympathetic eye or ear and even a certain degree of intuition, of understanding of people –

of the ways people tend to think in given sets of circumstances, and of some typical ways in

which people fail to express themselves clearly.

Nevertheless, the process can be undertaken in a systematic and more self-conscious way,

and there are general guidelines to follow. One of the most important of these is what we

call the principle of charity, which we now explain.

We have just said that argument-reconstruction is often a task of surmising what the

arguer had in mind, and was trying to express. Our primary evidence for this, naturally, is

the speciﬁc words actually used by the arguer. Beyond this, we look to various sorts of facts

about the context or circumstances in which the person employed the words that he or she

did. For example, consider this argument:

But he is still in Paris! Therefore, he cannot possibly be in Moscow by tomorrow.

Of course nowadays Moscow is only a few hours from Paris by aeroplane. If someone were

to give such an argument regarding some presently living person – Vladimir Putin, for

logic: deductive validity 57

example – then we would be puzzled. Since everyone is aware of air travel, nobody thinks

that it is impossible to get from Paris to Moscow in one day. So in the context of today, we

would have to inquire further to discover what the arguer thinks is preventing Mr Putin’s

journey. But suppose these words were given by someone in 1807, referring to Napoleon.

Then surely the arguer would be assuming, correctly, that it is not possible to get from

Paris to Moscow at such a speed. Indeed it would have gone without saying, which is

precisely why the arguer need not have expressed it explicitly. The fastest way to travel

then was by horse.

Such facts pertaining to the context in which the argument is given, together with the

speciﬁc words used by the person, will constitute the total evidence you have for

reconstructing the argument. In some cases, the context is known, and makes it obvious

what the arguer was implicitly assuming. In other cases, we may have to learn more about

the context; this happens especially when interpreting historical documents.

In still other cases, however, we may learn all the relevant contextual factors, yet it remains

possible to represent the person’s argument in more than one way. And it may happen

that one reconstruction represents the argument as a good one, another as a bad one. In

such a case, which reconstruction should you prefer? Which should you advance as the

reconstruction of the argument?

It depends upon your purpose. If you are hoping to convince others that the person

is wrong, you are most likely to succeed if you represent it as a bad one. Indeed, this is

a very common ploy. If your aim is to defeat your opponent – or to make it seem as if

you have defeated them – then success is more likely if you attack a weakened form

of your opponent’s argument. In a context like that of a public debate, this is often a

good strategy. For what you are trying to do is to appear, in the eyes of the audience,

to get the upper hand. By representing your opponent’s position as weaker than it really

is, you are more likely to appear to be the victor. You also put your opponent on the

defensive, forcing him to scramble, saying things like ‘that’s not what I meant’. If your

aim is to persuade, or to appear to be the victor, then you may be well advised to choose

the weaker version, especially if your audience is not aware that a stronger version is

available.

However, if what matters to you is whether or not the conclusion of the person’s argument is true,

then you should choose the best representation of the argument.

Why? Suppose you are wondering whether some particular proposition is true. You are

wondering, for example, whether increasing taxes for the wealthy would lead to a rise

in unemployment. Suppose further that you honestly have no idea whether or not

this is true. Now suppose that someone attempts to persuade you that this proposition

is true by giving you an argument for it. But you ﬁnd that this argument admits of

being reconstructed in either of two ways. On one reconstruction, the argument is good;

that is, it provides a good reason for accepting the proposition as true. On the other

reconstruction, however, it is no good at all; you ﬁnd that the reasons you have repre-

sented the person as giving in favour of this proposition do not support it at all. Suppose

logic: deductive validity58

you decide on this latter representation of the argument, the one which represents it

as bad.

Can you now conclude that the proposition is true, or that it is false? Since, reconstructed

that way, the argument was no good, you certainly cannot conclude, on the basis of it, that

the proposition is true. But nor can you conclude that the proposition is false. The fact that

someone has given a bad argument for some proposition is not, in itself, a reason to reject

the proposition as false. For example, someone might argue that since three is a lucky

number, there will not be a third world war. That is a bad argument; it gives you no reason

to believe that there will not be a third world war. But (fortunately!) its being a bad

argument provides no reason to believe that there will be a third world war. In short, the

fact that someone has given a bad argument for the proposition in question leaves you in

precisely the same position as you were when you started. If you began with no evidence

either for or against the proposition, then your position is unchanged – you’ve no reason to

accept the proposition as true, and none to reject it as false.

Suppose, then, that you accept the ﬁrst reconstruction of the argument. Since this con-

stitutes a good argument, you are now in a different position; now you do have some

indication as to whether or not the proposition is true. In particular, you have a reason for

its being true. Thus, insofar as we engage in critical thinking – insofar as our interest is in

discovering the truth of things, and not just in persuading or refuting people – we are

most interested to discover good arguments, not bad ones. So we should always choose the

best reconstruction of a given argument. That way, we discover reasons for accepting or

rejecting particular propositions, advancing the cause of knowledge. Thus the principle of

charity.

There is a further reason for observing the principle of charity, which has more to do with

ethics than with logic. When you give an argument, you may or may not succeed in

expressing yourself clearly, but you do want your listener to try to understand you. If your

listener impatiently seizes upon your words in order to refute your argument as swiftly as

possible without taking the trouble to understand you, naturally you feel ill-used, that the

person is not being fair to you. You think it wrong, unjust to be treated that way. If so,

then we ought to try to be equally receptive to others – to try to understand them, rather

than be too eager to refute them or discredit them.

The principle of charity, however, has a certain threshold, beyond which the nature of

what we are doing changes somewhat. If our task is to reconstruct the argument actually

intended by the person, then we must not go beyond what, based upon the evidence

available to us, we may reasonably expect the arguer to have had in mind. Once we go

beyond what we may reasonably assume the arguer to have had in mind, then we are no

longer in the business of interpreting their argument. Instead, we have become the arguer.

If our concern is with how well a particular person has argued, then we should not

overstep this boundary. However, if our concern is simply with the truth of the matter in

question, then to overstep this boundary is perfectly all right. It often happens that, in

reconstructing an argument, we hit upon another, similar or related argument for the same

logic: deductive validity 59

conclusion which is better than the one we are reconstructing. If what concerns us is simply

ﬁnding the best arguments on either side of an issue, then we will want to give a representation of

this better argument.

TRUTH

If your aim is to give the best possible reconstruction of an argument, then you have to

know something of what makes an argument good or bad. Fortunately, logic gives us some

very clear answers as to what does make arguments good or bad.

The fundamental concept of logic is the concept of truth.1 For one thing, the overarching

concern of the critical thinker is typically with the truth (or lack of it) of the conclusions of

arguments. Further, truth is the concept in terms of which the logician attempts to explain

everything else. Thus, we begin our discussion of the concepts of logic by saying a little bit

more about this uniquely important concept.

Many people are put off by the word ‘truth’. This is usually the symptom of a

philosophical worry that one cannot speak simply of ‘truth’. One might worry that

perhaps there is no one truth: that what is true for one person or group need not

be true for another person or group. Or one may worry that truth is in some way

beyond us, unapproachable by mere fallible human beings. But for our purposes we

can leave aside those sorts of abstruse philosophical worries as irrelevant. As noted in

Chapter 1, the way in which the logician uses the word ‘truth’ is really very simple

and down-to-earth. Properly understood, the word should not invite those sorts of

controversies.

Consider the following proposition:

(A) Fish live in water.

This proposition is true. What does it mean to say that this proposition is true? It means,

simply, that that is the way things are. To say that the proposition is true is to say nothing

more than: yes, ﬁsh do live in water. Thus, consider the proposition that says that (A)

is true:

(B) It is true that ﬁsh live in water.

(A) and (B) are equivalent in the sense that, necessarily, if (A) is true then so is (B), and if (B)

is true then so is (A). In other words, to say that it is true that ﬁsh live in water comes to

the same thing as saying that ﬁsh live in water. Used this way – which is all that is needed

for logic or critical thinking – the word ‘true’ is no more mysterious than the words

1 The great German logician Gottlob Frege – who is genuinely agreed to have the strongest claim to being the

inventor of the modern science of logic – said that the laws of logic are really the ‘laws of truth’, in something

like the way that the laws of physics are the laws of the physical world.

logic: deductive validity60

occurring in the sentence ‘Fish live in water’. In this sense, you cannot doubt that there

is ‘really’ such a thing as truth, or that truth is knowable, any more than you can doubt

that ﬁsh live in water, or that the sky is blue, or that the Earth is bigger than a grapefruit.

For these are all known truths.

Discomfort with the word ‘true’ is sometimes due to a failure to distinguish truth from

belief. If John says, ‘Fish live in water’, then he does, of course, show that he believes that

ﬁsh live in water (presumably he knows that ﬁsh live in water). Likewise, if Mary now

indicates what John said, and says, ‘That’s true’, then she also shows that she believes that

ﬁsh live in water. Despite their having done so by different means, both John and Mary

have asserted the proposition that ﬁsh live in water. Mary, unlike John, has used the word

‘true’. But they have asserted the same proposition; they have expressed the same belief,

the same commitment. Yet clearly the truth of this proposition has nothing to do with

what Mary believes. That depends only on how things stand as regards ﬁsh, and what ﬁsh

do does not depend upon what people think. So despite the fact that Mary has used the

word ‘true’ to assert something, the truth of what she asserts does not depend on her

beliefs in any way.

Of course, what Mary believes depends on her, and it is possible that people could have

different beliefs as regards ﬁsh. But that has no effect on ﬁsh (we will, however, return to

this issue in the ﬁnal chapter).

The reverse side of this is that to say that a proposition is false is just to deny it – in this

case, for example, some misinformed person who thought that snakes are ﬁsh might say,

‘That’s false; not all ﬁsh live in water’.

Sometimes we will speak of the truth-value of a proposition. This just means the truth of

the proposition, if it is true, or its falsity, if it is false. There are two truth-values, true and

false. For example, we can say that the truth-value of ‘Fish live in water’ is truth, that that

of ‘Fish live in the sky’ is falsity, and that the truth-value of ‘It is now Tuesday’ must always

differ from that of ‘It is now Friday’. To ask ‘what is the truth-value of that proposition?’ is

the same as asking whether or not that proposition is true.

A question might have occurred to you: If to say that a proposition is true is equivalent to

asserting it, then why do we have the terms ‘is true’ and ‘is false’? What is their purpose?

Why are they not just redundant, superﬂuous appendages? One reason is convenience;

saying ‘that’s true’ is quick and easy, like saying ‘yes’, or nodding one’s head. But a more

important reason is that we sometimes want to gain the effect of asserting propositions

without knowing which ones they are. For example, one might say, of someone whom one

trusts, ‘Whatever he said, it was true’. Connected with this is that we sometimes wish to

speak about true or false propositions in general, without specifying any propositions in

particular; an example is the law of non-contradiction, which says, ‘No proposition is both

true and false’. This is crucial in the formal study of logic, but less technical examples are

no less important. For example, we have characterised critical thinking as aiming at truth.

This means that we undertake it because we want to know whether capitalism is the fairest

economic system, whether so-and-so committed the crime, whether the danger of war is

logic: deductive validity 61

increasing or decreasing . . . and so on, for everything we might want to know. That critical

thinking aims at truth is a generalisation that sums this up.2

DEDUCTIVE VALIDITY

In fact, we need this sort of generalisation in order to deﬁne the important concept

of deductive validity, to which we now turn. For brevity, we will sometimes call it

simply ‘validity’. In studying it, you should forget whatever the word might mean to you

ordinarily. We mean logical validity, the concept of validity that concerns logic, the study

of reasoning.

Consider the following arguments:

P1) The Prime Minister’s dog is infested with ﬂeas.

P2) All ﬂeas are bacteria.

C) The Prime Minister’s dog is infested with bacteria.

P1) Colette owned a dog.

P2) All French Bulldogs are dogs.

C) Colette owned a French Bulldog.

Argument A speaks of ‘The Prime Minister’s dog’, but it is not made clear who that is, for

we are given no indication of when, or even in what country, this argument was given. So

we have no idea what dog, if any, has been referred to. Furthermore, P2 of A would be false

under any circumstances in which the argument might have been given – ﬂeas are insects,

not bacteria. But scrutinise these arguments carefully. You can easily recognise that there

is something right about A, and something wrong with B. The conclusion of A does follow

from its premises, and the conclusion of B does not follow from its premises. What you are

recognising is that A is valid, and that B is invalid.

Now, what does this mean? What, exactly, are you seeing when you see that A is valid and

B is invalid? Consider A. When you recognise its validity, you do not need to know

2 We speak of ‘gaining the effect’ of asserting, or ‘committing’ to an assertion, because it is infelicitous to

speak of asserting a proposition without knowing what it is. In fact, this is not quite right either, since one can

merely entertain the proposition that such-and-such is true, or doubt it and so on. ‘Such-and-such is true’ is better

thought of as a device for expressing the proposition indicated by ‘such-and-such’. This is, of course, just the tip

of an iceberg of issues surrounding the details of ‘true’; but everyone is agreed that a correct account of ‘true’

must deliver the expressive function we have described. See Chapter 8, pp. 242–251.

logic: deductive validity62

whether or not P1 or C of A is true or even precisely which dog of which Prime

Minister of which country is intended; nor do you care about the fact that P2 of A is

positively false. For what you are seeing is that if the premises of A were true, then

the conclusion would have to be true as well. In short, it would be impossible for the

premises to be true but the conclusion false. The truth of the premises, in any possible or

imaginable situation, would guarantee the truth of the conclusion. If ﬂeas were bacteria,

and the dog being referred to were infested with ﬂeas, then it would, in that case, be

infested with bacteria.

On the other hand, consider B. When you recognise that it is not a valid argument, what

you are recognising is that even if the premises were true, it would still be possible for the

conclusion to be false. The conclusion does not follow. Whether or not the premises are in

fact true, it would be possible or conceivable for the premises to be true and the conclusion

false. The truth of the premises would not guarantee the truth of the conclusion.

Now as it happens, the premises of B are true. The French author Colette did have a

dog, and of course French Bulldogs are dogs. Indeed, the conclusion of B is also true;

Colette’s dog was a French Bulldog. But that is beside the point, so far as validity is

concerned. It may be true that Colette had a French Bulldog, but this does not follow

merely from the fact that she had a dog. A person given only the premises of the

argument, and lacking any further information about Colette, would be in no position to

infer that Colette had a French Bulldog. If this point seems strange, remember that you

saw that the argument is invalid before you knew the truth-values of its premises or of its

conclusion. And that is as it should be. You can tell that an argument is valid or not

without knowing the truth-values of the propositions it comprises, because the validity

of an argument (or lack thereof ) does not depend upon the actual truth-values of those

propositions.

To put it another way: the concept of validity pertains to the connection between

the premises and conclusion of an argument, not their actual truth-values considered

individually. This is indeed the crucial lesson about the concept of validity: it pertains to

whole arguments (more exactly: it pertains to inferences; extended arguments may contain

more than one inference, and each one is subject to being valid or invalid).

Thus, it should be clear that it would be nonsense, to say of a single proposition, that it is

valid. That would be like saying, of a single word, that it rhymes (a rhyme requires a

relation between words). By the same token, it would be nonsense to say, of an argument,

that it is true. That would be like saying, of an entire tennis match, that it was a double-

fault. A single proposition can be true or false, but not valid or invalid; an argument can be

valid or invalid, but not true or false.

These two points should be borne in mind, as it is a common mistake to confuse the

notions of truth and validity, applying them to the wrong sorts of things.

Here, then, are two deﬁnitions of validity; they are equivalent (they come to the same

thing), so you are free to make use of the one you ﬁnd easiest to work with:

logic: deductive validity 63

To say that an argument is

valid

is to say: It would be impossible for all the

premises of the argument to be true, but the conclusion false.3

And the second one:

To say that an argument is

valid

is to say: If the premises are (or were) true, the

conclusion would also have to be true.

If the condition speciﬁed by the deﬁnition does not hold, then the argument is invalid.

A consequence of these deﬁnitions is that the following cases of valid arguments are all

possible:

1 The premises are all (actually) true, and the conclusion is (actually) true.

2 The premises are all (actually) false, and the conclusion is (actually) false.

3 The premises are all (actually) false, and the conclusion is (actually) true.

4 Some of the premises are (actually) true, some (actually) false and the con-

clusion is (actually) true.

5 Some of the premises are (actually) true, some (actually) false and the

conclusion is (actually) false.

The only case in which an argument cannot be valid is the case when the

premises are all (actually) true, but the conclusion is (actually) false. For if that is so,

then obviously there is a possible case in which the premises hold true when the

conclusion is false – the actual case.

This is easier to grasp by looking at some examples. The following are, respectively,

examples of cases 1–5 given above; the ‘T’s and ‘F’s in parentheses to the right of each

premise or conclusion indicates its actual truth or falsity, as the case may be:

1 P1) Janet Baker is an opera singer. (T)

P2) All opera singers are musicians. (T)

C) Janet Baker is a musician. (T)

3 This deﬁnition has the consequence that if any premise of an argument is a necessary falsehood, or if the

conclusion is a necessary truth, then the argument is valid (a necessary falsehood is a proposition that could not

possibly have been true; a necessary truth is a proposition that could not possibly have been false). In such cases

the premises may be entirely irrelevant to the conclusion. For example, ‘There is a married bachelor, therefore

the moon is made of green cheese’ is valid, as is ‘The moon is made of green cheese, therefore there is no married

bachelor’. Our deﬁnition, then, is quite useless as a guide to reasoning, where necessary truths and necessary

falsehoods are concerned. We believe this a reasonable price to pay, for the alternative – a deﬁnition of validity

whereby an argument is valid by virtue of its form – is too difﬁcult, for our purposes, to apply proﬁtably to

ordinary language. Further, it is really very seldom that necessary truths or falsehoods ﬁgure as the conclusions

or premises of arguments encountered ordinarily.

logic: deductive validity64

2 P1) Janet Baker is a baritone. (F)

P2) All baritones are Italians. (F)

C) Janet Baker is an Italian. (F)

3 P1) Janet Baker is a baritone. (F)

P2) All baritones are English. (F)

C) Janet Baker is English. (T)

4 P1) Janet Baker is a soprano. (T)

P2) All sopranos are English. (F)

C) Janet Baker is English. (T)

5 P1) Janet Baker is a soprano. (T)

P2) All sopranos are Italians. (F)

C) Janet Baker is an Italian. (F)

And here are some invalid arguments (we will consider further common invalid

argument-types in Chapter 7 in the section ‘Formal fallacies’):

6 P1) Janet Baker is a soprano. (T)

P2) Janet Baker is a musician. (T)

C) Janet Baker is an Italian. (F)

7 P1) Janet Baker is a woman. (T)

P2) All baritones are women. (F)

C) Janet Baker is a baritone. (F)

8 P1) Janet Baker is a woman. (T)

P2) All sopranos are singers. (T)

C) Janet Baker is a English. (T)

9 P1) Janet Baker is a baritone. (F)

P2) All singers are baritones. (F)

C) Janet Baker is a singer. (T)

logic: deductive validity 65

How to judge validity

The way to determine whether or not an argument is valid is to ignore the actual truth-

values of the premises and the actual truth-value of the conclusion (of course, if the

conclusion is actually false, and the premises are all true, then the argument must be

invalid. But normally when assessing arguments we do not know the truth-value of the

conclusion, because the whole reason for considering the argument is that we want to ﬁnd

out the truth-value of the conclusion). The way to do it – and this is what the deﬁnition of

validity should lead you to expect – is to reason as follows:

Whether or not they are actually true, suppose or pretend that the premises were

all true; then in that situation – aside from how things

actually

are – could the

conclusion conceivably be false? If it could not be false, then the argument is

valid

. If it could be false, then the argument is

invalid

The systematic study of validity is the concern of logic. Logicians are concerned to devise

perfectly reliable procedures for detecting validity, or the lack of it, even in the case of

extremely complex arguments such as those occurring in mathematical proofs. Since the

validity of an argument is independent of the truth-values of its premises, logic has a

unique status among the sciences; for other sciences are concerned to ﬁnd out the truth-

values of particular propositions about its characteristic subject-matter. Ichthyology, for

example, seeks to know which propositions about ﬁsh are true, and which false. The

logician has no particular concern with ﬁsh, nor with the truth as regards anything else in

particular. Logic has no concern with particular truths. The logician is concerned only with

relations between propositions, not with their actual truth-values.

Further examples

The examples so far of valid arguments have all been of the same type or form. Here

are some further, still quite simple, types of valid arguments. The examples are all ﬁctional.

Their being ﬁctional helps us to realise that the actual truth-values of premises and con-

clusions are usually irrelevant to determining whether or not arguments are valid:

P1) No Zormons are ticklish.

P2) Trozak is a Zormon.

C Trozak is not ticklish.

P1) Either Trozak is on Mars, or he is on Venus.

P2) Trozak is not on Mars.

C Trozak is on Venus.

logic: deductive validity66

P1) It is not possible to visit Mars and Venus in same day.

C If Trozak visited Mars today, then he did not visit Venus today.

P1) If Ichnik is ticklish, then Zadon is ticklish.

P2) If Trozak is ticklish, then Ichnik is ticklish.

P3) Trozak is ticklish.

C Zadon is ticklish.

P1) If Trozak is on Mars, he will visit Ichnik.

P2) Trozak is on Mars.

C Trozak will visit Ichnik.

P1) If Trozak ate all the biscuits, then the biscuit tin is empty.

P2) The biscuit tin is not empty.

C Trozak did not eat all the biscuits.

PRESCRIPTIVE CLAIMS VS DESCRIPTIVE CLAIMS

It is normal to try to distinguish fact-stating descriptive claims from claims which state or

express desires, values, norms or moral rules, which we shall call prescriptive claims. Here

are a few examples of each:

Descriptive

The cat is on the mat.

Jupiter is larger than Saturn.

2 + 2 = 4.

If Susie is late, then she will miss dinner.

There are some otters in the river.

Prescriptive

It is wrong to keep Rover on a chain all day.

You ought to allow John to attend the party.

Freedom is a basic value.

I want a pretzel.

The US needs a different health care system.

How exactly to formulate this distinction is a difﬁcult and contentious matter. But happily

for you, it is not necessary to do so. In Chapter 1, we said that a proposition is simply the

meaning of declarative sentence (as uttered in a given context). And in our discussion of

logic: deductive validity 67

truth in this chapter, we said that to claim that a proposition is true is the same thing as

agreeing with it, in the sense that, for example, ‘That’s true’ said in response to ‘Fish live in

water’ is the same as afﬁrming that ﬁsh live in water. It follows that the distinction

between descriptive and prescriptive claims is not to be made out in terms of truth. If

someone, for example, says that the US needs a different health care system, and you agree,

then you can say that it’s true; if you don’t agree, then you can say that it’s false.

In other words, descriptive and prescriptive claims are equally susceptible to being called

‘true’ and ‘false’. This is not because we assume a rampant objectivism about prescriptive

claims, or that we fail to recognise their difference from descriptive claims; it is just a

‘shallow’ consequence of the practical position we take as regards truth. For the purposes

of reconstruction and assessment of arguments, it is by far the simplest and easiest line to

take. It means, among other things, that our concept of validity can be applied across the

board, to all arguments irrespective of subject-matter.

CONDITIONAL PROPOSITIONS

This is a good point at which to distinguish arguments from a certain kind of statement,

which both logicians and grammarians call the conditional. Conditionals are most charac-

teristically expressed using the ‘if–then’ form of declarative sentences. For example:

If it is raining, then it is cloudy.

Conditionals can also be expressed in other ways, however. In fact, all of the following

statements express the very same proposition as the example just given; they represent

exactly the same connection between rain and clouds:

•It is raining only if it is cloudy.

•Either it is cloudy, or it is not raining.

•It is not raining unless it is cloudy.

•If it is not cloudy, then it is not raining.

•It is not raining if it is not cloudy.

•It is cloudy if it is raining.

At ﬁrst, it may not be obvious that each of these is equivalent to ‘If it is raining, then it is

cloudy’. So let us stop to consider the ones that people most often ﬁnd puzzling. Hence-

forth, for convenience, we shall adopt the device of substituting the letters ‘P’ and ‘Q’ for

arbitrary declarative sentences.

I. ‘If not . . . then not . . .’ If it is raining then it is cloudy; there is no rain without clouds.

Therefore, if it is not raining, then it is not cloudy. So if we have ‘If P then Q’, we also have

‘If not-Q then not-P’. But we can also go the other way, from ‘If not-Q then not-P’ to ‘If P

then Q’. You can see this by thinking about the rain example, but take another. The

detective says, ‘If there is no mud on Smith’s shoes, then Smith is not the murderer’. The

logic: deductive validity68

detective is not saying that if there is mud on Smith’s shoes, then Smith is the murderer.

What he is saying is that if Smith is the murderer, then there is mud on his shoes. So saying

‘If not-Q then not-P’ is equivalent to saying ‘If P then Q’.

II. ‘Either–or’. Usually, when two statements are joined by ‘either–or’, or just by ‘or’, to

form a compound statement, the compound is equivalent to a statement using ‘if–then’,

and vice versa. But to pass from the version using ‘or’ to the version using ‘if–then’, or vice

versa, we have to insert the word ‘not’. For example, the following pairs of statements are

equivalent:

Rangers will win the league or Celtic will win the league.

If Rangers do not win the league then Celtic will win the league.

Either Jane will practise diligently or she will fail her exam.

If Jane does not practise diligently then she will fail her exam.

A complication is that the word ‘or’ is used in either of two ways, known as the ‘inclusive’

and ‘exclusive’ sense. In the inclusive sense, ‘P or Q’ means that either P is true, or Q is

true, or they are both true; so the compound sentence is false only if both P and Q are false.

This is the sense intended if one says something like ‘He will lose if either he doesn’t serve

well or he doesn’t return serves well’. In the exclusive sense, ‘P or Q’ means that either P is

true or Q is true, but not both. This is the sense normally intended if one says something

like ‘Either you go to bed now or I will not read you a story’ (the child would rightly feel

cheated if he or she goes to bed immediately but doesn’t get a story).

A conditional statement ‘If P then Q’ is equivalent only to ‘Either not-P or Q’ only in the

inclusive sense of ‘or’. Where it is clear that the exclusive sense is intended, the

reconstructed argument should contain conditionals running in both directions. A

sentence such as ‘Either the murder took place here or there was an accident here’,

intended in the exclusive sense, would be represented as ‘If no accident took place here

then the murder took place here’ and ‘If an accident took place here then the murder did

not take place here’.

III. ‘Only if’. This one is trickier. It should be clear that the following are equivalent, in the

sense that they state the same relationship between rain and clouds:

•It is raining only if it is cloudy.

•If it is raining then it is cloudy.

In the ﬁrst, the word ‘if’ precedes the bit about clouds rather than the bit about the rain.

It says: ‘It is raining only on condition that it is cloudy.’ Thus if it is raining, then that

condition must be fulﬁlled – so it must be cloudy. Note that it would be false to put it the

other way round; it would be false to say: ‘It is cloudy only if it is raining.’ For the very

logic: deductive validity 69

same reason, it would false to say: ‘If it is cloudy, then it is raining.’ What makes these false

is that sometimes it is cloudy but not raining.

Take another, more real-life sort of example. Someone says: ‘Jane is coming to the party

only if Joe is.’ Suppose that’s true. Then if Jane is coming to the party, then Joe is coming to

the party also. Note further that someone who says, ‘Jane is coming to the party only if Joe

is’ is not committed to ‘If Joe is coming to the party then Jane is coming to the party’.

Perhaps Jane won’t come to the party without Joe being there, but might not come even if

Joe does.

We can express this last point by saying that ‘P only if Q’ makes the same assertion as ‘If P

then Q’, but does not logically commit one to ‘If Q then P’. What makes this difﬁcult to

appreciate is that in some cases ‘P only if Q’ implicates ‘If Q then P’ in the sense explained

in Chapter 1 (pp. 10–11). For example, suppose a parent says: ‘You’ll get ice cream only if

you ﬁnish your peas.’ This tells the child that if he does not ﬁnish his peas he won’t get ice

cream. And unless the parent is being mean, the child rightly assumes that if he eats his

peas, he will get ice cream. Still, the parent’s announcement does not actually assert ‘If you

ﬁnish your peas, you’ll get ice cream’. We know this because, if it did, then we would have

to say that to assert ‘It is raining only if it is cloudy’ is also to assert ‘If it is cloudy then it is

raining’, which it certainly is not. The reason that things seem otherwise in the ice-cream

case is that the parent’s announcement, though it does not assert that the child will get ice

cream if he eats his peas, implicates it.

Finally, care should be taken not to confuse ‘only if’ with another device: ‘if and only if’. To

say ‘P if and only if Q’ is to say ‘P if Q’ and ‘P only if Q’. ‘P if Q’ means the same as ‘If Q

then P’. According to what we have said about ‘only if’, ‘P only if Q’ means the same as ‘If

P then Q’. Therefore: ‘P if and only if Q’ means the same as ‘If P then Q, and if Q then P’. It

means ‘Either both P and Q, or neither’. So, for example, ‘It is raining if and only if it is

cloudy’ is false. On the other hand, if we wanted to say that Jane will not come to the party

without Joe, but will deﬁnitely come if he does come, we could say ‘Jane will come to the

party if and only if Joe comes to the party’.

IV.‘Unless’. Begin with these, each of which, again, states the same relationship between

rain and clouds:

•It is not raining unless it is cloudy.

•If it is raining then it is cloudy.

‘Unless’ is confusing in many of the same ways that ‘only if’ is confusing. For example,

someone says, ‘That plant will grow well unless it gets whiteﬂy’. Are they saying ‘If the

plant doesn’t get whiteﬂy it will grow well’, or ‘If the plant gets whiteﬂy it will not grow

well’? Look again at the example about rain and clouds. What it tells us is that ‘not-P unless

Q’ is equivalent to ‘If P then Q’. The transition from the ‘unless’ form to the ‘if–then’ form

can be represented as follows. Begin with ‘unless’:

Not-P unless Q. (It is not raining unless it is cloudy.)

logic: deductive validity70

Replace ‘unless’ with ‘if not’:

Not-P if not-Q. (It is not raining if it is not cloudy.)

This is clearly just another way of saying:

If not-Q then not-P. (If it is not cloudy then it is not raining.)

But according to what we said above (under I), this is equivalent to:

If P then Q. (If it is raining then it is cloudy.)

In other words, the trick for dealing with ‘unless’ is to think of it as meaning ‘if not’: ‘P

unless Q’ means ‘P if not Q’, which is the same as ‘If not-Q then P’. Therefore, the

statement ‘That plant will grow well unless it gets whiteﬂy’ means ‘If that plant doesn’t

get whiteﬂy then it will grow well’. It does not mean ‘If that plant gets whiteﬂy then it will

not grow well’. Similarly, ‘You will fail unless you study’ means ‘If you don’t study then

you will fail’, but not ‘If you study, then you will not fail’. On the other hand, ‘You will not

fail unless you don’t study’ means ‘If you do study then you will not fail’.

THE ANTECEDENT AND CONSEQUENT OF

A CONDITIONAL

In general, a conditional is a compound proposition consisting of two parts, each of which

is itself a proposition, where these two parts are joined by some connecting words (they

are called ‘logical connectives’) such as ‘if–then’, ‘either–or’, ‘unless’, or ‘only–if’, or some-

thing similar. However they are joined, what a conditional says is that the truth of one

proposition ensures that of another. In formal logic this relation is represented by a single

device, usually an arrow:

It is raining → It is cloudy.

P → Q.

The one from which the arrow points is called the antecedent; the one to which the arrow

points is called the consequent, for obvious reasons. We will use this terminology a lot, so

you should memorise it.

Now, here is a tricky and important point. In one way or another, the examples on p. 68

express the very same conditional proposition about rain and clouds. They express the

same relation between rain and clouds. Thus the antecedent and consequent in all those

examples is the same – in all of them, the logical antecedent is the proposition that it is

raining, and the logical consequent is the proposition that it is cloudy. In this sense, the fact

logic: deductive validity 71

that one proposition is the antecedent and another the consequent of a conditional state-

ment is a matter of the logic of the statements. It is not a matter of the grammar of the

sentences. It does not matter in what order, in the whole sentence, the two smaller

sentences occur; what matters is the logical relationship asserted by the sentence. You can

see this from the fact that in the sentences at the beginning of this section relating rain to

clouds, the bit about rain sometimes occurs before the bit about clouds and sometimes

occurs after it.

Conditionals vs arguments

Our example of a conditional is a true statement. Some conditionals are false, such as ‘If

it is cloudy, then it is raining’ (since, sometimes, it is cloudy but it is not raining).4

A conditional is said to be true or false, rather than valid or invalid. For a conditional is not

itself an argument. A conditional is one proposition that comprises two propositions as

parts, joined by ‘if–then’ or a similar device. An argument cannot be just one proposition.

It needs at least two.

The following, however, would be an argument:

It is raining. Therefore, it is cloudy.

This is not a conditional, but an argument composed of two propositions. Moreover, this

argument actually asserts that it is raining, and also that it is cloudy. A person giving it

would actually be asserting those things. Not so for the corresponding conditional: to say

‘If it is raining then it is cloudy’ is not itself to assert that it is raining, or that it is cloudy.

People sometimes make a mistake on this point; we sometimes witness conversations like

this:

Mary: If Edna gets drunk, then her graduation party will be a mess.

Jane: Why do you say Edna’s going to get drunk? You’re always so unfair to her.

Mary: I didn’t say Edna is going to get drunk, I said if Edna gets drunk...

Jane: Well, it’s the same thing!

Mary: No, it isn’t!

Jane: Don’t try to get out of it! You always think the worst of Edna, and you’re

always trying to take back what you say!

What Jane seems not to understand is that a conditional does not assert either its ante-

cedent or its consequent. An argument asserts its premises and its conclusion, but Mary is

not arguing that the party is going to be a mess; she is only saying that it will be if Edna gets

drunk (presumably because she thinks Edna misbehaves when she drinks too much).

4 Strictly, we should say that whereas all utterances of ‘If it is raining then it is cloudy’ are true, some utterances

of ‘If is cloudy then it is raining’ are false. This is a case of implicit indexicality, which we’ll discuss further in

Chapter 8.

logic: deductive validity72

Strictly speaking, she is not even saying that Edna is likely to get drunk. Of course, she

would not have brought the whole thing up if she did not think there was some danger of

Edna’s getting drunk. The grain of truth in Jane’s reaction is that the assertion of a

conditional often implicates that there is some probability that the antecedent of the

conditional is or will be true (on conversational implicature see Chapter 1, pp. 10–11).

Even so, Mary might well think this probability to be less than ﬁfty–ﬁfty, and she did not

say that Edna’s going to get drunk.

Finally, it is important to recognise that many arguments have conditional conclusions –

that is, conclusions which are themselves conditionals. For example:

P1) If Labour does not change its platform, it will not attract new supporters.

P2) If Labour does not attract new supporters, it will lose the next election.

C) If Labour does not change its platform, then it will lose the next election.

Here both premises as well as the conclusion are conditionals. This particular pattern is

very common, and is called a ‘chain’ argument. A chain of conditionals is set up, like a row

of dominoes. What the argument is saying is that if the antecedent of P1 comes true, then

the consequent of P2 is true. Chain arguments can have any number of links. One of the

‘Further examples’ earlier in this chapter (p. 67) involved a chain; the evaluation of such

arguments will be discussed in Chapter 6.

ARGUMENT TREES

An argument tree is a device that can be used for representing arguments in the form of a

diagram. They are helpful when we are reconstructing arguments, particularly complex

ones, because they provide a means of showing the ways in which the different parts of an

argument are related to each other. They show how the premises support the conclusion.

Constructing argument trees is a very valuable tool and you will ﬁnd it helpful to use them

in your own analyses of real-world arguments.

The process of constructing an argument tree is especially useful before you have supplied

missing premises, and before you have settled upon a reconstruction of the argument in

standard form. In fact, it can be useful to construct an argument tree at almost any stage in

the reconstruction, including when the reconstruction is complete, simply as a way of

illustrating the structure of the argument, of making it clear to oneself and to others.

But to illustrate, we stick to arguments already in standard form. Consider the following

simple arguments:

AP1) Susan is a marathon runner.

P2) Susan eats well and sleeps well.

C) Susan is healthy.

logic: deductive validity 73

BP1) Willy is in the music club.

P2) No member of the music club plays jazz.

C) Willy does not play jazz.

These arguments both infer a conclusion from two premises, but there is an important

difference.

In argument A, each premise supports the conclusion individually. That is, P1 is cited as a

reason for C, and P2 is cited as another reason for C. One could argue from P1 alone to C;

one could also argue from P2 alone to C. By contrast, in argument B, neither premise

supports C by itself. Neither P1 nor P2 would, by itself, be a reason to accept C. Rather,

they work together to support C. This is always the case when one premise is a conditional

and another is the antecedent of that same conditional.

Argument A is represented as in Figure 3.1 and argument B is represented as in Figure 3.2.

Figure 3.1

Figure 3.2

logic: deductive validity74

Now these examples are very simple. Argument trees are especially helpful when used to

represent more complicated arguments with intermediate conclusions. For example:

P1) Consumption is increasing.

P2) The pound is weakening against other currencies.

C1) Inﬂation will increase.

P3) Whenever inﬂation increases, mortgage rates rise.

C2) Mortgage rates will rise.

P4) Whenever mortgage rates rise, the building trade suffers.

C3) The building trade will suffer.

The correct argument tree for this is shown in Figure 3.3. Note that the ﬁrst sub-argument

is not valid as it stands. P1 and P2 may be said to support C1, but only by virtue of a

Figure 3.3

logic: deductive validity 75

relation that is not explicitly stated between consumption rates, the relative strength of

currencies and inﬂation. Thus the argument does not explicitly include what later in the

book we will call its ‘connecting’ premise or premises. The most plausible connecting

premise would be of the form, ‘If P1 and P2, then C1’. We had the same sort of situation

in the argument about Susan the marathon runner. The connecting premise was left

implicit. A plausible connecting premise, in this case, might be something like:

P3) No marathon runner who eats and sleeps well is not healthy.

If we do it this way, then the three premises work together to support the conclusion; an

instance of this generalisation would be: ‘If P1 and P2, then Susan is healthy.’ So the

argument would be represented as shown in Figure 3.4.

DEDUCTIVE SOUNDNESS

Normally, you assess an argument because you wonder whether or not the conclusion is

true. You want to know whether the arguer has given you a reason for thinking that

the conclusion is true. If you ﬁnd that the argument is invalid, then you know that even

if the premises are true, the conclusion could be false. Therefore, the reasons given by the

arguer – the premises – do not sufﬁce to establish the conclusion, even if they are true.

But suppose you ﬁnd that the argument is valid. Then there are two possibilities:

(A) One or more of the premises are (actually) false.

(B) All of the premises are (actually) true.

Now, as illustrated by examples 2 and 5 on p. 65, knowing that the argument is valid is

not enough to show you that the conclusion is true. In order to determine that, you need

a further step: you must determine the truth-values of the premises. You might already

know them. But if you don’t, then of course, logic is no help. If one of the premises is that

Figure 3.4

logic: deductive validity76

the octopus is a ﬁsh, then unless you know already, you have to consult a book or ask an

ichthyologist. Suppose now that you have done this, and what you have is a case of (A),

i.e. one (or more) of the premises is false. In that case, you can draw no conclusion as to

the truth-value of the conclusion (as illustrated by arguments 4 and 5 on p. 65, a valid

argument with one or more false premises may have either a true or a false conclusion).

But now suppose you ﬁnd the argument to be a case of (B) – that is, you have found it to

be a valid argument with true premises. Eureka! For, according to the deﬁnition of validity,

a valid argument with true premises cannot have a false conclusion. So the conclusion must

be true. The argument has accomplished its purpose; it has demonstrated its conclusion

to be true. We call this a deductively sound argument. Argument 1 above about Janet

Baker, for example, is a deductively sound argument:

To say that an argument is deductively sound is to say: The argument is valid, and

all its premises are (actually) true.

This reveals the importance of the concept of validity. Given the deﬁnition of validity, it

follows from the deﬁnition of deductive soundness that the conclusion of a deductively

sound argument must be true. Thus, there cannot be a deductively sound argument with a

false conclusion.

An argument that is not deductively sound – one which has one or more false premises, or

is invalid, or both – is said to be deductively unsound. Deductive soundness, like validity,

pertains to whole arguments, and not to single propositions.

It is important to recognise what follows if you happen to know that the conclusion of an

argument is not true. Suppose someone gives you an argument, the conclusion of which

is that there are platypuses at the local zoo. And suppose you know that this is not true.

You know that the local zoo has no platypuses. Therefore, you know that this argument

is not deductively sound. You should make it clear to yourself why this is so; check the

deﬁnitions again if this is not clear.

If you do know that there are no platypuses at the zoo, then you know it is possible to give

a deductively sound argument for that conclusion. But there cannot be deductively sound

arguments on both sides of the issue. For deductively sound arguments have true conclusions.

If there were deductively sound arguments on both sides of this issue, it would follow that

there are platypuses at the zoo, and also that there are not, which is impossible. This is

important to recognise, because frequently we do say that there can be ‘good’ arguments

on both sides of a given issue (especially a controversial one); we say this, perhaps, out of a

wish to show respect for different opinions, or simply to express our own indecision over

the issue. But in saying this, we cannot mean that there are deductively sound arguments on

both sides of an issue. Later, we will explain in exactly what sense there can be ‘good’

arguments on both sides of an issue (for, to be sure, there can be).

If we know that the conclusion of an argument is false, then we know that the argument

is deductively unsound. What follows from that? Look at the deﬁnition of deductive

logic: deductive validity 77

soundness. If the argument is deductively unsound, it follows that either the argument has

(at least) one false premise, or the argument is invalid (or perhaps both – perhaps it is

invalid and it has one or more false premises). Suppose then that you determine the

argument to be valid. Then you know that at least one premise must be false. On the other

hand, suppose that you ﬁnd that the argument is invalid. What can you conclude about

the truth-values of the premises? Nothing! For you know that an invalid argument with a

false conclusion may have either true premises or false premises.

THE CONNECTION TO FORMAL LOGIC

Occasionally in discussing logical points we have used ‘dummy’ letters to stand in place of

sentences. For example, we said that ‘P unless Q’ is equivalent to ‘If not-Q, then P’. The

letters ‘P’ and ‘Q’ were used to stand in place of arbitrary declarative sentences like ‘It is

raining’ or ‘The cat is on the mat’. We can do this because the point we wish to make does

not depend on what particular sentences we put for ‘P’ and ‘Q’. The point concerns only

the meanings or logical properties of such expressions as ‘unless’ and ‘if–then’, and it would

hold for any declarative sentences put for ‘P’ and ‘Q’.

Here is an example of a simple, valid argument form:

P1) If P then Q.

P2) P.

C) Q.

This inference is called modus ponens. This is one example of what is known as a valid

argument-form, sometimes called a valid argument schema. An instance of this form is given

on p. 67, the third example about Trozak: ‘If Trozak is on Mars, then he will visit Ichnik;

Trozak is on Mars; therefore Trozak will visit Ichnik.’ Others, together with their usual

names, include:

Modus tollens

P1) If P then Q.

P2) not-Q

C) not-P.

Disjunctive syllogism

P1) P or Q.

P2) not-P

C) Q

logic: deductive validity78

P1) P or Q

P2) not-Q

C) P

Chain

P1) If P then Q

P2) If Q then R

C) If P then R

The next step towards formal logic is to introduce surrogates for the logical expressions of

English that join sentences. We’ve already introduced ‘→’ for ‘if–then’ (sometimes ‘⊃’ is

used instead). Others include ‘∨’ for inclusive ‘or’, ‘∧’ (or ‘&’) for ‘and’, and ‘¬’ (or ‘∼’)

for ‘not’ or ‘it is not the case that’. We also require certain rules governing the use of

parentheses, so as to distinguish, for example,

P → (Q ∨ R)

from

(P → Q) ∨ R

The ﬁrst one says that if P is true, then either Q or R is true; the second one says that either

‘If P, then Q’ is true, or R is true. Such devices are all that is required for statement logic

or truth-functional logic.

But this is not the whole of formal logic. Again, the letters ‘P’ and ‘Q’ are placeholders for

whole sentences, not for expressions – ‘sub-sentential expressions’ – that do not

constitute sentences. Look now at the set of valid arguments about Janet Baker on

pp. 64–65. As we noted, they are all of the same form. We can display this form in the

following way:

P1) x is an F.

P2) All F are G.

C) x is a G.

This means that whatever name we put for ‘x’ – whether ‘Janet Baker’, ‘Mount Fuji’ or

‘Vienna’ – and whatever general terms we put for ‘F’ and ‘G’ – whether ‘soprano’, ‘volcano’

or ‘capital city’ – the resulting argument will be valid (so long as we always put the same

logic: deductive validity 79

name or general term for the same letter).5 The validity of the argument is independent of

the particular meanings of ‘Janet Baker’, ‘soprano’ and so on. Interestingly, you can readily

see that this is so: you can easily see that whatever ‘x’ is, and whatever is taken for ‘F’ and

‘G’, the argument-form will never have true premises and a false conclusion, i.e. that it

will be valid. In advance of studying formal logic, we already have a good eye for formal

validity.

Note that we used ‘F’ and ‘G’ for general terms, and ‘P’ and ‘Q’ for sentences (if more were

needed, we would use ‘H’, ‘I’ and so on for general terms, ‘R’, ‘S’ and so on for sentences).

We used lower-case letters in place of names. This is the usual practice in logic, but there is

no need for a strict rule in this context.

This is typical of what is known as formal logic: claims about logical relationships are made

most efﬁciently by abstracting from the particular subject-matter we talk about and con-

centrating on the logical forms of the arguments. However, logical forms are not completely

without content or meaning. In the ﬁrst example, what we are really focusing on is the

meaning of the word ‘All’; in the second, we are focusing on the meaning of the expression

‘if–then’. We don’t put in dummy letters for those. Accordingly, these words are often

known as ‘logical words’ or ‘logical particles’, and formal logic may appropriately be said to

concern itself with those. Other logical particles, in addition to those listed above, include

the quantiﬁers ‘(∀x) . . .’ for ‘everything is’ ‘(∃x) . . .’ for ‘something is’.

Representing the logical form of an argument by means of dummy letters can be very

useful for showing that an argument is invalid. For an argument-form is invalid if it has

what we call an ‘instance’ with true premises and a false conclusion. Thus consider invalid

argument number 7 on p. 65:

P1) Janet Baker is a woman. (T)

P2) All baritones are women. (F)

C) Janet Baker is a baritone. (F)

But suppose you weren’t sure about P2 and C. You could represent its logical form as the

following schema:

P1) x is an F.

P2) All G are F.

C) x is a G.

5 Of course this is to cut corners. Somewhat more exact: whatever denoting singular term is put for ‘x’, and

whatever indexical-free general terms are put for ‘F’ and ‘G’ – always putting the same singular term for the

same dummy letter – then, reading ‘is’ and ‘is an’ and ‘are’ as grammatical variants of the ‘is’ of predication, the

result is a valid argument of English. For an introduction to formal logic, see Goldfarb, Deductive Logic (Hackett,

2003) or Forbes, Modern Logic: A Text in Elementary Symbolic Logic (Oxford University Press, 1994).

logic: deductive validity80

Then put ‘Elton John’ for ‘x’, ‘human’ for ‘F’ and ‘women’ for ‘G’:

P1) Elton John is human. (T)

P2) All women are human. (T)

C) Elton John is a woman. (F)

Here you have an instance of this schema – that is, an argument with the same logical

form – that has true premises and a false conclusion, thereby proving that the logical form

of the original argument is invalid, and therefore that the original argument is itself

invalid. This technique is called ‘refutation by counterexample’; we will return to it in

Chapter 6.

There are sophisticated technical procedures for exploring formal logical relationships in a

systematic, detailed way. For the most part, it is necessary to invent artiﬁcial languages for

this purpose employing special symbols in place of the logical particles of English such as

the ‘→’ sign for the conditional ‘if–then’ we mentioned earlier. However, getting clear on

the exact meaning of the logical particles of English, and what is claimed when one writes a

fully symbolic sentence for one of English, prove to be somewhat contentious affairs. One

reason is that logical relationships in a ‘natural’ language such as English tend to be too

cumbersome and poorly deﬁned to represent clearly and systematically (look at all the

different ways of representing the conditional, when really only one way is needed!). By

contrast, the validity of arguments expressed in symbolic notation is determined by precise

rules, and the forms of the arguments are always exactly determined. Courses on ‘formal

logic’ – otherwise known as ‘mathematical logic’ or ‘symbolic logic’ – are taught in

Philosophy, Mathematics, Linguistics and Computer Science. In critical thinking we are

doing what you might call ‘practical logic’. We want to learn to identify the reasoning in

commonly encountered attempts to persuade us, and to assess it as good or bad. For this,

we need the concept of validity, but we do not need artiﬁcial symbols or elaborate

technical procedures for detecting validity with absolute precision. It’s better to leave in a

certain amount of slack. The reason is that the logic of the vast majority of arguments in

everyday life is rarely of any great complexity. Once we know what the argument is,

whether or not it is valid can almost always be seen by applying the deﬁnition given above.

Most of the work goes into the reconstruction. And as we have seen – and will see in more

detail later – we cannot proﬁtably reconstruct an argument without knowing what makes

a good argument, hence not without grasping the concept of validity.

Nevertheless, it will sometimes be useful to use ‘dummy’ letters as we have already done,

to draw attention to the forms of arguments and statements where appropriate.

CHAPTER SUMMARY

The aim of argument-reconstruction is to clarify, and make fully explicit, the argument

intended by an arguer. We do this by putting the argument into standard form. If

our main concern is whether or not the conclusion of the argument is true, then our

logic: deductive validity 81

reconstruction should be guided by the principle of charity: we should aim for the best

possible reconstruction of the argument.

In order to do this, we need precise concepts in terms of which to assess arguments. We

need, to begin with, the concepts of truth, deductive validity and deductive soundness. A

deductively valid argument (a valid argument, for short) is one whose premises could not

possibly be true without the conclusion being true also. A deductively sound argument is a

valid argument with true premises. It follows that a deductively sound argument must

have a true conclusion.

The conclusion of one argument may serve as a premise for another. We call such a

conclusion an intermediate conclusion for an extended argument.

A proposition is what is true or false, and is the meaning of a declarative sentence as used

in a given context. It follows that for our purposes, prescriptive statements – statements

of value, prescription and the like – are not fundamentally different from fact-stating or

descriptive statements on the score of susceptibility to agreement and disagreement, and

therefore of truth and falsity. The same methods of representation in standard form, and

the same concept of deductive validity, apply to each.

Individual propositions can be true or false, but not valid or invalid. Arguments can be

valid or invalid, but not true or false. Conditional propositions are not arguments, but

single propositions: a conditional proposition is a single proposition made up of two

propositions, the antecedent and consequent. Typically the antecedent and consequent of

a conditional proposition are joined by ‘if–then’, but many other devices can do the same

job. The crucial thing is the logical relationship between them.

Arguments do stand in a certain relationship to conditional propositions. If the argument

is valid, then this conditional proposition is true: if the argument’s premises are true, then

its conclusion is true.

It is sometimes useful to employ ‘dummy’ letters in place of sentences, names or general

terms in order to display the logical form of an argument; this is the ﬁrst step towards the

study of formal logic. From the formal point of view, the deﬁnition of validity is: an

argument is valid if (and only if ) its logical form is valid. A logical form is valid if (and only

if ) there is no instance of that form with true premises and a false conclusion (not even if

we are allowed to change the meanings of the non-logical expressions contained in an

instance). For our purposes the most useful implication of this is that if a given argument

has the same form as another argument with the same form, the given argument is invalid.

Showing invalidity in this way is called refutation by counterexample.

EXERCISES

1 Study the section that describes the principle of charity. Then, without looking at the

section again, and in your own words, write a short essay of about 250 words that

explains the principle, and why it should be observed.

logic: deductive validity82

2 Suppose that someone says: ‘The purpose of argument is to defeat the opponent.’

Write a short essay (about 250 words) commenting on this.

3 Again, without consulting the book, and in your own words, explain the purpose of

argument-reconstruction. Try to invoke some of the concepts you have learned in this

chapter, such as validity.

4 Suppose that Mr Smith argues as follows:

Mr Jones argues that the unemployment rate will rise this year. However, as we

have explained, Mr Jones’ argument is clearly invalid. Furthermore, we have

shown that the premises of the argument are false. Therefore, Mr Jones is

wrong. The unemployment rate will not rise this year.

Criticise Mr Smith’s argument.

5 Suppose that Bob says:

Sarah is so arrogant. She’s entitled to her opinions, of course. I don’t mind her

saying that landlords have an ancient right to prevent walkers’ access to their

property. That’s her opinion. But she has to say it’s true. I hate that. She always

thinks she’s right. She always thinks her opinion is the truth.

Does Bob have a point, or is he confused? Explain your answer an essay of about

150 words.

6 For each argument, decide whether or not it is deductively valid. If it is not valid,

brieﬂy explain why. Remember that being able to judge validity does not require any

familiarity with the particular subject-matter of the argument. If it seems useful, describe

a possible situation in which the premises are true, but the conclusion false.

Example

P1) Every Roman emperor before Constantine was a pagan.

P2) Julian was a Roman emperor.

C) Julian was a pagan.

✎Invalid. P2 says that Julian was a Roman emperor, but not that he ruled

before Constantine. It would be possible for the premises to be true but

the conclusion false, then, if Julian were a non-pagan Roman emperor

after Constantine.

P1) Either Jane is in the kitchen, or Mary is in the kitchen.a

P2) Jane is not in the kitchen.

C) Mary is in the kitchen.

logic: deductive validity 83

P1) Either inﬂation will increase, or personal debt will increase.b

P2) If the central bank does not increase interest rates, inﬂation will not

increase.

P3) The central bank will not increase interest rates.

C) Personal debt will increase.

P1) If the guerrillas have left the area, then there is trafﬁc on the roads.c

P2) There is no trafﬁc on the roads.

C) The guerrillas have not left the area.

P1) No member of the Green Party voted for the tax cut.d

P2) Mr Jacobs did not vote for the tax cut.

C) Mr Jacobs is a member of the Green Party.

P1) No member of the Green Party voted for the tax cut.e

P2) Mr Jacobs voted for the tax cut.

C) Mr Jacobs is not a member of the Green Party.

P1) Every member of the Conservative Party voted for the tax cut.f

P2) Mr Winterbottom voted for the tax cut.

C) Mr Winterbottom is a member of the Conservative Party.

P1) Some members of the Liberal Party voted for the tax cut.g

P2) Some who voted for the tax cut voted for new defence spending.

C) Some members of the Liberal Party voted for new defence

spending.

P1) If abortion is morally permissible, then infanticide is morally permissible.h

C) Abortion is not morally permissible.

P1) If abortion is not murder, then infanticide is not murder.i

P2) If infanticide is not murder, then killing innocent children is not murder.

P3) Killing innocent children is murder.

C) Abortion is murder.

P1) If each person has the right to determine what happens to his or her ownj

body, then suicide should be legal.

P2) Suicide should not be legal.

C) No person has the right to determine what happens to his or her own

body.

logic: deductive validity84

P1) Every regime is either corrupt or inefﬁcient.k

P2) The Soviet regime was inefﬁcient.

C) The Soviet regime was not corrupt.

P1) If there is no blown resistor, then there is failed connection.l

P2) There is a blown resistor.

C) There is no failed connection.

P1) Constantine ruled Rome before Constantius.m

P2) Constantius ruled Rome before Julian.

C) Constantine ruled Rome before Julian.

P1) Only democracies are just political systems.n

P2) Rome’s political system was unjust.

C) Rome’s political system was not a democracy.

P1) The only just political systems are democracies.o

P2) Rome’s political system was unjust.

C) Rome’s political system was not a democracy.

P1) Unless some historians have told lies, there were miracles during the ﬁrstp

century.

P2) There were no miracles during the ﬁrst century.

C) Some historians have told lies.

P1) Analysis has shown that Mr Cleever’s accident was caused by faultyq

brakes, not by drunk driving.

P2) If Mr Cleever was not drunk at the time of the accident, then he should be

acquitted of drunk driving.

C) Mr Cleever should be acquitted of drunk driving.

P1) If Constantius’ professed Christianity was genuine, then history hasr

represented him unfairly.

P2) There is no convincing evidence that Constantius’ professed Christianity

was not genuine.

C) History has represented Constantius unfairly.

logic: deductive validity 85

P1) If Germanicus had not died at the German front, he would have becomes

emperor.

P2) If Germanicus had become emperor, then Tiberius would not have

become emperor.

P3) If Tiberius had not become emperor, then Caligula would not have

become emperor.

P4) If Caligula had not become emperor, then he would not have been

murdered.

P5) If Caligula had not been murdered, then Claudius would not have become

emperor.

C) If Germanicus had not died at the German front, then Claudius would

not have become emperor.

P1) If any Roman emperor was wise, then Marcus Aurelius was wise.t

P2) Augustus was a Roman emperor.

P3) If Augustus was wise, then Marcus Aurelius was not wise.

C) Marcus Aurelius was wise.

P1) If any Roman emperor was wise, then Marcus Aurelius was wise.u

P2) Augustus was a Roman emperor.

P3) If Augustus was wise, then Marcus Aurelius was not wise.

C) Augustus was not wise.

P1) If John or Susan are late, then Mary will be disappointed.v

P2) John is late.

P3) Susan is late.

C) Mary will be disappointed.

P1) If John and Susan are late, then Mary will be disappointed.w

P2) John is late.

C) Mary will be disappointed.

P1) If John and Susan are late, then Mary will be disappointed.x

P2) John is late.

P3) Susan is not late.

C) Mary will not be disappointed.

P1) If John and Susan are married, then Mary will be disappointed.y

P2) John is married.

P3) Susan is married.

C) Mary will be disappointed.

logic: deductive validity86

P1) If the Prime Minister does what the opinion polls say the people want, thenz

he is cowardly.

P2) If the Prime Minister does not do what the opinion polls say the people

want, then he is arrogant.

C) If the Prime Minister is not arrogant, then he is cowardly.

7 Which of the following statements are true, and which false?

a It is impossible for all the premises of a valid argument to be false.

b It is possible for the conclusion of a valid argument to be false.

c It is possible for a deductively sound argument to have a false conclusion.

d A valid argument cannot have all true premises and a false conclusion.

e A valid argument cannot have all false premises and a true conclusion.

f It is impossible for all the premises of a valid argument to be true, if the

conclusion is false.

g A valid argument must have true premises.

h If the conclusion of a valid argument is false, then all the premises must be

false.

i If an argument has more than one premise, then if one of the premises is

true, then the others must also be true.

j If a valid argument is sound, then one of its premises must be false.

k A sound argument cannot have a false premise.

l An argument cannot be both valid and sound.

m If an argument has true premises and a true conclusion, then it is valid.

n If an argument does not have all true premises and a false conclusion, then it

is valid.

o An argument may have all true premises and a false conclusion.

p If a valid argument has a false conclusion, then all its premises must be false.

q If a valid argument has a false conclusion, the at least one of its premises

must be false.

8 In Exercise 7, a–f, various scenarios are said to be possible or impossible. In cases

where the thing is possible, give an example.

9 Rewrite the following sentences using ‘if–then’ and ‘not’, in order to express

the same relation between propositions (and do not use the expression ‘only if’).

Sometimes you may have to remove, rather than insert, a ‘not’.

a Either Trajan was great or Hadrian was great.

b Dogs are loyal to their masters unless they are mistreated.

c Unless there were no benevolent emperors, Marcus Aurelius was a benevo-

lent emperor.

d You will not pass unless you study.

e My dog will get the ball unless your dog gets the ball.

f You will be admitted only if you are wearing a tie.

logic: deductive validity 87

g You will not be admitted if you are not wearing a tie.

h My dog barks only if your dog barks.

i You will pass only if you do not drink every night.

j You will pass only if you study.

k You will only pass if you study.

l The champion will win only if he ﬁghts aggressively.

m Either your dog will get the ball or mine will, unless the ball goes in the

water.

n Galerius and Maximin were not both admired in Rome.

10 Can there be more than one deductively sound argument for the same conclusion? If

so, give an example. If not, explain why not.

11 Consider the following two sentences:

Lee Harvey Oswald murdered John Kennedy.

Lee Harvey Oswald did not murder John Kennedy.

Suppose we have two arguments, one with the ﬁrst as conclusion and the other with

second as conclusion. Could both arguments be valid? Could both arguments be

deductively sound? Why or why not?

12 Using the ‘dummy’ letters ‘P’, ‘Q’, ‘R’ and so on to stand in for sentences such as

‘Your dog barks’ and ‘Trajan was great’, rewrite the sentences in Exercise 9. Then

rewrite your answers in the same way, writing them next to the corresponding

original sentence.

Example

Either Trajan was great or Hadrian was great.

✎Either P or Q. If not-P, then Q.

13 Using the ‘dummy’ letters ‘P’, ‘Q’ and ‘R’ and so on for whole sentences, ‘F’ and ‘G’

for general terms, and ‘x’ and ‘y’ for names, try to construct argument-forms corres-

ponding to the following problems in Exercise 6, a, b, f–j, p–w.

Example

P1) Only fools are drug-users.

P2) Ross Lambeau is a drug-user.

C) Ross Lambeau is a fool.

✎P1) Only F are G.

P2) x is a G.

C)x is an F.

14 Draw tree diagrams for the ‘Further examples’, pp. 66–67. Consider the diagrams for

arguments with two premises. What do they have in common? Can you explain why?

logic: deductive validity88

logic: inductive

force

•Inductive force 90

Probability

•‘All’, ‘most’ and ‘some’98

•Soft generalisations: a reminder 99

•Inductive soundness 100

•Probability in the premises 100

•Arguments with multiple probabilistic premises 101

•Inductive force in extended arguments 104

•Conditional probability in the conclusion 105

•Evidence 105

•Inductive inferences 107

How representative is the sample?

•A programme for assessment 112

•Chapter summary 113

•Exercises 114

INDUCTIVE FORCE

Consider this argument:

P1) Fiona lives in Inverness, Scotland.

C) Fiona owns at least one item of woollen clothing.

Is this argument valid? You might think so. Inverness is a pretty cold place. And wool is

plentiful: Scotland has millions of sheep. So surely you may conclude that Fiona must have

a woollen jumper or two. Nevertheless, the argument is clearly invalid: it would not be

impossible for someone to live in Inverness, yet not have any woollen items of clothing.

Indeed, there probably are people there without any (some people are allergic to wool, for

example).

We could make the argument valid by adding the premise, ‘Everyone in Inverness owns at

least one woollen item of clothing’. Thus:

P1) Fiona lives in Inverness, Scotland.

P2) Everyone who lives in Inverness, Scotland, owns at least one woollen item of

clothing.

C) Fiona owns at least one woollen item of clothing.

But this argument, though valid, is probably not sound, since P2 is probably false. Yet the

original argument is surely a good argument, in some sense. The truth of the premise

would be a good reason for expecting the conclusion to be true; it would be surprising to

ﬁnd it was false. Certainly if you had to bet on whether or not the conclusion is true, then,

given no relevant information except for P1, you would bet that it is true, not that it is

false. It would be reasonable to infer the truth of C from P1, and unreasonable to infer

its falsity.

However, we must notice something very important about the inference from P1 to C.

A critical thinker might not be in a position to recognise the forcefulness of this argument

as we have written it so far. For in order to recognise it, one has to know certain facts about

Inverness – the facts that make it different from, say, a hot place around which they grow

cotton such as Cairo. Someone giving the argument is implicitly relying on a proposition

that is similar to P2 in the argument given directly above, but that is much more likely to

be true – namely, that the vast majority of people in Inverness own some items of woollen

clothing. Almost no one owns none. That is to say, the use of the quantiﬁer ‘everyone’

would be inappropriate here, but use of the weaker quantiﬁer ‘almost everyone’ is

appropriate. Given what we know about Inverness, we can be almost completely certain

that almost everyone in Inverness owns at least one woollen item of clothing. (Recall from

Chapter 2 that expressions such as ‘most’, ‘almost all’ and ‘few’ are called ‘quantiﬁers’.) We

can represent the argument, then, as follows:

logic: inductive force90

P1) Fiona lives in Inverness, Scotland.

P2) Almost everyone in Inverness, Scotland, owns at least one item of woollen

clothing.

C) Fiona owns at least one woollen item of clothing.

This argument is still not deductively valid, since Fiona still might conceivably be one of

those few who do not have any woollen clothing. Still, these premises, just by themselves,

do provide a good reason for accepting the conclusion; the critical thinker, knowing noth-

ing about the matter except the truth of P1 and P2, could happily accept that if the

premises are true, then, probably, so is C. We recognise this by calling such an argument

inductively forceful (the word ‘inductively’ is meant to contrast with ‘deductively’), and

inserting the word ‘probably’ before the conclusion:1

P1) Fiona lives in Inverness, Scotland.

P2) Almost everyone in Inverness, Scotland, owns at least one item of woollen

clothing.

C) Probably, Fiona owns at least one woollen item of clothing.

When judging the inductive force of an argument, the way to think of the word ‘probably’

is not to regard it as part of the conclusion. Like the words ‘therefore’ and ‘so’, think of

it as an indication to the reader that the argument has been judged, by the person doing

the reconstruction, to be inductively forceful. If we were to remove it from the

above reconstruction, the inductive force of the argument, and its status as not being

deductively valid, would be unaffected. Roughly, then, an inductively forceful argument is

one that is not deductively valid – the truth of the premises would not ensure the truth

of the conclusion – but whose premises provide good reason to expect the conclusion

to be true rather than false. Before we characterise the concept of inductive force more

accurately, however, it will be useful to look brieﬂy at the closely related concept of

probability.

Probability

We typically express the probability that a given proposition is true (or that a given event

has occurred or will occur) on a numerical scale between 0 and 1, expressed either as a

decimal or as a fraction. For example, the probability that a tossed coin will land heads up

1 Inductive force is often called inductive strength, and sometimes inductive cogency or simply cogency. It is also

common to speak of the degree of support provided by the premises for the conclusion. The term ‘inductive

validity’ is used by some writers and might have been expected, but it is not usual. The reason is that if

‘inductively valid’ is used, then ‘valid’ becomes ambiguous between the inductive and deductive variety, thus

spoiling the entrenched and convenient practice of using ‘valid’ as short for ‘deductively valid’.

logic: inductive force 91

is 0.5 or 1/2. Perhaps surprisingly, there are different ways in which to explain probability.

We will brieﬂy consider three: proportion, frequency and rational expectation.2

First, proportion. Many arguments contain a premise that says something like ‘Most X are

Y’ or ‘7/8 of Xs are Ys’. Such quantiﬁers as ‘most’ and ‘7/8 of’ indicate proportions, and are

importantly related to probability. Suppose you want to know the probability that the

card you have drawn from an ordinary, complete deck of playing cards is an ace. One way

to do this would be to assume that this probability is equal to the proportion of aces in the

deck to the total number of cards in the deck. Since this ﬁgure is 1/13 (there are four aces

and ﬁfty-two cards, and 4/52 =1/13), you assume that probability that you’ll draw an ace

is 1/13 (about 0.077).

Now frequency. Suppose you want to know the probability that it is going to snow in

December in London, when December is still several months away. One simple way to do

this would be ﬁnd out how frequently this has actually happened over the past – say, one

hundred years. Suppose you ﬁnd that, out of the past one hundred Decembers, it has

snowed during fourteen of them. Then you might infer that the probability that it will

snow in London this coming December is 14/100 (0.14).

These strategies are extremely important in the general theory of probability and statistics,

but they are not sufﬁciently general for our purposes. There seem to be cases for which

neither proportion nor frequency will serve as a direct indicator of probability. For

example, bookmakers sometimes give odds that a given politician will become the

next leader of his or her party. Suppose they say that the odds of Mr X becoming the next

leader of the Labour Party are 1:1 (i.e. the probability is 1/2). Estimates such as these are

often perfectly reasonable. But clearly the bookmaker, in this case, is not basing the

probability on the frequency with which Mr X has become leader of the Labour Party in

the past; that frequency is zero! Probability-estimates of this kind are sometimes quite

reasonable, but there is no immediate and simple recipe for basing them upon frequencies

or proportions.3 In such cases, we cannot simply convert a proportion or a frequency into a

probability.

2 Another common basis for probability-estimates is the use of models. For example, if an engineer wants to

estimate the probability that a new aeroplane design will be stable at very high speeds, he or she might build a

real or computer model and test it under simulated conditions; if the model is stable under the simulated

conditions, then the engineer might infer that the actual aeroplane is likely to be stable under actual conditions.

3 This is not to say that such estimates cannot be based upon proportions or frequencies. In fact, they typically

are: it is precisely the task of those whose profession is to estimate probabilities (in the insurance industry, for

example) to base the estimates upon relevant proportions, frequencies and other data. More generally, to say

that a degree of expectation is rational, it seems, is precisely to say that some such statistical facts are available in

terms of which the expectation can be justiﬁed. However, such justiﬁcations often turn out to be extremely

complex, and in many cases we seem to know that probability-estimates are well-founded even when we are

unable to explain them adequately. Since degree of rational expectation is arguably the most inclusive or general

characterisation of probability, our strategy here is to proceed without requiring that probability-claims always

be justiﬁed in terms of statistics. The science of such justiﬁcations – taught in courses in Statistics and

Probability Theory – is extremely interesting and of ever-increasing importance.

logic: inductive force92

Because of these complications, we shall take degree of rational expectation as our

general concept of probability.4 A person’s degree of rational expectation in a given

proposition is the degree to which he or she is entitled to believe it, given the evidence

he or she has. Besides the fact that this concept of probability is more widely applicable

than others, it has the further advantage that it corresponds to the way that the

word ‘probably’ is typically used: when we say, ‘That’s probably true’, we typically mean

that our total sum of evidence makes it reasonable to expect the proposition in question

to be true.

This can best be appreciated by thinking again of something like cards. Suppose George

has a card face down on the table before him; he doesn’t know what it is, but he has been

correctly informed that it is red. Since George knows that clubs are black, he can be

perfectly certain – rationally completely certain – that the card is not a club. So his

degree of rational expectation that the card is not a club is 1 (equivalently: his degree of

rational expectation that the card is a club is 0). Provided he knows that hearts and

diamonds are the only red suits, his degree of rational expectation that the card is a heart

is 1/2.

Notice two things about this characterisation of probability in terms of rational expect-

ation. First, it is clear that the basis for assigning degrees of rational expectation

may consist in proportions. It is because George knows the relevant proportions that we

can assign degrees of rational expectation in this case. In other cases, frequencies provide

the basis for assigning degrees of rational expectation. In further cases, we may assign

degrees of rational expectation without knowing either relevant proportions or relevant

frequencies.

Second, notice that when assigning degrees of rational expectation, we spoke of the degree

to which one is entitled to believe something, given such-and-such evidence. Since we are

taking the degree of rational expectation as our concept of probability, what this means

can be expressed by saying that our key concept is the concept of conditional probability.

That is to say, what we are interested in is the probability that a proposition is true, given

that, or on the assumption that, some given set of propositions is true. More exactly, this is

the degree to which it would be reasonable to accept a certain proposition, given no other

relevant information except that contained within a certain set of propositions. In George’s

case, his evidence is that the card is red (along with the fact that exactly half the red cards

are hearts). So the conditional probability of the proposition the card is a heart, relative to

the proposition the card is red, is 1/2.

We can now say more precisely what an inductively forceful argument is:

4 There are many terms in the existing literature for this; common ones include ‘epistemic probability’ and

‘rational credence’.

logic: inductive force 93

Let [P] stand for one or more premises, and let A stand for a conclusion. Suppose

we have an argument:

[P]...

C) A

To say that such an argument is

inductively forceful

is to say that the conditional

probability of A relative to the set [P] is greater than one-half, but less than 1. (The

degree of inductive force of an argument is the conditional probability of A relative

to [P].)

This is our ‘ofﬁcial’ explanation, but you may ﬁnd it more helpful to think of inductive

force along the lines of the following:

To say that an argument is

inductively forceful

is to say: The argument is not

deductively valid, but, if the premises are true (or were true), then, given no

information about the subject-matter of the argument except that contained in the

premises, it would be more reasonable to expect the conclusion to be true than it

would to expect it to be false.

Or we can say: relative to the information contained in the premises [P], the conclusion is

more likely to be true than false.

There are several further points to bear in mind as regards probability and inductive force.

1 It is true that we do not always express probabilities as conditional probabilities.

For example, if we simply pick a card at random from the deck, it seems we can say

outright that the chance of its being an ace is 1/13. So, it seems we do ordinarily

attribute probability to a single proposition without stopping to specify any further

information. Usually, however, this is only because the relevant further information

upon which the probability-claim is based is left implicit; it is sufﬁciently well-known

such that we don’t have to mention it explicitly. In this case, the relevant information

that one would normally take for granted is that the deck is standard and complete,

in which case four of its ﬁfty-two cards are aces. Sometimes, however, the relevant

background is relatively vague, as in the example above about the leader of the

Labour Party, but still the relevant information, though only dimly glimpsed, exists.

So long as it is kept in mind that there must be a relevant set of information or some

premises in the picture, it is perfectly harmless to attribute probability to single

propositions, and we will sometimes do so.

2 Probability of the kind that we are speaking of is not an alternative to truth or falsity

in the way that ﬁnishing in the middle of the league table (or standings) is an

logic: inductive force94

alternative to ﬁnishing at the top or at the bottom. Nor is probability a kind of truth.

To say that a proposition is probable, in this sense, is to say that it is most likely to be

true. It is to express an expectation, which falls short of perfect certainty, that a

proposition is correct. What one says is true, if the evidence upon which the claim is

based really does make the expectation rational. The idea is not that there is some

third thing between truth and falsity, namely probability. For example, if I know that

Reggie has taken his driving test today, and I say, ‘Probably, Reggie failed his driving

test’, I am not saying, ‘It isn’t true that Reggie failed his driving test, and it isn’t false;

it’s probable that he failed it’. No: either it is true that Reggie failed his driving test or

it is false. That is, there are two possible states of affairs: either he failed the test or he

did not. There is no mysterious third state of affairs, i.e. that he probably failed it.

Rather, the function of the word ‘probably’ is to indicate that the evidence makes it

rational to believe, but does not make it certain, that the proposition is true.

3 Unlike truth, probability is a matter of degree; different propositions may have

various degrees of probability (relative to a given body of information). For example,

given the information we have, it is very highly probable that in the year 863 BC

someone ate a mushroom. But there is a very tiny possibility that no one did. It is

somewhat less probable, but still probable, that someone will swim the English

Channel during the year 2046. It is possible, but improbable, that someone swam the

English Channel in the year 863 BC. We do sometimes specify probabilities in terms

of numerical values, but often the probability of something being the case cannot be

estimated with enough precision to justify assigning an exact numerical value. Some-

times the most we can do is to rank probabilities; for example, we can say with

conﬁdence that a certain man is more likely to eat a cucumber than he is to visit

Japan during the coming year, but we cannot assign precise numerical probabilities to

these propositions in the way that we can with the cards. And sometimes we cannot

even rank them with conﬁdence. Of single propositions, the most we can say in

such cases is ‘that’s probable’, or ‘that’s very probable’, or ‘that’s improbable’. (By

‘probable’, remember, we mean the case in which the probability is greater than 1/2;

by ‘improbable’ mean the case in which it is less than 1/2; something can be neither

probable nor improbable, if its probability is exactly 1/2.)

Because of this, inductive force, unlike deductive validity, is also a matter of degree.

We cannot say that one argument is more valid than another, but we can say that one

argument is more inductively forceful than another. Validity was deﬁned in terms of

impossibility, in which case the probability is zero (look at the deﬁnition of validity

again). Validity is thus all-or-nothing. Indeed, one could deﬁne validity simply as the

‘limiting case’ of inductive force – the case in which the conditional probability of

the conclusion relative to the premises is 1. That is, we can think of arguments as

being arranged on a scale of conditional probability, ranging from deductively valid to

a complete lack of inductive force (see Figure 4.1).

Thus an argument may be inductively forceful but only to a very small degree.

For example, if you know that ﬁfteen of the twenty-nine children in the class

are wearing white shoes, then you have an inductively forceful argument for the

logic: inductive force 95

conclusion that the child who got the highest mark in spelling is wearing white shoes.

But the probability of that conclusion, relative to the premise, is only slightly better

than 1/2; so the argument is just barely inductively forceful. It is inductively forceful,

but only to a low degree.

4 As ordinarily used, the term ‘probably’ is somewhat vague. Usually, when we say

something like ‘David will probably win the match’, we don’t just mean the

probability of his winning is greater than 1/2; we mean it is substantially higher than

that. But exactly how much higher must it be, if it is to be appropriate to say

‘probably’? Of course, there is no exact answer. The person saying this may be willing

to give a more precise ﬁgure, but they needn’t in order to be entitled to use the word

‘probably’. In fact, there is good reason to maintain that the use of ‘probably’ is

appropriate if, and only if, the intended probability exceeds 1/2. If you are asked ‘Is

David going to win?’, and you think his chances are better than 50–50 but only just,

it is appropriate to say ‘probably’ – but in doing so, you would normally use a

hesitating tone of voice to convey that you put the probability at only just over the

50–50 threshold.

What is very likely is that ordinary uses of ‘probably’ mean a probability of greater

than 1/2, but typically carry a conversational implicature that the probability

substantially exceeds that threshold (see Chapter 1, pp. 10–11, for discussion of

conversational implicature). We can cancel the implicature through tone of voice.

Exactly the same point goes for the quantiﬁer ‘most’. If someone were to make an

accusation by saying, ‘Most students cheated on the exam’, they would probably

intend to convey that substantially more than half of them cheated, not just a bare

majority. Nevertheless, if were to turn out that ﬁfteen of the twenty-nine students in

the class cheated, the accuser might be surprised, but would not thereby be found

to have spoken falsely. The concept of conversational implicature captures this point

perfectly.

Figure 4.1

logic: inductive force96

For these reasons we deﬁne inductive force as conditional probability of premises to

conclusion greater than 1/2. Because of this, it is sometimes important to make sure

we do not underestimate the inductive force of an argument; if an argument has a

high degree of inductive force, we should say so, and not pronounce simply that the

argument is inductively forceful. When assessing inductive arguments, it is usually

important to specify, as accurately as we can, the degree of inductive force.

5 Whether or not an argument is deductively valid does not depend on whether anyone

thinks it is. Likewise, probability, in our sense, is the degree to which it is rational or

reasonable to expect something to be true (given a certain set of premises), irrespec-

tive of how likely we actually think it to be. When we claim that an argument is

inductively forceful, we are not always correct. We may think that a set of premises

(our evidence) makes it reasonable to accept a conclusion, when in fact it is not.

Rational expectation concerns what is in fact reasonable, not what any particular

person thinks is reasonable.

We can reinforce this point by considering a case in which everyone will agree that

rational expectation depends on proportion. Suppose that Fiona is asked to pick a

card at random. Her chance of getting, say, a heart, is exactly one in four. Her chance

of not getting a heart, then, is three in four, or 3/4. So she will probably not get a

heart. If she is perfectly rational and well-informed, she will be 3/4 certain that she

won’t get a heart. Suppose, however, that Fiona is not perfectly rational. She thinks

that since she has recently fallen in love, she probably will choose a heart. She might

express her thinking so by saying, ‘I’ll probably choose a heart’. Nevertheless, the

probability that she will not choose a heart is greater – indeed, three times as great –

as the probability that she will. Fiona’s actual degree of expectation is higher than the

degree of rational expectation. More generally, we can observe that different people,

going on the same set of premises, can have different degrees of expectation that

something is or will be true; but by and large there is only one correct answer as to

how reasonable it is to infer the conclusion from the premises.

6 Like the validity or invalidity of an argument, the degree of inductive force of an

argument is independent of the truth-values of the premises. This can be seen most

easily in the case of a completely ﬁctional example, in which the question of the

truth-values of the premises cannot even arise:

P1) Almost all Zormons play chess.

P2) Trozak is a Zormon.

C) Probably, Trozak plays chess.

Of course this is not even a real argument, since there are no such beings as Zormons, and

no such being as Trozak. Nevertheless, if there were, then this certainly would be an

inductively forceful argument. If you did not know whether or not these beings exist, you

would still be right to say that if this did express a real argument, it would be inductively

forceful. Whether or not there is such a being as Trozak or such beings as Zormons, and

whether or not P1 is true, are thus irrelevant to the estimate of inductive force.

logic: inductive force 97

However, it is important to reiterate that we have adhered, so to speak, to a non-

mathematical deﬁnition of probability and hence of inductive force. Proportions, statistics

and frequency are not the whole; degree of rational expectation may be, but are not always,

based on them. This means that part of what we are doing in asking whether an inference

is inductively forceful relative to a set of premises is to ask whether a human agent – given

what human agents ordinarily know – would be rational or reasonable in expecting the

conclusion to be true. This is precisely what our deﬁnition of probability as degree of

rational expectation brings to the fore: some estimates of probability depend inscrutably

on human ‘intuition’. True, this means that in some cases, two arguers, with the best

intentions as critical thinkers, may legitimately disagree on the inductive force of an

argument. But the correct response to this possibility is not to conclude that both are

correct, hence that there is an unresolved element of irrationality in critical thinking. The

correct response is to insist that such possibilities should be resolved by working harder at

making the implicit propositions that divide people explicit.

‘ALL’, ‘MOST’ AND ‘SOME’

To say that all rodents have tails is the same as saying, ‘Every rodent has a tail’, or ‘Any

rodent has a tail’, or ‘No rodent has no tail’. To say that most rodents have tails is to say

that more than half of all rodents have tails, or that there are more rodents with tails than

there are without them. But what about ‘Some rodents have tails’? What proportion of

rodents must have tails for that to be true? In fact, that is a bad question. Such a statement

does not tell you what proportion of rodents have tails. Consider this argument:

P1) Some patients who have been treated with X have developed liver disease.

C) If I am treated with X, then I will develop liver disease.

This argument is not inductively forceful. P1 could be true even if, say, three patients

developed liver disease upon being treated with X, yet thousands were treated with X

without developing liver disease.

That much should be fairly obvious. But the word ‘some’, as ordinarily used, can be rather

tricky. Often, when we actually say something of the form ‘Some A are B’ (such as P1), we

say it when we believe that more than one A is B, but that not all A are B. Often when

using the word this way, we say, ‘Only some A are B’. Other times, we say it when we

believe that more than one A is B, but do not know whether or not all A are B. For

example, a medical researcher who discovers a few patients that have developed liver

disease after being treated with X might use the sentence P1 to announce the discovery –

but this would be to leave open the possibility that perhaps all patients treated with X

develop liver disease. He would not be ruling it out.

For the purpose of reconstructing arguments it is most convenient to assume the latter

understanding of ‘some’, whereby ‘some A are B’ does not rule out that all A are B. It does

logic: inductive force98

not say, ‘Some, but not all, A are B’. In this sense, ‘Some A are B’ means ‘Some, perhaps all,

A are B’.

Further, when using ‘some’ in our argument-reconstructions, we will take it to mean

‘at least one’. That is: if only one A is B, then it will be true that some A are B. On this

understanding of ‘some’, what ‘Some rodents have tails’ means is simply that it is not the

case that no rodents have tails. Similarly, ‘Some rodents do not have tails’ means the same

as ‘Not all rodents have tails’. This departs slightly from what ordinary language typically

suggests, but it is much more convenient for our purposes. If, when reconstructing an

argument, it is clear that by ‘some’ the arguer means ‘at least two’, then we can simply

make this explicit in the reconstruction, writing ‘at least two’.

SOFT GENERALISATIONS: A REMINDER

It is worth re-stressing a point introduced in Chapter 1 (pp. 36–38), namely that in

reconstructing arguments with generalisations, we should always supply missing

quantiﬁers. We often run across arguments like this:

The Government’s policy is based on the claim that violent offenders re-offend.

I resent and refute this claim utterly. My nephew was imprisoned in his late teens

on an armed robbery conviction but unlike a lot of these wasters he thoroughly

sorted himself out; he’s now been married with a steady job for many years and

there is no way he’s going to commit a crime again.

The arguer seems to argue that the generalisation ‘violent offenders reoffend’ is refuted by

the existence of a violent offender who has not re-offended. And of course this argument

would be valid:

P1) My nephew is violent offender who has not re-offended and will not.

C) Not all violent offenders re-offend.

But it’s very unlikely that the Government asserted that all violent offenders re-offend.

More likely, they asserted that most do, or that the frequency of violent offending among

those who have already committed a violent crime is signiﬁcantly higher than it is among

those who have not, or some such thing. If so, then the single example of the arguer’s

nephew does little or nothing to undermine the Government’s claim.

The issue arises frequently in everyday life, and is a common but easily avoided source of

misunderstanding and tension between people. For example, Sandra arrives late yet again

for a date with Peter, who is justiﬁably peeved:

Peter: You’re always late!

Sandra: That’s not true! Why do you attack me so? Last Friday I was early! Let’s have

some champagne, Mr Grouch.

logic: inductive force 99

If Peter had said, for example, ‘You’re late most of the time’, then, although it wouldn’t be

quite as pungent as what he did say, it would focus Sandra on the relevant issue; it

wouldn’t have invited Sandra to make the diversionary response that she did. Precise

generalisations make it harder to set up smokescreens and red herrings.

INDUCTIVE SOUNDNESS

You can probably guess what this is, by analogy with the deﬁnition of deductive soundness:

To say that an argument is inductively sound is to say: It is inductively forceful and

its premises are (actually) true.

The important thing to note here is that an inductively sound argument, unlike a deduc-

tively sound argument, may have a false conclusion. That possibility is precisely what is

left open by the deﬁnition of inductive force – an inductively forceful argument is the

case where the truth of the premises makes the truth of the conclusion probable, but does

not guarantee it. Look again at the last argument given concerning Fiona, who lives in

Inverness. Suppose it is true that Fiona lives in Inverness, and that almost everyone there

has some woollen garments. An argument with those two facts as premises, and that Fiona

has at least one woollen garment as a conclusion, would be inductively sound – even if, as

it happens, Fiona has no woollen garments.

Note that we have not said that one should always be convinced by inductively sound

arguments. You could know that an argument is inductively sound, but also know, for

independent reasons, that the conclusion is false (review the discussion of inductive

soundness if this is surprising). We will return to this point in Chapter 6.

PROBABILITY IN THE PREMISES

So far in this chapter we have mostly considered premises expressing proportions, such

as ‘Most Zormons plays chess’. Proportions are expressed using quantiﬁers such as ‘most’,

‘95 per cent of’, and the like. But consider this case:

P1) If Napoleon is not ill then the French will attack.

P2) Probably, Napoleon is not ill.

C1) Probably, the French will attack.

This argument is inductively forceful, but it does not contain any quantiﬁers. The reason

that the truth of the premises would not guarantee that the French will attack, of course, is

the presence of the word ‘probably’ in P2; it is only said to be probable that Napoleon is

logic: inductive force100

not ill. (We would get the same result if in place of P2 we wrote ‘Napoleon is probably not

ill’, or ‘It is unlikely that Napoleon is ill’, or some other sentence synonymous with P2 as

written.)

Note that words such as ‘probably’ can also occur in the antecedents and consequents of

conditionals. For example:

P1) If Napoleon is not ill then, probably, the French will attack.

P2) Napoleon is not ill.

C1) Probably, the French will attack.

This too is an inductively forceful argument.

ARGUMENTS WITH MULTIPLE PROBABILISTIC

PREMISES

Sometimes, probabilistic elements can occur in more than one premise. Assessing such

arguments can be tricky. For example, suppose we have just dropped James off at the

airport, and are wondering whether he made it to his ﬂight in time. You argue:

P1) James is not likely to have lost his passport.

P2) James is not likely to have been delayed by a long queue at check-in.

C) Probably, James made it to his ﬂight on time.

If ‘not likely’ means ‘probability is less than one-half’, then the argument, as stated, is not

inductively forceful. Nor does it become inductively forceful if we make it explicit that the

only things that could prevent James from making his ﬂight on time are the loss of his

passport or being delayed by a long queue at check-in:

P1) James is not likely to have lost his passport.

P2) James is not likely to be delayed by a long queue at check-in.

P3) If James has not lost his passport or been delayed by a long queue at check-in,

then he will have made it to his ﬂight on time.

C) Probably, James made it to his ﬂight on time.

The reason is that, in this case, the ways in which James could fail to make his ﬂight,

though individually not likely, may be collectively likely; that is, the probability of losing his

passport or being delayed by a long queue at check-in may, for all that the premises state,

exceed one in two (1/2). So in order to have an inductively forceful argument, we would

require the premise that the probability of his losing his passport or being delayed by a long

queue at check-in is less than one in two.

logic: inductive force 101

The example about James is an example of multiple probabilistic premises where the

probabilities are independent: whether or not one loses one’s passport has no bearing

on whether one is delayed by a long queue at check-in, and whether or not one is delayed

by a long queue at check-in has no bearing on whether one loses one’s passport. But other

examples exhibit probabilistic dependence; for example, James’s accidentally and unknow-

ingly leaving his passport at the check-in counter and his failing to get through passport

control are not independent outcomes, since if the former happens then the latter is sure

to happen.5

The example just given above in standard form involves two independent probabilistic

premises that each bear upon the conclusion separately (although, as stated, they do not

add up to a reason to accept the conclusion). But independent probabilistic premises can

also cause confusion in another way, when used in combination. Consider the following,

which has the underlying structure of a chain argument discussed in Chapter 3:

P1) Most Americans are people who were born in America.

P2) Most people who were born in American are white.

C) Most Americans are white.

Note that the argument tree for this is as shown in Figure 4.2.

5 The exact meaning of the independence of two events is: B and C are independent if and only if the

conditional probability of B given C is equal to the probability of B. When B and C are independent, then some

simple, useful relationships hold. First, the probability that event A does not happen is always 1 − A. Then the

probability of the conjunction of B and C (i.e. both happen) is simply the probability of B multiplied by the

probability of C. In symbols: Pr(B and C) = Pr(B) Pr(C). Then since ‘B or C’ means the same as ‘Not both: not-B

and not-C’, it follows that the probability of the disjunction (B or C) is 1 minus the probability of neither B nor

C. In symbols: Pr(B or C) = 1 − [Pr(not-B and not-C)]. The conditional probability of B given C is normally

written Pr(B/C), and is deﬁned as the probability of the conjunction (B and C) divided by the probability

of C. In symbols:

Pr(B/C) =Pr(B and C)

Pr(C)

A familiar example of a set of possible outcomes that are independent is the case of rolling a die; if the possible

outcomes are speciﬁed as the six possibilities of rolling a one, a two and so on, then each outcome has no bearing,

either logically or causally, on any other. So if you roll it n times, you have n independent outcomes. A familiar

example of a set of possible outcomes that are not independent is the case of drawing cards. What are the

chances that the ﬁrst card you draw from a complete deck is a heart? One in four cards in the deck is a heart, so

the chance 0.25. What is the chance that your next card is a heart? It depends, and it is not 0.25! If the ﬁrst card

you drew was a heart, then 12 of the remaining 51 cards are hearts, so the probability is about 0.235. If the ﬁrst

card was not a heart, then 13 of the remaining 51 are hearts, so the probability is about 0.255. The outcome of

the second draw is not independent of the outcome of the ﬁrst, and this shows up in the difference between the

conditional probability of drawing a heart given that you ﬁrst drew a heart, and that of drawing a heart given

that you ﬁrst drew a non-heart. This is only scratching the surface of the vast subject of probability and statistics.

However, you can learn enough from the most basic textbooks on probability or statistics to equip you to be far

more savvy and critical than most people in interpreting and evaluating the sorts of statistical claims made in the

media and elsewhere.

logic: inductive force102

This argument, as stated, is not inductively forceful. Strictly speaking, ‘most’ guarantees

only that the statement is true of more than half of the given group. The premises could

well be true, then, in the following circumstances: slightly more than half the American

people were born in America; slightly more than half the American-born people are white.

If that were so, then the proportion of white Americans would be slightly more than half

of slightly more than half the American population. Since half of a half is 1/2 ×1/2 =1/4,

this means that, in these circumstances, the proportion of white Americans would be a

little bit more than 1/4. It is important, in such cases, to determine whether or not the

proportions indicated by ‘most’ are sufﬁcient for the purpose of the argument.

The same sort of thing applies when a word such as ‘probably’ occurs more than once in

the premises, or a premise with a word like ‘probably’ and a premise with a quantiﬁer such

as ‘most’:

P1) Probably, James will gain a science degree.

P2) Most people with science degrees earn better-than-average salaries.

C) James will earn a better-than-average salary.

Once again, this argument is not inductively forceful. However, if the argument were

changed so as to indicate a sufﬁciently high probability of James’s gaining a science degree,

and/or to indicate a sufﬁciently high proportion of science degree-earners earning better-

than-average salaries, then the argument would be inductively forceful.

Another tricky situation that sometimes arises is illustrated by the following:

P1) Nine out of ten Green Party members are vegetarians.

P2) Only one in ten non-Green Party members are vegetarians.

P3) Alastair is a vegetarian.

C) Alastair is a Green Party member.

Figure 4.2

logic: inductive force 103

It is tempting to think that this argument is inductively forceful; you might reason: very

few outside the Green Party are vegetarians, and almost all Green Party members are

vegetarians; so surely if Alastair is a vegetarian, then mostly likely he’s a Green Party

member. But this would be a mistake (the mistake is known as the ‘base rate fallacy’;

see the discussion in Chapter 7, pp. 206–207). In fact, even if P1 said that all Green Party

members are vegetarians, the inference would be mistaken. For suppose that only one out

of every 101 people (in the UK, for example) is a member of the Green Party. If the

remaining (non-Green) population is 10 per cent vegetarian, then, since every Green is

vegetarian, eleven out of every 101 people are vegetarian. But only one of those eleven is a

Green. Thus ten out of every 101 people are non-Green vegetarians, and the non-Green

vegetarians outnumber the Green vegetarians by ten to one! So if you meet a vegetarian

such as Alastair, then, unless you had other reasons to think he is a Green, the reasonable

expectation would be that he is not a Green. Summing up, then, the premises do not give

you a good reason to think that Alastair is a Green.

Similarly: all plumbers own pipe wrenches, and few non-plumbers own them; but these

facts do not entitle us to say that if someone owns a pipe wrench, then probably, they are a

plumber. As a matter of fact, many DIYers own pipe wrenches. And there are a lot more

DIYers than there are plumbers. So the number of non-plumbers owning pipe wrenches

may well outnumber the plumbers.

INDUCTIVE FORCE IN EXTENDED ARGUMENTS

The conclusion of an inductively forceful argument may serve as a premise for a further

argument, which may itself be deductively valid, inductively forceful or neither. However,

if any sub-argument of an extended argument is not deductively valid, then the argument

as a whole is not deductively valid. At most, it is inductively forceful. Here is a hybrid

extended argument that illustrates the point:

P1) If Napoleon is not ill then the French will attack.

P2) Probably, Napoleon is not ill.

C1) Probably, the French will attack.

P3) If the French attack, then the Prussians will be routed.

C2) Probably, the Prussians will be routed.

If the ﬁrst argument were valid, entitling us to assert C1 categorically – that is, without

the qualiﬁer ‘probably’ – then since the argument from C1 and P2 to C2 is deductively

valid, there would be no need to write ‘probably’ beneath the second inference bar. As it

stands, however, C2 inherits the qualiﬁer ‘probably’ from its ultimate source in P2. The

logic: inductive force104

simplest way to think of this is to think of C2 as a proposition inferred from three

premises: P1, P2 and P3. If the word ‘probably’ were deleted from P2, then that argument

would be deductively valid. As it stands, however, that argument is only inductively

forceful.

CONDITIONAL PROBABILITY IN THE CONCLUSION

Consider the following argument:

If you start a new internet company, then probably it will fold, or get bought by

another company within three years. Most new internet companies do.

The conclusion of this argument is not ‘Probably, your new internet company will fold or

be bought by another company within three years’. It is, rather, ‘If you start a new internet

company, then, probably, it will fold or get bought by another company within three

years’. Its conclusion, then, states a conditional probability. We can reconstruct it like this:

P1) Most new internet companies either fold, or get bought by another company,

within three years.

C) If you start a new internet company, then, probably, it will either fold, or be

bought by another company, within three years.

As before, when judging the inductive force of this argument, the thing to do is to suppress

the word ‘probably’ in the conclusion. So understood, the conclusion might be false when

the premise is true – if you started the new company but it survived beyond three years –

so the argument is not valid. But according to P1, if you do start an internet company,

chances are that it will not survive for three years. So we may insert the word ‘probably’.6

EVIDENCE

Arguments presented as being inductively forceful may have several premises. Consider

the following:

6 Note that a conclusion of the form ‘If P, then, probably, Q’ is quite different from something of the form

‘Probably, if P then Q’. In fact in ordinary speech, the latter form is quite unusual, and we never use it in this

book. Even when we say, for example, ‘Probably if Ronaldo plays, he’ll score’ what we mean is ‘If Ronaldo plays,

then, probably, he will score’. It depends on exactly what the English ‘if–then’ is taken to mean, but at least on

one orthodox reading of it, the probability that a conditional ‘If P then Q’ is true is much higher than the

conditional probability of Q relative to P. Thus ‘Probably (If P then Q)’ can be true when ‘If P, then, probably,

Q’ is false. For example, if the initial probability of P and Q are both very low, then the former can be true even

though P and Q are completely independent, so the conditional probability is low (in which case the latter

statement is false).

logic: inductive force 105

The case against Dr X can be summed up as follows: Dr X, a medical doctor, has the

knowledge, and had the opportunity, to carry out the type of gradual programme of

strychnine poisoning that killed the victim. He had a strong motive for the murder.

And ﬁnally, Miss Y, a reliable witness, has testiﬁed that Dr X expressed to her his

wish that the victim were dead.

Let us grant that the case against Dr X is compelling. Here are four facts that seem jointly

to condemn Dr X as the murderer. The case does not take the form of a deductively valid

argument; it would not be impossible for these facts to be as the arguer says, yet Dr X

be innocent. But it is crucial to recognise that the case should not be reconstructed as

four separate arguments, each presented as inductively forceful in its own right. The

prosecutor’s case is based on four premises:

P1) Dr X has the knowledge to carry out the type of gradual programme of

strychnine poisoning that killed the victim.

P2) Dr X had the opportunity to carry out the murder.

P3) Dr X had a strong motive for the murder.

P4) Miss Y, a reliable witness, has testiﬁed that Dr X expressed to her his wish that

the victim were dead.

These constitute the evidence against Dr X. But an argument for the conclusion that Dr X

murdered the victim, based on P1 alone, would not be inductively forceful. If it were, then

the argument would point with equal force to the guilt of a great many other people with

the requisite knowledge of strychnine. Nor would an argument similarly based only upon

P2, P3 or P4. If the prosecutor were to advance any of these four separate arguments by

itself, then the jury could only conclude that the prosecutor lacks a compelling case: none

of the arguments would be inductively forceful. It is essential to the prosecutor’s case that

these four items of evidence point jointly though independently to the defendant’s guilt, as

indicated by the argument tree in Figure 4.3:

Figure 4.3

logic: inductive force106

The argument, then, should be constructed like this:

P1) Dr X has the knowledge to carry out the type of gradual programme of

strychnine poisoning that killed the victim.

P2) Dr X had the opportunity to commit the murder.

P3) Dr X had a strong motive for the murder.

P4) Miss Y, a reliable witness, has testiﬁed that Dr X expressed to her his wish that

the victim were dead.

C) It is highly probable that Dr X murdered the victim.

This is how it is with items of evidence: if both B and C are evidence for A, the conjunction

of B and C is (typically) stronger evidence than B or C alone.7 Put in terms of arguments,

the argument with B and C as premises is more forceful than either the argument with B

as a premise or that with C as a premise.

Note also that in this example we have a case where the estimate of inductive force does

not appeal to a proportion or a frequency, and does not depend on the presence of a

probabilistic premise. The basis for the inference from premises to conclusion is left

inexplicit. This does not mean that we could not at least to some degree make it more

explicit. For example, we might include the premise that very few people have the kind of

knowledge described in P1. But it is not always appropriate to try to do so; for example, the

exact ways in which P2–P4 contribute to the argument cannot easily, and probably not

very usefully, be spelled out.

INDUCTIVE INFERENCES

Consider the following argument:

So far, every one of several goldﬁsh I’ve had has died when I fed it cat food. There-

fore, if I feed my new goldﬁsh cat food, it will die.

This inference seems reasonable, but how do we reconstruct the argument? We might try:

P1 (a) All goldﬁsh die if fed cat food.

C) My new goldﬁsh will die if I feed it cat food.

7 This holds so long as B and C are independent: whether or not B occurs has no bearing on whether or not C

occurs, and vice versa. Otherwise the situation is more complicated; see footnote 5.

logic: inductive force 107

Or:

P1 (b) Most goldﬁsh die if fed cat food.

C) Probably, my new goldﬁsh will die if I feed it cat food.

The ﬁrst argument is valid and the second inductively forceful. But there is a problem

with these reconstructions. The arguer has not asserted either version of P1. What he

has asserted is that all the goldﬁsh to which he has fed cat food have died. The sample of

goldﬁsh with which the arguer has had this experience is only a tiny fraction of the total

number of goldﬁsh in the universe. So the arguer has not said anything about all, or most,

goldﬁsh. Presumably the arguer does believe either P1(a) or P1(b), but, if so, he does so on

the basis of his previous experience with goldﬁsh and cat food. Somehow, the arguer must

get from the proposition ‘Every goldﬁsh I’ve had has died when I fed it cat food’ to ‘My

new goldﬁsh will die if fed cat food’, or even ‘Most (or all) goldﬁsh die when fed cat food’.

So far, in our discussions of arguments, we have said nothing to help us with this sort of

inference.8

However, this kind of inference is very common, both in science and in ordinary life. We

call it an inductive inference. This is our name for the case when you extrapolate from a

sample of a total population of things either to something outside the sample, or to a

generalisation about the population as a whole (so far, we have always gone the other way

– either from a generalisation about a whole population to a claim about some smaller

sample, or from the whole population to a claim about a single member of it). In the above

case, the arguer needs to extrapolate directly from the sample of goldﬁsh they have

experimented with to a proposition about the new goldﬁsh:

P1) Every observed goldﬁsh has died when fed cat food.

C1) My new goldﬁsh will die if I feed it cat food.

If we judge this inference to be inductively forceful – let as assume for the moment that it

is – then, just as with any inductively forceful argument, we write ‘probably’ before the

conclusion:

8 As we pointed out, many probabilities can be based upon proportion. One of the tasks of statistical analysis

is to show how this is so, even in cases that might initially seem to resist this strategy. Inductive inferences

represent a class of cases where proportion certainly cannot be applied straightforwardly. If we know that, say,

74 per cent of the past 956 cases of A have been cases of B, we cannot without further ado assume that the

probability that the next case of A will be a case of B is 74 per cent. The next case of A is not among the set of

cases for which that proportion is known to have held. So it is not like the case of a card face down on the table,

which is drawn from set of cards for which the relevant proportion is known. In the inductive case we have to

make the further assumption that probabilities taken from proportions of known cases can be transferred to

unknown cases. Of course such inferences do often seem to be rationally justiﬁed; the question of why this is so

– the ‘Problem of Induction’ – was ﬁrst raised by David Hume in his Treatise of Human Nature (1739), and

remains an open problem.

logic: inductive force108

P1) Every observed goldﬁsh has died when fed cat food.

C1) Probably, my new goldﬁsh will die if I feed it cat food.

Alternatively, the arguer could have obtained this conclusion by a slightly longer route.

The arguer might have reached the conclusion by means of an extended argument, com-

prising an inductive inference to a generalisation about all goldﬁsh, together with a second,

deductively valid inference from that generalisation to the conclusion concerning the

arguer’s new goldﬁsh:

P1) Every observed goldﬁsh has died when fed cat food.

C1) All goldﬁsh die if fed cat food.

C2) My new goldﬁsh will die if I feed it cat food.

However, assuming the truth of P1, one could not assert the conclusion here with

quite as much conﬁdence as in the ﬁrst case. We may assert C2 with as much, but no

more, conﬁdence than that with which we may assert C1. But since C1 is a generalisa-

tion about all goldﬁsh, it stands a greater chance of being false than C1 of the ﬁrst

goldﬁsh-argument – a statement about a single goldﬁsh. The reason is that the second

argument depends upon a more ambitious extrapolation than the ﬁrst, one that is not

needed for the desired conclusion. Yet, the inferences to C1 in either case are funda-

mentally of the same type. They are both extrapolations from observed cases to

unobserved cases. Each can be thought of as an extrapolation from a sample to a larger

population of which the sample is a part. In the ﬁrst case we can think of the larger

population referred to as comprising the sample (the observed goldﬁsh) plus this one

new goldﬁsh. In the second case, obviously, the larger population is simply the total

population of goldﬁsh. Some inductive inferences are concerned to make a broad gen-

eralisation (all goldﬁsh); others are concerned only to extend to a few new cases, or to

a single new case (the new goldﬁsh). But they are fundamentally the same type of infer-

ence. Thus we deﬁne:

To say that an inference is an inductive inference is to say: (a) it is not deductively

valid; (b) its premises include a generalisation about a sample of a given

population; and (c) its conclusion extrapolates the generalisation to all or part of

the total population from which the sample is drawn.

Requirement (a) is to avoid counting the following sort of inference as inductive: ‘Some

black cats have no tails; therefore not all cats have tails.’

Inductive inferences frequently extrapolate from past to future. For example, if we infer,

from Ireland’s never having won the football World Cup, that probably it never will, our

logic: inductive force 109

sample is all the World Cups that have so far been contested, and the total population is

the set of all World Cups – past, present and future.

Often the conclusion of an inductive inference is a statistical generalisation such as ‘37 per

cent’. For example, when a pollster ﬁnds that 37 per cent of a sample of the adult British

population supports a given political party, the pollster might conclude that 37 per cent of

the adult British population supports that party. In such a case, the sample is the sample

polled, and the total population is the entire adult population of Great Britain. Instead

of extrapolating 100 per cent (‘all’) from sample to total population, we extrapolate the

ﬁgure ‘37’.

How representative is the sample?

In our characterisation of inductive force, we said that it should concern itself only with

the probability of the conclusion relative to the information given by the premises. The

inductive force of an argument is the same as the conditional probability of the conclusion

relative to the premises. This means that, in order to maximise the inductive force of an

argument, everything known to be relevant to the inductive force of an inference should

be stated in the premises.

We said that we would assume the ﬁrst standard formulation of the inductive inference

about goldﬁsh to be forceful as stated, but it lacks one bit of information to genuinely

make it so. For, as stated, the premises could be true, even though one had only one

goldﬁsh in the past, whereas the original statement of the argument speaks of several past

goldﬁsh. If so, then the inference to the new goldﬁsh would be rather weak. What is

missing is a premise that says that the sample forming the basis of the inductive inference is

representative.

To illustrate further, suppose you live near the North Pole, and every bear you’ve ever seen

is white. So you argue:

P1) Every observed bear is white.

C) All bears are white.

Formally, this argument is just like the one about the goldﬁsh. But, whereas the goldﬁsh-

inference seemed at ﬁrst to be correct, this one deﬁnitely seems not to be. Only a minority

of bears are white (polar bears, and perhaps some albinos of other species). The difference

is that, whereas the goldﬁsh-arguer can reasonably assume that the sample of observed

goldﬁsh was representative of the total population of goldﬁsh, the bear-arguer cannot.

That is, the goldﬁsh-arguer can reasonably assume that the sample of goldﬁsh was

relevantly similar to the total population, but the bear-arguer cannot. Polar bears are only

one of many species of bears, and if you know anything about zoology and adaptation,

you know that a trait like colour, though somewhat likely to be similar across a single

species, is not nearly so likely to be similar across different species, even within the same

logic: inductive force110

genus or families of species. Further, you can reasonably assume that mammals living in

non-snowy regions are much less likely to be white than ones living in perpetual snow (it is

advantageous to carnivores to blend visually into the background, so in snowy regions

white bears will have a greater chance of survival and procreation, in which case the gene

for white fur is more likely to get passed on). Being a different species, which lives in a

completely different climate, is certainly a relevant difference when drawing inductive

inferences about colour with respect to classes of mammals, even if the species is a closely

related one.

How do you know whether a sample is representative of the total population, i.e. rele-

vantly similar to it? There is no simple rule for this; our estimate of relevant similarity

must be based upon our knowledge of the subject-matter in question. For example, we

drew upon some basic evolutionary biology in criticising the bear-inference. Where

such statistical inferences as the one mentioned above are concerned, the question is

much more complicated, calling for more specialised expertise. A pollster sampling the

population for voting preferences must study the many ways in which voting behaviour

correlates with factors such as income, geographical location, profession and so on, and

then ensure the that polled sample reﬂects the distribution of these factors in the popula-

tion as a whole.

Nevertheless, in general, the larger and more representative the sample used for a given

generalisation, the more inductively forceful, or the stronger the inductive inference.

An inductive inference that is not forceful – one whose premise does not really support

its conclusion – is a weak one. For example, suppose someone argues: ‘My brother is a

fool. Therefore, probably, all boys are fools.’ That is a very weak inductive inference. The

bear-arguer’s inference is not quite as bad as that, but it is also very weak. Also, from a

given sample, an inference to a generalisation about most of the totality is a stronger one

than an inference to a generalisation about all of the totality, since obviously the latter is

less certain.

Thus we can adopt the following generalised schemata for inductive inferences:

Inductive Inference Style No. 1

P1) X% of the observed sample of Fs are G.

P2) The observed sample of Fs with respect to G is representative.

C) X% of Fs are G.

Or:

Inductive Inference Style No. 2

P1) X% of the observed sample of Fs are G.

P2) The observed sample of Fs with respect to G is representative.

C) The probability is .X that this F is G.

logic: inductive force 111

To recapture the goldﬁsh argument, put in ‘goldﬁsh’ for ‘F’, ‘dies when fed cat food’ for

‘G’, and either ‘All’ or ‘100%’ for ‘X%’ (either style of argument would be suitable). For the

argument about polls and the voting public, put ‘member of the UK voting public’ for ‘F’,

‘supports such and such political party’ for ‘G’, and ‘37%’ for ‘X%’ (in this case, the ﬁrst

style would be suitable).

A PROGRAMME FOR ASSESSMENT

We are now in a position to outline a basic procedure for the assessment of arguments

represented in standard form. We ﬁrst consider arguments that have only one inference

(that is, ones that are not extended arguments). When you represent an argument in

standard form, do not include the word ‘probably’, or any similar word, in the conclusion

– not yet. Put such words in the premises only. Once you have reconstructed the

argument in this way, you should proceed as follows (and you should, looking back at

the deﬁnitions given in this chapter, stop to see why the chart is arranged as it is):

1 Is the argument deductively valid?

If not, proceed to 2.

If yes, are all the premises true?

If yes, the argument is deductively sound. Stop.

If not, the argument is valid but unsound. Stop.

2 Is the argument inductively forceful?

If not, the argument is neither valid nor inductively forceful. Stop.

If yes, how forceful is it? Write ‘probably’, or suitable variant, in the appropriate place

in the conclusion. Are the premises true?

If yes, the argument is inductively sound. Stop.

If not, the argument is neither deductively nor inductively sound. Stop.

Of course as critical thinkers we may be unable to decide the soundness of an argument,

since that will depend on matters of fact calling for specialised knowledge. A premise

might state, say, the number of species of amphibians in Nepal; few people have such

knowledge. So don’t think you’ve got to complete the above routine in every case.

In the case of extended arguments, this procedure is to be carried out ﬁrst with respect to

the sub-arguments whose conclusions are premises of the extended argument. For

example, suppose we have an extended argument whose form is like this:

P1) . . .

P2) . . .

C1) . . .

P3) . . .

C2) . . .

logic: inductive force112

In this case the argument whose conclusion is C1 is a sub-argument for an extended

argument whose conclusion is C2. You would ﬁrst assess the argument from P1 and P2 to

C1; you would then assess the argument from C1 and P3 to C2. Finally, you would use

these results to assess the total argument from P1, P2 and P3 to C2.

Assessment is to be distinguished from reconstruction, which is discussed in more detail

in the next chapter. Broadly speaking, assessment may be said to fall into two categories.

The ﬁrst we may call logical assessment, which is that whereby we make judgements of

deductive validity and inductive force. The second we may call factual assessment; here is

where we ask after the truth-values of premises, in determining the soundness of argu-

ments already found to be deductively valid or inductively forceful. However, as noted,

the evaluation of inductive force is not purely independent of matters of fact in the way

that judgements of validity are. For example, the evaluation of inductive inferences

depends on judgements about how representative a sample is, which requires knowledge

of matters of fact. In other cases, such as judgements in jury cases, it is asking far too much

to demand that all the reasons be made explicit.

It is important to realise that if your verdict is that the argument, as you have

reconstructed it, is not deductively sound, you might be able to reconstruct it so as to make

it inductively sound. Look again at the example involving Fiona and wool. An early

attempt at reconstructing it used the premise ‘Everyone in Inverness owns at least one

article of woollen clothing’. So rendered, the argument was valid, but not sound. We then

weakened the premise to ‘Almost everyone in Inverness owns at least one article of woollen

clothing’. The result was not deductively valid, but it was inductively forceful. In general,

it is best to sacriﬁce validity to soundness when reconstructing; an inductively sound

argument is more useful than a valid but unsound argument.

Later, we will learn some techniques that aid logical assessment. There is, to repeat, no

readily deﬁnable procedure for factual assessment; for this is simply the task of deter-

mining whether particular propositions are true – e.g. whether there are whales in the

Black Sea, whether inﬂation rose in 1993, and so on. For that we must look outside logic

books!

CHAPTER SUMMARY

The conditional probability of a proposition relative to a set of a premises is the degree to

which it would be rational to expect it to be true, given the information relevant to the

conclusion given in the premises. Estimates of rational expectation are often based upon

other measures of probability such as proportion and frequency, but need not be.

A deductively valid argument enables us to be certain of the truth of its conclusion, if we

are certain of the truth of its premises. An inductively forceful argument does not allow

this, but it does allow us to think its conclusion more likely to be true than not: an

inductively forceful argument is one for which the conditional probability of the conclu-

sion relative to the premises is greater than 0.5.

logic: inductive force 113

Like deductive validity, both probability and inductive force are objective: the conditional

probability of a conclusion relative to a given set of premises is independent of people’s

actual estimates of conditional probability, as shown by the possibility of mistakes about

the latter. But unlike deductive validity, both probability and inductive force are a matter

of degree. An argument maybe inductively forceful but only just barely. It is important to

estimate the degree of an argument’s inductive force as accurately as the case allows.

Inductively sound arguments are inductively forceful arguments with true premises.

Unlike deductively sound arguments, they may have false conclusions.

Some arguments contain inductive inferences. An inductive inference is a deductively

invalid inference whose premise is a generalisation about some sample of a given popula-

tion, and whose conclusion is a generalisation about the population as a whole, or about a

particular member or set of members of the population outside the sample. In general, the

force of an inductive inference depends on the degree to which the sample is representa-

tive of the population.

EXERCISES

1 Each argument below contains at least one premise with a missing quantiﬁer.

(A) Reconstruct the argument, adding appropriate quantiﬁers. Use the strongest

quantiﬁers you can, so long as the resulting premises are what someone giving the

argument would have intended (that is, don’t use ‘most’, if it seems that the arguer

would have intended all or almost all, or some such). (B) If the resulting argument

is deductively valid, say so. If the argument is inductively forceful, say so, and insert

‘probably’ before the conclusion.

a Sex crimes are committed by people who have themselves been victims of

child abuse. The defendant has committed a sex crime. Therefore, the

defendant was a victim of child abuse.

b Children love Harry Potter books. Therefore your child will love the Harry

Potter books.

c If doctors in this country are overworked, then the general health of the

population will decline. Doctors in this country are overworked. Therefore,

the general health of the population will decline.

d Old people have poor eyesight. People with poor eyesight should not be

allowed to drive. Therefore, old people should not be allowed to drive.

e In countries colonised by Spain, there are many people of Spanish descent.

There are very few people of Spanish descent in Laos. Therefore, Laos was

not colonised by Spain.

logic: inductive force114

2 Consider the following pair of arguments:

P1) Most HIV-positive patients in California are homosexual.

P2) Mr X is a California HIV-positive patient.

C) Mr X is a homosexual.

P1) Most residents of Orange County, California, are not homosexual.

P2) Mr X is a resident of Orange County, California.

C) Mr X is not homosexual.

Assume that this is the same Mr X referred to in each argument. (A) Are these

arguments inductively forceful? (B) Could both arguments be inductively sound? If

not, explain why not. Otherwise, describe a scenario in which they would both be

sound. (C) If we knew the premises of both arguments to be true, would we have

reason to believe, or not to believe, that Mr X is homosexual?

3 Statements are said to be incompatible if it is impossible for both of them to be true

(if they are incompatible, it may or may not be possible for both to be false). Which

of the following pairs of statements are incompatible?

a Some hamsters are black. All hamsters are white.

b Some hamsters are black. Some hamsters are white.

c Some hamsters are black. Most hamsters are not black.

d Some hamsters are black. All hamsters are black.

e Many hamsters are black. Many hamsters are white.

f Every hamster is black. This hamster is white.

g This hamster is black. Some hamsters are white.

h No hamster is black. No hamster is not black.

i No hamster is black. No hamster is white.

j Few hamsters are black. Many black hamsters are small.

k Most hamsters are black. Many hamsters are white.

l Most hamsters are black. All my hamsters are white.

m Most hamsters are black. Every English hamster is white.

4 Reconstruct the following as either three separate arguments or as one, depending on

which strategy would amount to a more forceful case. Also draw a tree diagram for it.

Lance Armstrong is probably not going to win another Tour de France. He is

now older than any previous winner of the event. He hasn’t got any racing

experience this year, and his training has been inadequate lately because of a

back injury.

5 (A) Reconstruct the following arguments. (B) Say whether or not they are valid or

inductively forceful. (C) If the argument is neither valid nor inductively forceful,

logic: inductive force 115

change or add one premise, or change the conclusion, so that it becomes valid or

inductively forceful. There may be more than one reasonable answer. (D) Add any

further remarks that seem appropriate to evaluating the argument.

a If alcohol advertising is banned, then, probably, drinking would decline. If

drinking declines, then domestic violence would decline. Therefore, if alco-

hol advertising is banned, then, probably, domestic violence would decline.

b If alcohol advertising is banned, then, probably, drinking would decline. If

drinking declines, then, probably, domestic violence would decline. There-

fore, if alcohol advertising is banned, then, probably, domestic violence

would decline.

c Most children who go without breakfast have trouble concentrating at school

in the morning. Johnny concentrates well at school in the morning. There-

fore, probably, he does not go without breakfast.

d If this meat was grown in Scotland, then it is extremely unlikely it is infected

with BSE. And even if it is infected, then it is very unlikely that eating it

will make you ill. Therefore, if this meat was grown in Scotland, eating this

meat will not make you ill.

e Brazil is more likely to win the World Cup than Argentina. Therefore,

probably, Brazil will win the World Cup.

f Scotland has never won the World Cup. Therefore, probably, Scotland will

never win the World Cup.

g Probably, English football fans will make trouble at the next World Cup. If

English football fans do make trouble at the next World Cup, then England

may be expelled from the European Cup. Therefore, it is likely that England

will be expelled from the European Cup.

h If the murderer passed through here, then, probably, there would be hairs

from the victim on the rug. But there are no hairs from the victim on the rug.

Therefore, the murderer did not pass through here.

i Very few habitual cannabis users are violent. The murderer is clearly very

violent. Mr X is a habitual cannabis user. Therefore, probably, Mr X is not

the murderer.

j UN intervention in local conﬂicts usually leads to a more stable political

situation. A more stable political situation usually leads to economic growth.

Therefore, probably, UN intervention in this local conﬂict will lead to

economic growth.

k Almost all successful athletes have trained long and hard to become success-

ful. Therefore, if you train long and hard, you will become a successful

athlete.

l Many teachers at Lenman secondary school are known to smoke cannabis.

Mr X is a teacher at Lenman secondary school. Therefore, probably, Mr X

smokes cannabis.

m Most vegetarians eat eggs. A great many people in Berkeley are vegetarians.

Roger is from Berkeley. Therefore, probably, Roger eats eggs.

logic: inductive force116

n If Hansen is leaving early tomorrow, then, probably, he isn’t in the bar.

Hansen isn’t in the bar. So he is probably leaving early tomorrow.

6 The following passages contain inductive inferences. (A) Rewrite them as arguments

in standard form. (You may have to supply a missing quantiﬁer.) (B) Can you think

of any reasons why the sample might not be representative? If so, list them, and add

any comments you think relevant.

a The elimination of sweets and other junk food from school lunch menus has

resulted in improved student performance in schools all over the country,

and in every case in which it has been tried. If we do this at our school, then

we can look forward to improved performance.

b No communist system can succeed. Since communist regimes began early in

the twentieth century, every one has either collapsed, or is near collapse.

c Surprisingly, musicians have a higher average IQ than either doctors or

lawyers. A study of seventeen conductors of major orchestras found their

average IQ to be 17 points higher than that of UK doctors, and 18 points

higher than that of UK lawyers.

d Most teenagers who take illicit drugs have serious family problems. I know,

because as a counsellor for teenagers I have found that most of those who

have come to me and confessed to taking illicit drugs do have serious family

problems.

e Manchester United are an English team that have won the treble once

(domestic league championship, league cup tournament, and the European

tournament known as the ‘Champions League’), but they’re not going to win

it again. No English team has won it twice.

f Take vitamins for a long life; my uncle Bill is ninety-three, and hasn’t missed

a day of taking his vitamins for almost ﬁfty years.

g Studies have shown that people who regularly take vitamins live longer than

average. Jenna takes vitamins regularly, so probably she will live longer

than average.

logic: inductive force 117

the practice of

argument-

reconstruction

•Extraneous material 119

•Defusing the rhetoric 122

•Logical streamlining 123

•Implicit and explicit 125

•Connecting premises 132

•Covering generalisations 133

•Relevance 135

•Ambiguity and vagueness 138

Ambiguity • Vagueness

•More on generalisations 144

The scope of a generalisation

•Practical reasoning 147

•Balancing costs, beneﬁts and probabilities 150

•Explanations as conclusions 153

•Causal generalisations 156

•A short-cut 158

•Chapter summary 159

•Exercises 160

The goal of argument-reconstruction is to produce a clear and completely explicit state-

ment of the argument that the arguer had in mind. The desired clarity and explicitness is

achieved by putting all of the argument, and nothing but the argument, into standard

form: this displays the argument’s premises, intermediate conclusions and conclusion, and

indicates the inferences between them. The strength of the argument is understood in

terms of the concepts discussed in Chapters 3 and 4 – validity, inductive force, deductive

and inductive soundness. In this chapter, we begin to see, in more detail, how the practice

of reconstruction goes; in particular, we learn some ways of coping with commonly

encountered difﬁculties.

EXTRANEOUS MATERIAL

The ﬁrst step in analysing and reconstructing an argument is to identify its conclusion,

then its premises. But, as discussed brieﬂy in Chapter 1, much of what people say or write,

when advancing an argument, plays no argumentative role. Much is there for emphasis, or

is rhetorical, or plays some other role than that of expressing the propositions that properly

constitute the argument. When reconstructing arguments, then, we have to hive off this

extraneous material. Here’s a more extended example; again we’ve given each sentence a

number in order to facilitate a detailed discussion of it:

(1) Once again the problem of young people drinking in city centres and generally

creating chaos rears its ugly head. (2) The recent trouble in York was some of the

worst. (3) It happens over and over, so much that people just seem to shrug their

shoulders, accepting it as a fact of life, or a law of nature. (4) So are we simply

resigned to it? (5) Do we simply accept that our young people are going to waste the

best years of their lives acting like hooligans? (Or rather, being hooligans?) (6) Do we

stand idly by? (7) I don’t think so. (8) Not I, at any rate. (9) And there’s a ready

solution. (10) Let us turn to an old solution for a new problem: compulsory military

service. (11) Because they would learn habits of discipline, and something about

community spirit, it’s pretty obvious that young people would be a lot less likely to

cause trouble when ﬁnished.

The arguer’s conclusion here seems to be that Britain should introduce compulsory

military service for its youth. The most important premise is the conditional state-

ment that if compulsory military service were introduced, then the problem of drunken-

ness and hooliganism among British youth would be curtailed. Sentence 11 seems to

be provided as a premise in a sub-argument for that claim. But there is a lot of other

material:

•The ﬁrst two sentences function as stage-setting: they alert the reader to the problem

being discussed, and perhaps serve to emphasise the immediacy and severity of the

problem. Sentences 1–8, as a group, are intended to persuade the reader that the

problem is serious enough that something ought to be done about it. That much is

the practice of argument-reconstruction 119

surely a premise of the main argument; but it should be evident that they do not

provide an argument for that claim. They merely assert the claim in a rhetorically

charged way.

•The function of sentence 9 is simply to announce that the author is now going to turn

from stressing the gravity of the problem to suggesting a solution – in other words, that

the author is now going to give the argument.

•Sentence 10 asserts the conclusion. But it does not do so in the most economical or

straightforward way. The bit about the ‘old solution for a new problem’ is a rhetorical

ﬂourish that should be omitted from the reconstruction. Also, it seems clear that the

arguer is saying that compulsory military service should be introduced, not just that it

would solve the problem. The conclusion, then, should be rewritten as ‘Compulsory

military service should be introduced’ (there will be more on this type of ‘practical’

conclusion later in the chapter).

•Sentence 11 includes the words ‘it’s pretty obvious that . . .’ Phrases of that kind –

phrases that merely serve to emphasise the claim being made – should always be

eliminated from reconstructed arguments.

•Sentence 11 exempliﬁes a use of the word ‘because’ that should always be eliminated

from reconstructed arguments. Often we use ‘because’ when speaking of cause and

effect, as in ‘The cake is dry because it was baked too long’. In sentence 11, however,

the word does something else: it indicates a relation between premise and conclusion of

a sub-argument to the main argument. In particular, the arguer is giving the following

sub-argument:

P1) If British youth were to acquire habits of discipline and community spirit,

then the problem of drunkenness and hooliganism among them would be

reduced.

P2) If made to perform military service, British youth would acquire habits of

discipline and community service.

C1) If British youth were made to perform military service, the problem of

drunkenness and hooliganism among them would be reduced.

C1 serves as an intermediate conclusion in the arguer’s overall argument. The word

‘because’, in this usage, is equivalent to the word ‘since’, which functions in the following

way. If we say, ‘If there are no clouds, it isn’t raining’, then we have not asserted either that

it isn’t raining, nor that there aren’t any clouds (review the section in Chapter 3 on

conditionals if this is not clear). If we say, however, ‘Since there are no clouds, it isn’t

raining’, then we’ve asserted both. So what the word ‘since’ does is to transform a con-

ditional statement into a statement that asserts both the conditional and the antecedent

of that conditional, and thereby asserts its consequent. It provides a compact way of

expressing simple arguments of the form: ‘If P, then Q; P, therefore Q’. ‘Because’, in the

usage we are discussing, does exactly the same thing. And since our aim in reconstructing

arguments is to lay out the arguments explicitly and clearly, we should eliminate such uses

of ‘because’ and ‘since’, and unpack the arguments they serve to indicate. (The causal use

the practice of argument-reconstruction120

of ‘because’ is another matter, however; it will be discussed later in this chapter; see also

the discussion of ‘because’ in Chapter 1, pp. 20–22.)

Bearing in mind that the above argument laid out in standard form is a sub-argument for

C1, a reconstruction of the remainder of the argument might go like this:

C1) If British youth were made to perform military service, the problem of

drunkenness and hooliganism among them would be reduced.

P3) Something should be done to reduce the problem of drunkenness and

hooliganism among British youth.

C2) Britain should introduce compulsory military service for its youth.

We will be in a better position later in the chapter to say whether or not such an argument

is valid. The main lesson here is that the ﬁrst step in reconstructing an argument is to make

a list of the argument’s premises and conclusion that leaves out extraneous material, and

that expresses the premises and conclusion as concisely and clearly as possible. Note,

however, that making such a list is only the ﬁrst step towards a complete reconstruction.

A complete reconstruction also includes premises and conclusions that are only implicit in

the original argument (and which therefore do not appear on the initial list). A complete

reconstruction also displays the structure of an extended argument by displaying

intermediate conclusions. It should be clear that the correct argument tree is as shown in

Figure 5.1.

Figure 5.1

the practice of argument-reconstruction 121

DEFUSING THE RHETORIC

Much of the task of reconstruction is the task of clariﬁcation. In Chapter 2, we discussed

several linguistic phenomena that frequently impede clarity, including ambiguity,

vagueness, the differing roles of primary and secondary connotation and conversational

implicature, rhetorical questions, ﬁgures of speech, irony and implicit relativity. We will

deal with the speciﬁc problems of ambiguity and vagueness later in this chapter. At this

point we deal with some other impediments to clear reconstruction. Suppose Kemp has

been caught stealing money from the company, and someone says:

That damned Kemp’s been caught with his hand in the cookie jar again. He’s

history.

The arguer is reasoning is follows:

P1) If Kemp has been caught stealing money from the company, then he is going to

be ﬁred.

P2) Kemp has been caught stealing money from the company.

C) Kemp is going to be ﬁred.

As you can see, in giving the reconstruction, we have eliminated the metaphor ‘caught

with his hand in the cookie jar’, the expressive epithet ‘that damned Kemp’, and the slang

‘he’s history’. Not as colourful, but much more amenable to logical analysis. When

reconstructing, eliminate metaphors, expressive epithets and slang.

What exactly are expressive epithets? These are terms used to refer to some person, group

or other entity – just like a proper name such as ‘Gary Kemp’ or ‘Paris’ – but that

characterise the entity referred to for rhetorical purposes (non-logically persuasive pur-

poses, or non-persuasive purposes such as humour). Let us look at a well-known real

example that demonstrates how complex their use can be. In 2003, US and British forces,

along with smaller forces from some other countries, invaded Iraq, for the purpose of

removing the government and military capabilities of its president Saddam Hussein. His

military capabilities, it was claimed, included the so-called ‘Weapons of Mass Destruction’

(note that this itself might be regarded as an expressive epithet). American Secretary of

State Colin Powell had in March of that year announced a list of thirty countries that had

agreed to be named as supporting the invasion, including, of course, those that would

actually be contributing troops or other military assistance. He announced it as ‘The

Coalition of the Willing’. In the weeks before the invasion, however, leaders of France,

Germany and Belgium had strongly opposed the invasion, arguing that UN inspection

teams should be given more time to verify whether or not Iraq possessed illegal weapons,

which constituted the primary reason for the invasion. Here is a comment from a public

debate held at the time:

the practice of argument-reconstruction122

You think our coalition of the willing needs the Gang of Three? They can sit on the

fence; let ’em.

In the context, it was clear that the ﬁrst sentence was a rhetorical question: the speaker’s

intention was to assert that the answer is no, the coalition of the willing does not need the

Gang of Three. Rhetorical questions should always be rewritten as declarative sentences.

Now, as for the epithets. What the terms stand for, literally, are simply two groups of

countries: one supporting the invasion, and one opposed. ‘Coalition of the willing’ has a

rather positive ‘spin’ to it (for the others are made to sound ‘unwilling’, hence complacent

or perhaps cowardly), but ‘Gang of Three’ sounds distinctly negative, owing to the

connotation of ‘Gang of Four’, which signiﬁed a notorious group within the Chinese

communist government in the 1970s who were partly responsible for the disastrous

‘cultural revolution’ of Mao Tse-Tung’s later years. But shorn of all this spin and rhetoric,

these emotive associations, the factual content of the sentence is merely something like

this:

In order to undertake the invasion successfully, the invading countries and their

supporters do not require approval or support from France, Germany and Belgium.

The phrase ‘sit on the fence’ is, in this context, another pejorative phrase; the sentence

containing it seems to mean that approval and support from those countries is not needed.

The intended argument, then, was probably this:

P1) In order to undertake the invasion successfully, the invading countries and their

supporters do not require approval or support from France, Germany and

Belgium.

P2) If, in order to undertake the invasion successfully, the invading countries and

their supporters do not require approval or support from France, Germany and

Belgium, then they should undertake the invasion without it.

C) The invading countries should undertake the invasion without approval

or support from France, Germany and Belgium.

LOGICAL STREAMLINING

In Chapter 3 we devoted a good deal of attention to certain expressions whose logical

nature is comparatively easy to grasp. These include ‘if–then’, ‘not’, ‘every’, ‘all’ and ‘or’.

For example, one exercise asked you to translate sentences containing the comparatively

difﬁcult expressions ‘only if’ and ‘unless’ into easier forms using ‘if–then’ and, where

needed, ‘not’. So we learned that ‘A unless B’ means the same as ‘If not-B, then A’. In

general, when reconstructing arguments we should strive to display the logical relation-

ships in an argument in the simplest, clearest and most familiar ways possible. An example

will illustrate this:

the practice of argument-reconstruction 123

We read over and over that when all is said and done, what is best for the child is the

family. But what would the elimination of the marriage tax-credit mean? Less incen-

tive to marry. And what would that mean? Fewer couples getting married. And what

would that mean? A reduction in the proportion of children living in families.

It should be clear after the ﬁrst sentence that the arguer is expressing some conditionals: if

the marriage tax-credit is eliminated, then there will be less incentive to get married. If

there is less incentive to get married, then fewer couples will get married. If fewer couples

get married, then the proportion of children living in families will be reduced. But this,

according to the arguer’s ﬁrst sentence, should be avoided. Thus the argument might be

reconstructed like this:

P1) If the marriage tax-credit is eliminated, then there will less incentive to get

married.

P2) If there is less incentive to get married, then fewer couples will get married.

P3) If fewer couples get married, then the proportion of children living in families

will be reduced.

P4) The proportion of children living in families should not be reduced.

C) The marriage tax-credit should not be eliminated.

This reconstruction, however, leaves two intermediate conclusions implicit. A completely

explicit reconstruction represents it as an extended argument:

P1) If the marriage tax-credit is eliminated, then there will be less incentive to get

married.

P2) If there is less incentive to get married, then fewer couples will get married.

C1) If the marriage tax-credit is eliminated, then fewer couples will get

married.

P3) If fewer couples get married, then the proportion of children living in families

will be reduced.

C2) If the marriage tax-credit is eliminated, then the proportion of children

living in families will be reduced.

P4) The proportion of children living in families should not be reduced.

C3) The marriage tax-credit should not be eliminated.

The point we want to stress here is that we have replaced the language used by the arguer

to express these conditional propositions with explicit ‘if–then’ sentences. The language

used by the arguer is not especially unclear, but it is awkward to deal with because it does

the practice of argument-reconstruction124

not even take the form of proper sentences. Rewriting the material in terms of ‘if–then’

sentences makes the argument easier to handle and its logic more obvious.

This is just one example of what we mean by logical streamlining. There are many, many

ways in which ordinary language can be awkward to reconstruct, and in which logical

relationships can be concealed; so we cannot give anything like an exhaustive list of exact

rules for logical streamlining. But here are some ‘rules of thumb’ that you should apply

whenever you can do so in a way that remains faithful to the arguer’s apparent meaning:

1 Where appropriate, rewrite sentences as either conditional or disjunctive sentences of

one of the following forms:

If A then B. If not-A then not-B.

If not-A then B. If A then not-B.

A or B. A or not-B.

Not-A or B. Not-A or not-B.

2 Rewrite generalisations in one of the following forms, where the blank ‘ ’ is ﬁlled by

a quantiﬁer such as ‘all’, ‘some’, ‘most’, ‘no’, ‘almost all’, etc.:

F are G.

are not-G.

We will not stick to this religiously, as it is not always possible, and doing it will sometimes

distract from other points we are trying to make. What we will do, rather, is continue

to practise it on many occasions throughout the book. For example, in the section on

rewriting for rhetorical neutrality we employed simple ‘if–then’ sentences. If you pay

attention, you should gradually develop a feel for logical streamlining.

IMPLICIT AND EXPLICIT

Not only do actual statements of arguments typically include a lot of material that is

inessential to the argument, they often exclude some of what is essential to the argument:

some essential propositions are left implicit. Our task in reconstruction is to make the

argument fully explicit. To say that a proposition is implicit in an argument is to say that it

is part of the argument intended by the arguer – either as a premise or as the conclusion –

but that it has not actually been stated by the arguer. To make the proposition explicit

is simply to state it – in particular, to include it in our reconstruction of the argument. So a

large part of argument-reconstruction is to make explicit what was merely implicit in the

original statement of the argument.

Consider a very simple case:

Is Mr Jenkins well-educated? Well of course. Didn’t you know that he’s a successful

politician?

the practice of argument-reconstruction 125

The arguer might be presumed to be arguing as follows:

P1) Mr Jenkins is a successful politician.

C) Mr Jenkins is well-educated.

So rendered, the argument is invalid. Nor is it inductively forceful, since in order to know

whether or not the premise makes the conclusion probable, you have to know something

the argument’s premise does not tell us – namely whether or not successful politicians, at

least usually, are well-educated. But it is clear that, in drawing this inference, the arguer is

making the assumption that successful politicians are well-educated. We have to make this

assumption explicit:

P1) Mr Jenkins is a successful politician.

P2) All successful politicians are well-educated.

C) Mr Jenkins is well-educated.

Or perhaps we should write ‘almost all’ rather than ‘all’.

Let us now consider a real and more complicated example. The moa was a very large,

ﬂightless bird, which was native to New Zealand but which is now believed to be extinct.

The yeti is a large, white-furred ape, which is probably only mythical, but which some

people believe actually inhabits the Himalayas. Here is the argument:

The moa is thought to have been extinct for at least a hundred years. So naturally a

great deal of scepticism is met by Paddy Freaney’s claim to have seen a moa in 1993.

But as Freaney himself has pointed out, Freaney has climbed Mount Everest twice,

and has not claimed to have seen a yeti. So we ought to believe Mr Freaney’s claim.1

The ﬁrst task of argument-reconstruction should be to identify and, if necessary, to restate,

the conclusion of the argument. Now in this case it might seem obvious that the con-

clusion of this argument is stated explicitly in the last sentence: ‘we ought to believe Mr

Freaney’s claim.’ But this is not the most straightforward and informative way to put it.

Ask yourself: exactly what proposition is the ultimate concern of the arguer here? The

arguer attempts to persuade us to accept a certain claim of Paddy Freaney’s; but this does

not really tell us the ultimate concern of the arguer until we specify what claim that is.

Freaney’s claim, the one that ultimately concerns the arguer, is the claim that he saw a

moa. So what the arguer is really trying to persuade us of is that Paddy Freaney did see

a moa. Here then is a case in which the conclusion is at least partly implicit; none of the

sentences directly says that Paddy Freaney saw a moa. Indeed, it might plausibly be

suggested that the conclusion ultimately at issue here is one that is inferred from the

11 Sunday Star-Times, Auckland, New Zealand, 10 December 1995, p. C5.

the practice of argument-reconstruction126

proposition that Freaney saw a moa, namely, that the moa is not extinct. In that case it

would be even more obvious that the conclusion of the argument is only implicit in the

original statement of the argument. But let us not push the matter quite as far as that. For

simplicity we shall take the conclusion to be that Paddy Freaney saw a moa.

Once we have identiﬁed the conclusion, we must identify the argument’s premises. It is

clear that the ﬁrst two sentences in the example function as stage-setting, informing the

reader of some of the relevant concerns surrounding the issue, and are not premises of

the argument. The arguer is arguing that Paddy Freaney saw a moa; this proposition is

certainly not supported by the fact that the moa is thought to be extinct, nor by the fact

that many people doubt Freaney’s claim to have seen one. If anything, those facts make it

less credible that Freaney saw a moa. So, by the principle of charity, we should not take the

arguer to be citing those facts in support of the conclusion that Freaney saw a moa. Rather,

the function of these propositions is to acknowledge that there is reasonable resistance to

Freaney’s claim. This sort of thing is very common: very frequently, an arguer will begin by

explaining why there is opposition to his or her conclusion.

The only premise explicitly given is that Freaney has twice climbed Mount Everest, and

has not claimed to see a yeti. So our ﬁrst shot at a reconstruction might look like this:

P1) Paddy Freaney climbed Mount Everest twice, and did not claim to see a yeti.

C) Paddy Freaney saw a moa.

Now this is a start, but clearly it does not do justice to the arguer’s intentions. As it stands,

the argument is neither deductively valid nor inductively forceful. To see this, suppose the

only information you are given is that a certain person climbed Mount Everest twice, and

that that person did not claim that he saw a yeti. Does that give you any reason to infer that

that person saw a moa? Obviously not. P1 does not support the conclusion by itself.

Yet the argument as originally intended by the arguer surely does have at least some

inductive force. Therefore, the arguer must be implicitly relying upon some further

premise or premises, which we should try to make explicit. One proposition, which

is surely relied upon by the argument, but which is not explicitly stated in the

argument, is simply that Paddy Freaney claimed he saw a moa. The second sentence

almost states this explicitly, but does not quite do so. So we should include this in our

reconstruction:

P1) Paddy Freaney has claimed he saw a moa.

P2) Paddy Freaney climbed Mount Everest twice, and did not claim to see a yeti.

C) Paddy Freaney saw a moa.

This is better. We now have in the premises, it seems, a statement of all the particular

facts about Paddy Freaney from which the arguer is inferring that Paddy Freaney saw a

the practice of argument-reconstruction 127

moa. But still we have not made everything explicit. In order to see this, ask yourself, why

does P2 – in view of the fact that Paddy Freaney claimed he saw a moa – support

the conclusion that he did see a moa? It is something like this: the arguer seems to be

responding to the charge that Freaney is a liar, that he wishes fraudulently to claim credit

for a certain sort of zoological discovery. As against this, the arguer points out that Freaney

climbed Everest twice without claiming a yeti-sighting. But surely, reasons the arguer, if a

person were the sort to go around making false claims about seeing strange creatures, then

if he has twice climbed Mount Everest, he would probably have claimed to see a yeti (for

such a person, having visited Everest, surely would not be able to resist claiming to have

seen the notorious yeti). But Freaney climbed Everest twice without making such a claim,

so he must not be such a person. If he is not such a person, then he didn’t lie about the

moa. So, if he said he saw a moa, he did see a moa.

What is missing from the preceding reconstruction, then, is an assumed generalisation:

a person who has visited Mount Everest without claiming to see a yeti is not a person

who would fabricate the sighting of a creature whose existence is disputed. This is a

generalisation because it is not something said on the basis of knowledge about Paddy

Freaney in particular. It is plausible to say, as a general fact about human nature, that a

person who wishes to tell ‘tall tales’ about some particular kind of thing is unlikely to pass

up a favourable opportunity to do so.

The argument implicitly depends upon this generalisation as a premise; hence in our

reconstruction we should make it explicit:

P1) Paddy Freaney has claimed he saw a moa.

P2) Paddy Freaney climbed Mount Everest twice, and did not claim to see a

yeti.

P3) A person who lies about sighting creatures whose existence is disputed would

claim to see a yeti, if he or she were to climb Mount Everest.

C) Paddy Freaney saw a moa.

Note that, although we could have produced a valid argument by writing ‘everything

Paddy Freaney says is true’ (or an inductively forceful argument by writing ‘most of what

Paddy Freaney says is true’), doing so would have failed to take into account the relevance

of P2. If we had written that premise in place of the actual P3, then the conclusion could

have been inferred from that premise along with P1, and P2 would have played no role in

the argument. This is important, because the arguer clearly means to give us a very speciﬁc

reason to believe this particular claim of Freaney’s; he or she is clearly not simply relying on

Freaney’s general honesty or trustworthiness.

This reconstruction of the argument now seems to include the relevant facts about Paddy

Freaney upon which the arguer is relying, and it includes the generalisation upon which

the arguer is (implicitly) relying. We could make its structure a bit more explicit by

the practice of argument-reconstruction128

making an intermediate conclusion explicit, and adding one further relevant point about

the moa (note that we have had to change the numbering of the premises):

P1) Paddy Freaney climbed Mount Everest twice, and did not claim to see a yeti.

P2) A person who lies about sighting creatures whose existence is disputed would

claim to see a yeti, if he or she were to climb Mount Everest.

C1) Paddy Freaney does not lie about sighting creatures whose existence is

disputed.

P3) Paddy Freaney has claimed he saw a moa.

P4) The moa is a creature whose existence is disputed.

C2) Paddy Freaney saw a moa.

The argument is not deductively valid. To see this, suppose that the premises P1–P4 of the

argument are indeed true. In that case, Paddy Freaney was not lying, making up a story, in

saying that he saw a moa. But it does not follow that Paddy Freaney did see a moa, for he

could have been mistaken rather than lying. In that case, his claim to have seen one was not

a lie, but nor was it true. Thus the inference from C1, P3 and P4 to C2 is invalid. So the

argument as a whole is invalid. In order to make this clear, we can represent the argument

like this:

P1) Paddy Freaney climbed Mount Everest twice, and did not claim to see a yeti.

P2) A person who lies about sighting creatures whose existence is disputed would

claim to see a yeti, if he or she were to climb Mount Everest.

C1) Paddy Freaney does not lie about sighting creatures whose existence is

disputed.

P3) Paddy Freaney has claimed he saw a moa.

P4) The moa is a creature whose existence is disputed.

C2) Either Paddy Freaney saw a moa, or he was mistaken in believing he did.

C3) Paddy Freaney saw a moa.

This makes the argument’s invalidity quite obvious: the inference from C2 to C3 is

invalid. Might the argument be inductively forceful, then? What follows from the prem-

ises is that Freaney either saw a moa or was mistaken. In order to conclude that Freaney

probably saw a moa, we would thus need to know which of these alternatives is more

likely. Since the argument does not give us any information relevant to this, we are not

really in a position to judge the argument inductively forceful.

Note ﬁnally that having begun with an argument whose structure was like this:

the practice of argument-reconstruction 129

We arrived at a much more complicated one like this:

Let us now look at an example from down under (Australia this time), which shows how

making a generalisation explicit can reveal the weakness of an argument:

Figure 5.2

Figure 5.3

the practice of argument-reconstruction130

The suggestion, that in order to protect children from sunburn a rule should be

instituted requiring all children at our school to wear a sun hat when they are

outside after 11 a.m., is unacceptable. For clearly such a rule would be an infringe-

ment upon the freedom of the individual.

The conclusion, obviously, is that a sun hat rule at school would be unacceptable. The only

explicit premise is that given in the second sentence. So we may begin with:

P1) A sun hat rule at school would infringe upon the freedom of the individual.

C) A sun hat rule should not be instituted.

Obviously a generalisation is being implicitly assumed. A ﬁrst shot at making it explicit,

and which might well seem to capture what the arguer must have been thinking, might

be this: that no rule that infringes upon the freedom of the individual is acceptable. So

we write:

P1) A sun hat rule at school would infringe upon the freedom of the individual.

P2) No rule that infringes upon the freedom of the individual is acceptable.

C) A sun hat rule at school is unacceptable.

Here is a deductively valid argument. If the premises are true, then certainly the con-

clusion is true. However, this does not establish that the conclusion is true. For that, we

have to ask whether the premises are true – whether the argument is not only deductively

valid but deductively sound.

Surely P1 is true, in a sense: by deﬁnition, a rule of any kind restricts, hence infringes

upon, the freedom of those to whom it applies – in this case the children of the school

in question. So let us grant that P1 is true. But look at P2. We often hear this sort of

statement, and we are often so impressed by such a phrase as ‘the freedom of the indi-

vidual’ that we accept the statement as true. We have the feeling that ‘the freedom of the

individual’ is something important and valuable; therefore that anything which takes it

away must be a bad thing. But, as stated here, this proposition is absurd. For, as we just

said, all rules ‘infringe upon the freedom of the individual’. So what P2 amounts to is

the absurd proposition that all rules are unacceptable. Unless you are a kind of radical

anarchist, you have to conclude that this argument is not deductively sound.

Now there may be some less sweeping generalisation that the argument might employ

instead of P2, which would be more plausible, yet sufﬁcient to obtain the desired con-

clusion. But the arguer has not given any hint as to what generalisation this might be. So

we cannot credit the arguer with actually having supplied a helpful argument on the issue.

They may have something more plausible in mind, but they have not conveyed it.

This argument, by the way, is a good illustration of the importance of distinguishing

between argument and rhetoric. It was by thinking carefully about the precise literal

the practice of argument-reconstruction 131

meanings of the words expressing the argument that we came to see that the argument is

unsound. In order to do this, however, we had to have some courage: a phrase such as ‘the

freedom of the individual’ is rhetorically powerful; nevertheless, it is just not literally true

that every rule that ‘infringes upon the freedom of the individual’ is unacceptable – on the

contrary, it is absurd to suggest it.

CONNECTING PREMISES

Look back at the argument about successful politicians (pp. 125–126). And now consider

this argument:

We can assume that inﬂation will increase, because we know that consumer conﬁdence is

increasing.

Reconstructing, we might write:

P1) Consumer conﬁdence is increasing.

C) Inﬂation will increase.

As it stands, the argument is neither valid nor inductively forceful. But we can see that the

arguer is implicitly assuming that, if consumer conﬁdence is increasing, then inﬂation will

increase. So we write:

P1) Consumer conﬁdence is increasing.

P2) If consumer conﬁdence is increasing, then inﬂation will increase.

C) Inﬂation will increase.

In each case – the inﬂation argument and the politician argument – the premise, which

had to be made explicit in order to make the argument valid, is what we call a connecting

premise. We have had to add connecting premises in many of the arguments we have so

far considered. Usually, when people give arguments, the premises they give explicitly will

be only those which pertain to the particular facts or subject-matter they are talking about.

For example, someone might say, ‘My cat won’t have kittens; she’s been spayed’. The

arguer explicitly sets forth the relevant fact about her particular cat, but doesn’t bother to

state explicitly the generalisation she assumes, that spayed cats can’t have kittens. Probably

she assumes this to be common knowledge; if she did not, then she would have made the

premise explicit. The point then is that arguers very often leave implicit the more general

assumptions they make. That is what happened in the inﬂation case and the politician case

discussed earlier.

We cannot assume, however, that whenever an argument, as explicitly given, is neither

valid nor inductively forceful, the intended argument is valid or inductively forceful. It is

the practice of argument-reconstruction132

not always the case that the arguer is implicitly relying on an appropriate connecting

premise. Sometimes people just do give bad arguments, ones that are neither valid nor

inductively forceful. That is what may have happened in the Paddy Freaney case. In

further cases, the implicit connecting premise is just not true, in which case the argument

is unsound. That’s what happened in the sun hat case.

COVERING GENERALISATIONS

In the politician case, the connecting premise was a generalisation (review the discussion

of generalisations in Chapter 2 if you are not clear about what a generalisation is).

Connecting premises are usually generalisations. But in the inﬂation case the connecting

premise we used was a conditional (see Chapter 3). This is also common. However, there

is an important relationship between conditionals and generalisations that must be

appreciated. Consider the following propositions:

a If Betty is a Siamese cat, then she has blue eyes.

b All Siamese cats have blue eyes.

(a) is a conditional, (b) is a generalisation. The special relationship in which they stand is

that (b) is a covering generalisation for (a). (We can also say that (a) is an instance of (b),

as is common in logic.) Note that (a) may be inferred from (b); the argument from (b) to

(a) would be valid. But covering generalisations need not be hard generalisations: ‘If Jane’s

cat is Siamese then its eyes are blue’ is an instance of ‘All Siamese cats have blues eyes’, but

it is also an instance of ‘Most Siamese cats have blues eyes’. In such a case the inference

from generalisation to instance is inductive rather than deductive.

There is one further aspect to the relationship between covering generalisations and their

instances that should be appreciated. Another way to express the proposition expressed by

the generalisation (b) is this:

c If something is a Siamese cat, then it has blue eyes.

Or we could say, ‘Whatever X may be, if X is a Siamese cat, then X has blue eyes’. This

is exactly like (a), except we use the indeﬁnite pronoun instead of the name ‘Betty’; this

makes the conditional statement into a generalisation. In other words, generalisations of

the ‘All A are B’ sort are themselves conditionals, except they are generalised. (b) and

are B’, as in ‘No ungulates are carnivores’. This says, in effect, that all ungulates are

non-carnivores. So it could be expressed as ‘If something is an ungulate, then it is not a

carnivore’.

Very often, when people assert conditionals, they do so on the basis of some covering

generalisation. It is important to be aware of this when reconstructing arguments. Suppose

you are given the inﬂation argument, but without a connecting premise:

the practice of argument-reconstruction 133

P1) Consumer conﬁdence is increasing.

C) Inﬂation will increase.

Suppose you reply to the arguer by saying that you just have no idea whether or not P1

constitutes a reason to infer C, that inﬂation is going to increase. You point out that the

argument, at any rate, is certainly not valid as it stands, and would not be inductively

forceful. Suppose that the arguer now tries to satisfy you with:

P1) Consumer conﬁdence is increasing.

P2) If consumer conﬁdence is increasing, then inﬂation will increase.

C) Inﬂation will increase.

Does this really improve the argument? It does make it valid. But this doesn’t really help

you. All that P2 says is that if P1 is true, then so is C. You have already said that you have

no idea whether P1 constitutes a reason to infer C. The arguer is not going to convince you

merely by asserting P2; to do so is merely to assert that P1 is a good reason to infer C. So

the new version is not really an advance on the ﬁrst version; although you cannot deny that

the new version of the argument is valid and fully explicit, you can’t really say whether the

argument is sound, even if you grant that the arguer does know that P1 is true (for more

on this, see the section on begging the question in Chapter 7, pp. 233–234).

Suppose, however, that you wished to ﬁnd out whether or not to believe P2. Well P2 says

that if consumer conﬁdence is now increasing (which it is), then inﬂation will increase. So

the only way to ﬁnd out whether P2 is true would be to look into the future to see whether

inﬂation does increase. But that you cannot do. So what do you do? What you need is to

ﬁnd out whether, in general, increases in consumer conﬁdence bring about increases in

inﬂation. And that you can ﬁnd out, by doing some statistical research (consumer con-

ﬁdence is deﬁned in terms of how much people buy, and how much they borrow in order

to buy). So what you really need to know, and what it is possible to ﬁnd out, is whether the

following covering generalisation is true:

Whenever consumer conﬁdence increases, inﬂation increases.

Probably it isn’t, but the corresponding soft generalisation might well be true:

Usually, when consumer conﬁdence increases, inﬂation increases.

This could be established by inductive inference from a survey of past cases in which

consumer conﬁdence increased.

So, the arguer giving the inﬂation argument gives a conditional premise rather than a

generalisation, but if the arguer believes the conditional, he or she probably does so on the

the practice of argument-reconstruction134

basis of believing the corresponding covering generalisation. Since that is what the arguer

is assuming at bottom, that is what should be included in the reconstruction of the

argument. If we do not do this, then our analysis of a given argument may be superﬁcial.

Indeed, it is easy to reconstruct an argument as valid in a completely superﬁcial way,

if we do not take pains to discover what connecting premises an arguer is relying on at

bottom. For example, the following argument might have been given on the evening of the

28 June 1914:

P1) If the Austrian Archduke Ferdinand has been assassinated today, then a

general war involving all the European powers will soon break out.

P2) The Austrian Archduke Ferdinand has been assassinated today.

C) A general war involving all the European powers will soon break out.

Now in fact this argument would have been sound: the Archduke was assassinated that

day, and that single event touched off what would become known as the Great War,

later as the First World War. But someone not well-apprised of the political situation in

Europe at the time would have needed a lot of explanation in order to see why they should

accept P1. P1 is a connecting premise that ensures validity, but it hardly begins to tell us

why the arguer thinks that a single assassination will lead to a general war involving several

countries. In reconstructing, we should try to bring out as much of this as we can. Con-

necting premises are almost always necessary, but they can fail to be sufﬁcient to bring

out the real basis of an argument.

Finally, you should take care to distinguish the relationship we have just been discussing

between conditionals and generalisations from the following sorts of cases:

If all men are mortal, then all women are mortal.

If no men are mortal, then no women are mortal.

If all men are mortal, then Socrates is mortal.

If Socrates is mortal, then all men are mortal.

These are conditionals that have generalisations as antecedents, as consequents, or as both.

They are quite common.

RELEVANCE

This chapter began with a discussion of the necessity of eliminating extraneous material

from argument-reconstructions. We turn now to some further aspects of this, and to some

cases where the matter is more complex. Consider this argument:

the practice of argument-reconstruction 135

At Les Champignons they are usually fully booked (Professor Gilmour once took me

to dine there). So we can safely expect Les Champignons to be fully booked tonight.

Without bothering to reconstruct, you can see that this would be an inductively forceful

argument (of course it isn’t deductively valid). You might try reconstructing the argument

like this:

P1) Les Champignons is usually fully booked.

P2) Professor Gilmour once took me to dine at Les Champignons.

C) Probably, Les Champignons will be fully booked tonight.

But, if you think about it, there is no point in including P2 in the reconstruction of the

argument. P1 alone is the basis for thinking that the restaurant will be fully booked; that

the arguer once dined there with Professor Gilmour is irrelevant. When a proposition

stated by the arguer is irrelevant to the reasoning that delivers the conclusion, that

proposition should not be included in a reconstruction of the argument.

It might seem that the only reason not to include irrelevant material in an argument is that

it would be distracting. But in fact it can affect our assessment of the argument in a more

important way. For suppose P1 is true, but P2 is not; the arguer, wishing to boast of a

greater intimacy with Professor Gilmour than they in fact enjoy, ﬁbbed when telling us

that they dined out with him. If we were to discover this, yet persist in the above

reconstruction of the argument, we should have to pronounce the argument to be

unsound. Indeed, upon discovering the lie and becoming annoyed with the arguer, we

might well be eager to do just this. But this would be wrong, because P2 is irrelevant to the

argument. The argument should be represented like this:

P1) Les Champignons is usually fully booked.

C) Probably, Les Champignons will be fully booked tonight.

Since P1 is true, and the inductive inference is reasonable, the argument is inductively

sound.

This is an obvious point, but some cases are more subtle. In such cases it is a point that

is easy to lose sight of, especially when we wish to refute the argument. Consider this

example:

If the tuna industry is not regulated more stringently, it will collapse altogether,

because tuna populations will vanish. The evidence is obvious: tuna catches have

decreased signiﬁcantly every year for the past nine years. Indeed, because of

depleting stocks, the Mid-Paciﬁc Tuna Company went out of business.

Suppose we initially reconstruct the argument as follows:

the practice of argument-reconstruction136

P1) Tuna catches have decreased signiﬁcantly every year for the past nine years.

P2) Last year, the Mid-Paciﬁc Tuna Company went out of business.

C) If the tuna industry is not regulated more stringently, it will collapse

altogether.

For the moment, we leave out connecting premises. Here the arguer is claiming that P1

supports the conclusion by itself. But the arguer also seems to regard P2 as providing some

additional evidence, in the form of an inductive inference from one case to the general

proposition that tuna stocks have declined sufﬁciently to cause difﬁculty for the tuna

industry as a whole. So surely P2 is not completely irrelevant to the argument. Both P1 and

P2 support the conclusion. Suppose now you discover that, although P1 is true, P2 is false,

because the Mid-Paciﬁc Tuna Company did not go out of business; rather, it was taken

over by the larger Pan-Paciﬁc Tuna Company. You might then conclude that since P2 is

false, the argument is unsound, end of story. You might, indeed, exploit this mistake in

attempting to discredit the arguer. If you were a person who opposed greater regulation of

tuna ﬁshing, drawing attention to this factual error might be a good rhetorical strategy to

use in persuading people not to listen to arguments for increased regulation. Nevertheless,

it would be a mistake from the point of view of critical thinking. This is simply because P1,

by itself, constitutes a good reason for accepting the conclusion. To ﬁxate upon the falsity

of P2 simply diverts attention from the arguer’s having cited P1. According to the

principle of charity, we should simply omit P2 in our ﬁnal reconstruction of the argument.

More exactly: both P1 and P2, quite independently of each other, would support the

conclusion. So really we should regard the arguer as having given two arguments for the

conclusion, one of which we know to be unsound. So according the principle of charity,

we should now focus on the other argument, the one utilising P1. Adding the needed

connecting premises and an intermediate conclusion, we get:2

P1) Tuna catches have been decreasing signiﬁcantly for the past nine years.

P2) If tuna catches have been decreasing signiﬁcantly for the past nine years, then,

if the tuna industry is not regulated more stringently, the tuna population will

vanish.

C1) If the tuna industry is not regulated more stringently, the tuna population

will vanish.

P3) If the tuna population vanishes, the tuna industry will collapse altogether.

C2) If the tuna industry is not regulated more stringently, it will collapse

altogether.

2 It might be more plausible to reconstruct this argument as inductive rather than deductive, but we have

ignored this in order to maintain the focus on the point about relevance.

the practice of argument-reconstruction 137

This reconstruction makes for a plausible argument as it stands. There are two comments

that it may be useful to make.

First, note that, as usual, we have deleted the phrase ‘the evidence is obvious’, which

adds nothing to the substance of the argument. Second, note that we have applied our

policy of logical streamlining fairly rigorously in this case. Most conspicuously, the

argument contained a non-causal use of ‘because’, functioning in a way similar to ‘since’

(see pp. 20–22). We replaced it with a conditional and a statement of the antecedent

of the conditional as a separate premise, thereby ‘opening up’ the logical texture of the

argument.

It is easy to see that the argument from C1 and P3 to C2 is valid. Suppose that the tuna

industry is not regulated more stringently. Then according to C1, the tuna population

will vanish. But if so, then according to P3, the tuna industry will collapse. So it follows

from C1 and P3 that if the tuna industry is not regulated more stringently, then the

tuna industry will collapse; which is exactly what C2 says. (This is an example of a ‘chain

argument’, as discussed near the end of Chapter 3.)

Returning now to the main theme of this section. The basic moral of this section is that the

truth-values of the premises actually advanced by an arguer can be more or less relevant

to the soundness of the argument. Sometimes it is highly relevant that a given premise is

false, sometimes it is much less so. It depends upon the nature of the mistake, and upon

the role played in the argument by the premise. The degree of relevance must therefore be

taken into account in the process of reconstruction.

AMBIGUITY AND VAGUENESS

If our explanations of ambiguity and vagueness are not clear to you, then you should

review the discussions of those concepts in Chapter 2. In this section, we explain how to

cope with vagueness and ambiguity when you encounter it in arguments.

Ambiguity

In reconstructing arguments, we have to eliminate any ambiguities in the original state-

ment of the argument. If the original statement contains an ambiguous sentence, we have

to decide which of the possible interpretations was most likely intended by the arguer,

and, in our reconstruction of the argument, rewrite the sentence, choosing a form of words

that conveys the intended meaning unambiguously.

Let us take an example. Suppose that Jane, a Londoner, decides to invest some money in

the share market (the stock market). She decides to look for an investment advisor, and

ﬁnds an advertisement which runs as follows:

Sharemasters: London’s leading personal investment advice service!

the practice of argument-reconstruction138

Suppose that this expresses a true proposition, and Jane accepts that what it says is true;

she accepts that Sharemasters is London’s leading personal investment service. Assuming

that it would be fraudulent to publish such a claim if it were not true, Jane reasons as

follows (for simplicity, we will ignore the reference to London in the advertised claim; this

will not affect the point we are making):

P1) Sharemasters is the leading personal investment service.

P2) If I employ a personal investment service, then I should employ the leading

personal investment service.

C) If I employ a personal investment service, then I should employ

Sharemasters.

This looks to be a deductively valid argument. But this is not quite clear, because P1 is

ambiguous. What does ‘leading’ mean, in this context? It could mean (and this is no doubt

what the advertisers hope that people like Jane will think it means) that Sharemasters is

the most effective personal investment service – that it secures better returns for its clients

than other personal investment services. But it could also mean that Sharemasters is

the biggest such organisation – in the sense of having the most clients (this is the sense

in which McDonald’s is the world’s leading restaurant); it might even mean that Share-

masters is the most proﬁtable personal investment service – that is, that it makes the

most proﬁts for the owners of Sharemasters itself, not necessarily for its clients (after all,

this organisation is a business, and proﬁtability can plausibly be said to be the measure of

who is the ‘leader’ in a certain ﬁeld of business). Suppose now that you wish to evaluate

Jane’s argument. You are aware of the ambiguity, so you rephrase P1 in each of the three

ways, yielding three arguments:

A P1) (a) Sharemasters secures higher returns for its clients than any other

personal investment service.

P2) (a) If Jane employs a personal investment service, then she should

employ the personal investment service that secures higher returns for its

clients than any other personal investment service.

C) If Jane employs a personal investment service, she should employ

Sharemasters.

B P1) (b) Sharemasters makes more proﬁts for its own shareholders than any

other personal investment service.

P2) (b) If Jane employs a personal investment service, then she should

employ the one that makes more proﬁts for its own shareholders than any

other personal investment service.

C) If Jane employs a personal investment service, she should employ

Sharemasters.

the practice of argument-reconstruction 139

C P1) (c) Sharemasters is the biggest personal investment service.

P2) (c) If Jane employs a personal investment service, then she should

employ the biggest personal investment service.

C) If Jane employs a personal investment service, she should employ

Sharemasters.

Now all three arguments are deductively valid. But are any of them sound? First of all

consider arguments B and C. Even if we assume that P1(b) and P1(c) are true, it does not

seem that these are sound arguments, because it does not seem that either P2(b) or P2(c)

are true. Perhaps they have some plausibility – since presumably if Sharemasters were

highly unsuccessful at making money for its clients, then it would not have grown so big or

become so proﬁtable. But these would not be very reliable assumptions; to reason in the

manner of C, for example, would be like concluding that since McDonald’s is the biggest

restaurant in the world it has the best food.

So you can conclude that Jane’s argument has a good chance of being sound only if

argument A is what she had in mind. Suppose you investigate, and ﬁnd that it is true that

Sharemasters is the biggest as well as the most proﬁtable personal investment service in

London. Suppose you ﬁnd, however, that it is not the most effective personal investment

service in London; its size and proﬁtability are due to its high fees, its organisational

efﬁciency and effective advertising. Hence P1(b) and P1(c) are true, but P1(a) is false. You

must therefore conclude that, although it is valid, argument A is unsound. Since neither

B nor C seems to be sound, you must conclude that Jane’s original argument is unsound;

in none of the three possible interpretations does it appear to be sound.

Eliminating the ambiguity of the original argument was crucial in discovering this, for

one could very easily think that the original argument was sound. Advertisements of

this kind may be said to exploit this sort of ambiguity. If Sharemasters is indeed the

largest personal investment service in London, but not the most effective, then the slogan

does express something true; yet the advertisers might hope that readers will interpret the

claim along the lines of argument A (or possibly along the lines of B, making the

questionable assumption that the biggest service of a given sort is likely to be the most

effective).

Remember that a primary purpose of reconstruction is to represent the propositions that

constitute an argument in the clearest possible way. Thus we should have no qualms about

changing the language used to express those propositions; in changing it, we are only trying

to gain a better grasp of what the arguer was thinking. There is no guarantee that we will

not change or distort the arguer’s thinking, but there is no point in allowing ambiguous

language to remain unchanged. For we simply cannot evaluate an argument if we do not

know exactly what argument we are evaluating. If we simply cannot decide between two

interpretations of an ambiguity, then we must give both interpretations of the argument,

and evaluate the two arguments independently.

the practice of argument-reconstruction140

Vagueness

As noted in Chapter 2, many words and phrases are vague in the way that ‘bald’ is vague.

Examples include ‘tall’, ‘orange’, ‘heap of sand’ (i.e. we cannot draw a precise boundary

between tall and not-tall, between orange and red, and cannot say exactly how many grains

of sand you need to have a heap). Each such word pertains to a certain quality, such as

height, region of the colour spectrum (which proceeds gradually from red through orange,

yellow, green, blue and violet), or amount of sand, which has ‘fuzzy’ boundaries, but the

meaning of the term is clear. The terms have vague extensions (the range of things to which

they apply) but the concepts or ideas they express are not vague.

These sorts of words seldom present problems for actual argument-reconstruction and

assessment.3 More important for critical reasoning are words whose actual meanings are

vague. Indeed, many of the most rhetorically powerful or emotionally provocative words

in public (and private) discourse are vague in this way. Consider:

As pointed out in Chapter 2, we often have the feeling that these things are bad, or that

they are good, without any precise idea of what we mean by them. What they signify is

typically a whole group or cluster of things that are not uniﬁed in any exact way.

Let us take ‘conservative’ (in the political sense) as our example. There are various

attributes often associated with someone’s being ‘conservative’:

Conservative

•Believes in minimum government.

•Favours free market economics.

•politics/political •radical

•liberal •ideology

•elitism •rights

•racism •responsibility

•conservative •love

•sovereignty •weapons of mass destruction

•terrorism •political correctness

•freedom ﬁghter

3 But they do cause trouble for logic. Consider the term ‘sand dune’. There is no exact rule for how much

sand is needed to constitute a sand dune, but here is one proposition about sand dunes that seems undeniable: if

X is a sand dune and one grain of sand is removed from X, then X is still a sand dune. But now suppose that X is

a sand dune. If we remove one grain of sand from X, then X is still a sand dune. But then if we remove one grain

of sand from this, we still have a sand dune. And so on. But then eventually we run out of sand, so we have no

sand dune. So at some point, X was a sand dune consisting of n grains of sand for some number n, such that X

ceased to be a sand dune, upon the removal of one grain of sand. But that seems absurd; we cannot imagine

a sand dune such that removing one grain of sand destroys its status as a sand dune. So we seem to have a

contradiction. This paradox – Paradox of the Heap or Sorites Paradox – was puzzled over by the ancient Greeks,

and there is still no consensus as to how to avoid the apparent contradiction.

the practice of argument-reconstruction 141

•Favours privatisation of government industries and services.

•Against the dole, welfare, etc.

•Supports ‘traditional’ values – pro-family, anti-gay, etc.

•Against government help for minorities, women, etc.

•Supports strong police, military, severe prison sentences.

•Supports business as against labour, environmental groups.

Someone could rightly be called ‘conservative’ without exhibiting all these attributes or

tendencies. Exactly which attributes you must have, and which you must not have, to be a

conservative, is simply not clear. So ‘conservative’ is vague.

Now, in reconstructing arguments, the best thing to do with vague words is simply to

eliminate them. This can be seen from the following example:

MP Jeremy Price has made his conservative stance clear by favouring ‘traditional

values’ and stronger sentencing for criminals. Therefore, we can certainly assume he

will oppose any new laws protecting the environment.

It might occur to you to represent this as a two-stage argument, thus:

P1) Jeremy Price favours ‘traditional values’ and stronger sentencing for

criminals.

C1) Jeremy Price is a conservative.

C2) Jeremy Price will oppose new laws protecting the environment.

The inferences from P1 to C1, and from C1 to C2, depend upon implicit generalisations,

which, having learned earlier lessons well, you know you would do well to make

explicit:

P1) Jeremy Price favours ‘traditional values’ and stronger sentencing for criminals.

P2) All those who favour ‘traditional values’ and stronger sentencing for criminals

are conservatives.

C1) Jeremy Price is a conservative.

P3) All conservatives oppose new laws protecting the environment.

C2) Jeremy Price opposes new laws protecting the environment.

The argument from C1 and P2 to C2 is deductively valid, but it might then occur to you

that P3 is implausible. Surely not every conservative is so disdainful of environmental

restriction. So you replace ‘all’ with ‘most’:

the practice of argument-reconstruction142

P1) Jeremy Price favours ‘traditional values’ and stronger sentencing for criminals.

P2) All those who favour ‘traditional values’ and stronger sentencing for criminals

are conservatives.

C1) Jeremy Price is a conservative.

P3) Most conservatives oppose new laws protecting the environment.

C2) Probably, Jeremy Price will oppose new laws protecting the environment.

Now this argument might seem plausible to the average person; it might seem to be

inductively sound. But the argument appears better than it is, because of the presence of

the word ‘conservative’. And in fact, all the actual logic of the original argument can be

reproduced without making use of that word at all. It is simple: The actual evidence the

arguer has for their conclusion that Jeremy Price will oppose new environmental laws is

that Price favours traditional values and stronger sentencing for criminals. The arguer

supplies no further evidence, and the word ‘conservative’ plays no role at all. Thus, adding

the necessary generalisation, we might just as well represent the argument like this:

P1) Jeremy Price favours traditional values and stronger sentencing for criminals.

P2) Most people who favour traditional values and stronger sentences for criminals

oppose new laws protecting the environment.

C) Probably, Jeremy Price opposes new laws protecting the environment.

This remains inductively forceful, and it is no less inductively forceful than the previous

version. But the inductive soundness of this argument is far from certain, because P2 is

far from certain. This reconstruction thus makes the weakness of the original argument

perfectly clear. It does so by removing the distraction created by the word ‘conservative’

(even if you do think that P2 is true, you have to admit that this reconstruction centres our

attention on the real issue).

Since many of the most rhetorically highly charged words in public discourse are

also vague, eliminating them from our argument-reconstructions achieves two things: it

clariﬁes the argument, and, by eliminating emotionally provocative words, enables us to

focus without distraction upon the logic of the argument.

The best thing to do with ambiguous or vague language, then, is simply to replace it with

language that is not vague or ambiguous. The aim is to employ language that will express

the intended propositions without ambiguity or vagueness. But this is not always possible.

Where a sentence is ambiguous, we cannot always tell which of the different possible

interpretations was intended by the arguer, even if we apply the principle of charity. In

such a case we can assess each of the possible versions of the argument, but we may have

to confess that we cannot tell which version the arguer intended. And – especially where

the language used by the arguer is vague rather than ambiguous – we have to admit that

the practice of argument-reconstruction 143

the arguer’s thinking may simply have been vague or confused, not just his or her language.

Indeed, where vague words such as those listed above play a role in an argument, this is

very often the case. In constructing your own arguments, such words are best simply

avoided. They tend to obscure the issue rather than clarify it. However, not all vague

language can be removed. We will return to this in the next chapter.

MORE ON GENERALISATIONS

As we noted in Chapter 2, only hard generalisations can rightly be conveyed by using a

quantiﬁer-word like ‘all’, ‘no’ or ‘every’. Indeed, that is the usual function of those words –

to make it perfectly explicit that a hard generalisation is what is intended. For example,

someone at a meeting of Parliament might say, ‘Every single MP in this chamber takes

bribes’, rather than ‘MPs in this chamber take bribes’. Soft generalisations, indeed, are very

often expressed without any quantiﬁer at all, as in ‘Children like sweeties’. Other times, we

add a quantiﬁer such as ‘most’ or ‘almost all’ to a soft generalisation, in order to make it

clear that a soft generalisation is what is intended, and also to make it clear just how soft

(or how close to being hard) it is meant to be.

Since there is often confusion over the difference between hard and soft generalisations,

we should, when reconstructing arguments, always make it clear whether a generalisation

is hard or soft (the one exception to this is the case of statements about cause and effect;

this will be discussed near the end of this chapter). The confusion most often arises when

the generalisation, as stated, lacks an explicit quantiﬁer. The intended quantiﬁer is merely

implicit, so there is room for misinterpretation. A generalisation in which the quantiﬁer is

merely implicit is thus a kind of ambiguity. The way to eliminate the ambiguity is to add

an explicit quantiﬁer.

The scope of a generalisation

Consider the following hard generalisations:

1 All cows are herbivores.

2 All black cows are herbivores.

The subjects of these generalisations – what the generalisations are about – are cows and

black cows, respectively. Both generalisations are true, and they stand in a special relation-

ship. There are two aspects of this relationship. First, they attribute the same feature to

their subjects (that of being herbivores). Second, the subject of the second is a subset of the

ﬁrst (all black cows are cows, but not all cows are black). Thus we say that the scope of (1)

is wider than that of (2) and conversely that the scope of (2) is narrower than that of (1).

Note that we can compare generalisations in this way only when the subject of one is a

subset of the subject of the other. We cannot, for example, say that the generalisation ‘All

lions are carnivores’ is narrower than, or wider than, either (1) or (2). Nor can we compare

the scope of ‘All sheep are herbivores’ to that of either (1) or (2).

the practice of argument-reconstruction144

Figure 5.4 represents the situation expressed by (1) and (2).

It can sometimes be important to adjust the scope of a generalisation, making it either

narrower or wider. Usually, in reconstructing arguments, we have to narrow them;

hardly ever do we have to widen them. Suppose, for example, you are a fervent

environmentalist, and believe that radical measures must be taken immediately to pro-

tect the environment from air pollution. In particular, you believe that our reliance

upon petroleum products – such as petrol (gasoline) for cars – must be halted as soon

as possible. So you argue:

Private vehicles that emit carbon monoxide should not be allowed.

We must ban automobiles.

The reasoning here is pretty clear, but in reconstructing, some care must be taken with the

generalisation implicit in it. The implicit generalisation, obviously, is that automobiles

emit carbon monoxide. The argument might be reconstructed as follows:

P1) We should ban all private vehicles that emit carbon monoxide.

P2) All automobiles emit carbon monoxide.

C) We should ban all automobiles.

Note that in writing P1, we added the quantiﬁer ‘all’. Usually when someone speaks of

‘banning’ something they don’t add the word ‘all’ (or any equivalent word), but they do

mean that none should be allowed. Still, as always, it is worthwhile when reconstructing

to make the quantiﬁer explicit. Now assume you really do believe P1. This argument is

deductively valid. However, you must admit that it has a weak point. For P2, as written,

is clearly untrue. Some automobiles, for example, are electric, and run on batteries. Since

Figure 5.4

the practice of argument-reconstruction 145

they do not burn petrol (or any other petroleum product), they do not emit carbon

monoxide (indeed they do not pollute the air at all, at least not directly). So even if P1 is

true, you have failed to give a sound argument.

Now you could make the argument inductively sound by changing the word ‘all’ in P2 to

‘most’. But you could do better, for two reasons.

First, it could become false that most automobiles emit carbon monoxide, without any

reduction at all in the number of petrol-driven cars, in which case the pollution (and

other problems) caused by the burning of petrol might not have been curtailed at all. For

it would be possible that so many electric cars or other alternatives to be produced over a

few years’ time that they outnumber petrol-driven cars without any reduction in the

number of petrol-driven cars. In that case, P2 would be false but you would still want to

argue against petrol-driven cars, since they would still be emitting the same amount of

pollution.

Second, changing ‘all’ to ‘most’, although it renders the argument sound, does not clarify

the issue as much as another alternative.

This other alternative is to change the scope of the generalisation expressed by P2 – in

particular, to reduce its scope. Instead of ‘All automobiles emit carbon monoxide’, we can

more accurately write ‘All petrol-driven automobiles emit carbon monoxide’, rewriting the

argument thus:

P1) We should ban all private vehicles that emit carbon monoxide.

P2) All petrol-driven automobiles emit carbon monoxide.

C) We should ban all petrol-driven automobiles.

Assuming the truth of P1, this is a deductively sound argument. Even if you doubt P1, this

is, at any rate, a much better argument than the earlier version; since the new P2 is a

narrower generalisation than the old P2, its premises have a better chance of being true.

Furthermore, by narrowing the generalisation, the issue is deﬁned more exactly. We now

have it explicitly before us that the point at issue is the use of petrol-driven automobiles,

not automobiles in general.

Thus, when reconstructing arguments, we should take care not to employ a hard

generalisation that is wider in scope than we need, if there is anything doubtful about

the wider one that could be eliminated by employing a narrower one. If a narrower (but

hard) generalisation will sufﬁce for constructing an argument for the desired conclusion,

then we should employ the narrower one. This is not to say we should always choose

narrower generalisations whenever possible. For example, it would not improve the

argument to rewrite P2 as ‘All blue petrol-driven automobiles emit carbon monoxide’.

For adding the word ‘blue’, besides not making the generalisation any more likely to be

true (or at least not appreciably so), renders the argument for the desired conclusion

invalid. The point is that if one generalisation is narrower than another and more likely to

the practice of argument-reconstruction146

be true, then, provided that it is sufﬁcient for obtaining the desired conclusion, the

narrower one should be employed.

Note that in some cases there is no natural word or phrase for the class of cases we wish to

generalise about. In such cases we have to reduce the scope of a generalisation by explicitly

excepting a certain class of what would otherwise be counterexamples. For example,

consider the inference ‘That is a mammal; therefore it doesn’t ﬂy’. The generalisation

needed is ‘No mammals except bats ﬂy’, since ‘No mammals ﬂy’ is false (and of course we

would also need the premise that the creature in question is not a bat; we ignore ﬂying

squirrels).

PRACTICAL REASONING

The above argument about the automobile is one that has a practical conclusion: it enjoins

or commends a particular action. What the argument says, roughly, is that doing one thing

(banning the petrol-driven automobile) is necessary if a certain desirable outcome or end

(ﬁnding alternatives to vehicles that emit carbon monoxide) is to be achieved. Other

arguments with practical conclusions are those that say that a certain action would be

sufﬁcient to bring about the desired end, and for that reason ought to be performed. Still

others say that a certain action would lead to a certain undesirable outcome, and therefore

ought not to be performed. Reasoning of this kind is often called practical reasoning, or

means–end reasoning, and is normally based upon two sorts of considerations: First, an

outcome is speciﬁed as being either desirable or undesirable (in this book we prefer to use

‘must’ or ‘should’ to specify the outcome, as illustrated below; normally, ‘must’ expresses a

stronger demand or requirement than ‘should’). Second, there is a proposition put forward

that says either:

(1) that if such-and-such action is performed, the outcome will result;

(2) that if the action is performed, the outcome will not result;

(3) that if the action is not performed the outcome will not come about; or

(4) that if the action is not performed then the outcome will come about.

This gives rise to eight different types of argument that concern a relation between

action and outcome. Just for the purpose of illustration, then, suppose that the outcome

is that the amount of chocolate in the world be increased, and the action in question

is X. Then, using ‘should’, the eight types of practical reasoning can be sketched like

this:

1 P1) The amount of chocolate in the world should be increased.

P2) If action X is performed, then the amount of chocolate in the world will be

increased.

C) Action X should be performed.

the practice of argument-reconstruction 147

2 P1) The amount of chocolate in the world should be increased.

P2) If action X is not performed, then the amount of chocolate in the world will

not be increased.

C) Action X should be performed.

3 P1) The amount of chocolate in the world should be increased.

P2) If action X is not performed, then the amount of chocolate in the world will

be increased.

C) Action X should not be performed.

4 P1) The amount of chocolate in the world should be increased.

P2) If action X is performed, then the amount of chocolate in the world will not

be increased.

C) Action X should not be performed.

5 P1) The amount of chocolate in the world should not be increased.

P2) If action X is performed, then the amount of chocolate in the world will be

increased.

C) Action X should not be performed.

6 P1) The amount of chocolate in the world should not be increased.

P2) f action X is not performed, then the amount of chocolate in the world will

not be increased.

C) Action X should not be performed.

7 P1) The amount of chocolate in the world should not be increased.

P2) If action X is not performed, then the amount of chocolate in the world will

be increased.

C) Action X should be performed.

8 P1) The amount of chocolate in the world should not be increased.

P2) If action X is performed, then the amount of chocolate in the world will not

be increased.

C) Action X should be performed.

There is, however, an important complication that is most easily explained in connection

with type 1. Suppose that we believe that increasing the number of doctors would improve

the NHS (the UK National Health Service). We might set out the argument like this:

the practice of argument-reconstruction148

P1) The NHS should be improved.

P2) If the number of doctors were increased, the NHS would improve.

C) The number of doctors should be increased.

This is a start, but as it stands it is really not adequate. For if you think about it, the

argument is clearly not valid. It does not follow, from the fact that such-and-such would

bring about some desirable result, that we should do such-and-such (also look again at the

earlier argument about the sun hat rule). There are two reasons.

First, we need to know that the cost of the proposed action does not outweigh the beneﬁt

of the outcome. For example, it would certainly improve the NHS if the Government were

to increase its budget by tenfold. But that would not be a good idea, as the cost would be

far too great. This sort of thing – ‘weighing the costs’ – is clearest where money is at stake,

but it is not limited to monetary considerations. If you want stronger muscles, for

example, then you have to weigh the desirability for you of stronger muscles against the

‘cost’ of exercising (the time expended, the pain, etc.). Indeed, even in the argument about

the NHS, we are not assuming that the value of an improved NHS can be assessed in

monetary terms.

Second, we need to know that there is not some other means that would bring about the

same beneﬁt but at a lower cost. We need to know, that is, that the proposed action is the

most efﬁcient or economical way to bring about the desired outcome.

In reconstructing practical reasoning, then, we have to incorporate both of these points as

premises. The argument concerning the NHS, then, would go something like this:

P1) The NHS should be improved.

P2) If the number of doctors were increased, the NHS would improve.

P3) The beneﬁts of improving the NHS would outweigh the costs of increasing the

number of doctors.

P4) Increasing the number of doctors would be the most efﬁcient means of

improving the NHS.

C) The number of doctors should be increased.

This argument is valid. Strictly speaking, P1 and P2 are now redundant, since they can be

inferred from P3 and P4; but it is harmless, and it makes it clearer, to leave them in. Of

course, the argument is a bit vague: it does not say to what extent the NHS should be

improved, nor by how many the number of doctors should be increased. Someone actually

advancing this argument would want to ﬁll in these details.

In considering this issue we focused on an argument of type 1, but the weighing of costs

and beneﬁts may enter into four of the eight types of practical argument. Types 2, 4, 5 and

7 are valid as they stand, but types 1, 3, 6 and 8 are invalid types, and must always be

supplemented by premises outlining costs, beneﬁts and efﬁciency. For example, consider

the practice of argument-reconstruction 149

type 3. It might be that the cost of not performing action X would be greater than the

beneﬁt of increasing the amount of chocolate (that is to say, it might be that the beneﬁt of

performing it is greater than the beneﬁt of increasing the amount of chocolate).

BALANCING COSTS, BENEFITS AND PROBABILITIES

Practical reason, as we’ve just seen, involves a weighing of one value – the value of the

desired result – against another – the negative value of the cost of the envisaged means of

bringing about the desired result. It’s important to recognise that almost any action could,

in principle, be rationalised by practical reason. For example, if I get up to make a cup of

coffee, then I could reasonably be said to act according to practical reasoning; roughly,

I take it that the cost (the effort) would be outweighed by the beneﬁt of coffee. So this sort

of calculation is thoroughly normal; all that we are doing here is making the calculation

more explicit.

Someone giving the above argument about the NHS might concede that there is some

possibility, even if the number of doctors were increased, that the NHS would not

improve. So long as he or she is reasonably certain that it would, however, it would be

simplest to leave the conditional P2 as it is, rather than inserting ‘probably’ before its

consequent, thereby making the argument inductive rather than deductive. In that case

the problem is relatively simple: If the beneﬁt exceeds the cost, then the action should be

performed.

But in other cases – when the argument must be represented as inductive – we have to

juggle three factors: cost, beneﬁt and probability. We have pointed out that there is no

general guide for weighing costs and beneﬁts, and it is likewise with probability: we often

have to rely on our best, most informed guesses. But there are constraints that any weighing

should obey. For example, suppose you are repairing a window. Having removed it, you are

invited to a party, which is taking place now. You know the party would be a lot of fun,

but although you could very easily repair the window tomorrow, there is no time to

replace the window before going to the party; either you leave the window off and go to

the party, risking the possibility of rain getting in (assume the window is too high up for

there to be a risk of burglary), or you continue working on the window and miss the party.

What should you do?

Obviously the beneﬁt of going to the party is high, but so would be the cost of rain getting

in. If we assume that these are roughly equal, then clearly your decision should rest on the

probability of rain: if the probability of rain is less than 1/2, then you should go to the

party; if it is higher than 1/2, then you should not. But suppose the cost of rain getting in

would be much greater than the beneﬁt of attending the party. In that case you should not

risk going to the party even if the chance of rain is fairly low. We can represent this in a

table:

the practice of argument-reconstruction150

Here we are assuming that the unpleasantness of the rain, if you leave the window off and

go to the party, would be roughly twice the positive pleasure of going to the party if it

doesn’t rain, and that not going to the party would be neither bad nor good. Note that

it does not matter that we used −10 and +5 to represent this relationship; we could just

as well have used −4 and +2, or −2 and +1; the crucial thing is the relation: rain if you go to

the party would be twice as bad as the pleasure of going to the party if it does not rain.

Also, these are only rough estimates: no one assumes that anyone can specify exactly how

bad or how good outcomes would be relatively to each other. But that does not mean that

we have no idea as to what outcomes are preferred; everyone agrees, for example, that

pinching one’s toe has about the same disvalue as pinching one’s ﬁnger, and that neither

is nearly as bad as breaking one’s leg. The idea is to get these estimates to the best of our

ability; we do not require anything more.

In this situation, then, you should stay home, unless the probability of its raining is less

than half the probability of its not raining. That is, you should stay home unless the

probability of rain is less than one third.

What we are leading up to is the concept of expected value:

Let o1, o2 ... o

n be the possible outcomes of an action A; let V(o) be the value (cost

or beneﬁt) of each outcome o, and let P(o) be the probability of each outcome

(given that action A was performed). Then the expected value of an action A is:

[P(o1) × V(o1)] + [P(o2) × V(o2)] + . . . [P(on) × V(on)]

That is, for each possible outcome of the action, you multiply the probability of the

outcome by its value (its cost or beneﬁt, as the case may be). Then you add these ﬁgures

together to get the expected value of the action. The idea behind this is that, given a range

of possible actions, one should do whatever maximises expected value. This is what we

spoke of as a constraint on rational action. If one’s possible actions are A1, A2, ... A

n, and

one of these – say Ak – has the highest expected value, then one should perform Ak. In the

case of the window and the party, the possibilities are: stay and repair the window, or go to

the party. If we assume that the probability of rain is 0.5, then the expected value of going

to the party, according the values given in the chart above, would be:

(0.5 ×(−10)) +(0.5 ×5) =(−5) +2.5 =−2.5

Rain No rain

Go to party −10 +5

Not go to party 0 0

the practice of argument-reconstruction 151

The expected value of not going to the party is:

(0.5 ×0) +(0.5 ×0) =0

Since the expected value of staying to repair the window (0) is greater than that of going to

the party (−2.5), you should stay to repair the window.

It is very helpful to have a ﬁrm grasp of the concept of expected value, because it is one of

the areas in which people most frequently make mistakes in reasoning. For example, we

often see arguments like this:

The bottom line is this: no matter how safe the Government says it is, they cannot

rule out the possibility of a catastrophic accident. We should decommission all

nuclear power plants as soon as possible.

If the arguer is right, then the expected value of decommissioning all nuclear plants

should be greater than that of not doing so. But, although this may be true, the arguer

has given us no reason to believe it. In order to reach that conclusion, we would need to

know the actual probability of an accident; we would also need to know how the cost of

an accident would compare with the beneﬁts and other costs of continuing to use nuclear

power, as well as the beneﬁts and costs of relying on other sources of energy. The arguer

has provided none of this, and the mere fact that an accident is not impossible is not

disputed by anyone. Nor does anyone dispute that a nuclear accident would be a very

bad thing. But the mere fact that something bad – no matter how bad – is a possible

outcome of some action certainly does not establish that the action should not be

performed.

It is somewhat controversial to suppose that the rationality of all action depends on its

expected value. Suppose, for example, that there are ten people who will certainly die

unless they are treated with a rare enzyme that happens to be present in your brain. It

cannot be found anywhere else, and extracting it from your head will kill you. A doctor

decides forcibly to extract it from your head – thus killing you – but justiﬁes this on the

grounds that since ten people will die if the enzyme is not extracted, and only one will die

if it is, the expected value of the action is positive. (Assume that no other harm would

result; e.g. the doctor would not be charged with murder or anything like that.) It might be

noble of you to volunteer for this, but it seems wrong to say that the doctor would be right

or justiﬁed in extracting the enzyme from your brain. The reason is that his doing so would

violate your rights. Alternatively, we might hold that there is an absolute moral rule, that

(outside the context of war) it is always wrong to kill an innocent person, or to use a

person’s life against their will. Thus there is a certain limit to the application of expected

value calculations: the expected value of a proposed action tells us whether or not it would

be rational to do something, unless it is overridden by the existence of rights or moral

rules. Normally, moral rules are invoked in a very straightforward way: x has property F;

actions with property F must never be performed, therefore x must not be performed. The

main difﬁculty faced by reasoning in terms of moral rules is that, at least on the surface,

the practice of argument-reconstruction152

they sometimes come into conﬂict, as when one person’s or group’s rights seem to be

incompatible with another’s. Courses in ethics or moral philosophy are often concerned

to ﬁnd principled ways of resolving such dilemmas. Another central concern is the inter-

play between moral rules and expected value (or utility, as it is often called), and the

degree to which the former might be explained in terms of the latter. A way to accom-

modate this without complicating our argument-reconstructions is simply to think of

rights and duties as entering into the calculation of cost and beneﬁt in their own right,

without any assumption that can be explained in terms of some independent conception

of cost and beneﬁt.

EXPLANATIONS AS CONCLUSIONS

In the ﬁrst chapter, we took care to distinguish arguments from explanations. An

argument supplies reasons why we should believe a certain proposition whose truth-value

is in question. By contrast, an explanation tells us why it is that a certain proposition

is the case, when the truth-value of that proposition is not in question. It is especially

important to observe this distinction when dealing with arguments whose conclusions

are themselves explanations. The aim of this sort of argument is to persuade the audience

that such-and-such is the actual cause of a fact or event. Such arguments are very common.

For example:

We must not have fertilised that plant. It hasn’t got a disease. We’ve watered it

correctly, and it gets enough sun, but it still isn’t growing well.

This passage does involve an explanation; but it is, nevertheless, an argument. The con-

clusion is that the cause of the plant’s poor growth is that it wasn’t fertilised. So we might

reconstruct it like this:

P1) If a plant is not growing well, then either it has a disease, it is getting the wrong

amount of water, it isn’t getting enough sun or it has not got enough fertiliser.

P2) This plant is not growing well.

P3) This plant has not got a disease, it gets the right amount of water and it gets

enough sun.

C) This plant has not got enough fertiliser.

This argument is valid. But it is not quite right, because the conclusion does not say that

the plant’s poor growth is caused by its not having enough fertiliser. It is a perfectly good

argument, and indeed it is part of what the arguer is trying to establish; but it is not all of

it. In order to display the full force of the argument, we need to use the word ‘cause’ in

both the premises and the conclusion:

the practice of argument-reconstruction 153

P1) If a plant is not growing well, then the cause is either that it has a disease, that it

is getting the wrong amount of water, that it isn’t getting enough sun or that it

has not got enough fertiliser.

P2) This plant is not growing well.

P3) This plant has not got a disease, it gets the right amount of water and it gets

enough sun.

C) The cause of this plant’s not growing well is that it has not got enough

fertiliser.

Or, as we might more naturally put it, this plant is not growing well because it has not got

enough fertiliser – that would be the causal use of ‘because’ that was discussed in the ﬁrst

section of this chapter. Note that in order to obtain the desired conclusion, it was necessary

to include the word ‘cause’ (or the word ‘because’) in P1. If we had left P1 as it is in the

ﬁrst version, then the inference to the conclusion in the second version would have been

invalid. For it is certainly not true that if A is true (the plant hasn’t enough fertiliser), and

B is true (the plant isn’t growing well), then A is the cause of B (though of course if A is the

cause of B, then A and B must both be true).

In fact this is not quite the whole argument, but only a sub-argument. In order to get the

ﬁnal conclusion, ‘This plant is not growing well because we did not fertilise it’, we’d have

to add another premise after the given conclusion: ‘If we had fertilised this plant, then it

would have had enough fertiliser.’

Note that the correct reconstruction is not like this:

P1) If a plant has got a disease, it is getting the wrong amount of water, it isn’t

getting enough sun, or it has not got enough fertiliser, then it doesn’t grow

well.

P2) This plant is not getting enough fertiliser.

C) This plant doesn’t grow well.

In the passage, the arguer assumes that the audience agrees that the plant isn’t growing

well. This fact is not in question. The aim of the argument is to persuade the audience as to

the cause, that is, the explanation, of this fact.

All such arguments begin with an accepted fact – some proposition that the arguer expects

his or her audience already accepts. The arguer’s aim is to answer the question ‘What is the

correct explanation of this fact?’ by giving an argument. In the above example, the arguer

recognises that there are several possible causes of the agreed fact, and, by eliminating all

but one, advances the remaining one as the correct explanation. The pattern can be

represented like this:

the practice of argument-reconstruction154

P1) (The agreed fact).

P2) (The agreed fact), was caused by either A or B (or C, or . . .).

P3) B is not the case (nor is C, nor . . .).

C) (The agreed fact) was caused by A. 4

Normally P2 will be backed by a covering generalisation, of the form ‘Whenever such-

and-such happens, it is caused by . . .’. But not always; sometimes we know what the

possible causes of a given fact or event are, but are unable to articulate generalisations

from which they may be inferred. In cases where we do know the appropriate general-

isations, however, we should, as always, include them in the reconstruction. That is

what we did in the plant example. Of course, the list of possible causes listed in P2

may be of any length.5

The generalisations appealed to in arguments of this kind are often soft rather than hard.

For example, a sudden increase in the temperature of an automobile engine’s cooling

system is usually, but not always, caused either by a leak in the cooling system or a broken

fan belt. In such cases, we must insert ‘usually’, or ‘probably’ or some suitable variant, into

the appropriate place in P2. Likewise, we may not be able to rule out with certainty the

possible explanations listed in P3. Again, in such cases we should have to insert ‘probably’,

‘usually’ or some suitable variant, into the appropriate place in P3 (or perhaps ‘probably

not’, etc.). In these cases the arguments will be inductive rather than deductive. Such an

argument might look like this:

P1) The temperature of the engine’s cooling system has suddenly increased.

P2) Almost always, a sudden increase of the temperature of an engine’s cooling

system is caused by a broken fan belt, or a leak in the cooling system.

P3) It is very unlikely that the fan belt has broken.

C) Probably, the increase of the temperature of the engine’s cooling system

was caused by a leak in the cooling system.

In this case, P3 might be the conclusion of another argument; for example, it may have

been inferred from the fact that the fan belt is new.

4 A more complex kind of case is one where we know that the cause was A or B, and that A and B were both

true, yet we still wish to determine which was the actual cause (e.g. we might know that the patient’s death was

caused by either heart disease or liver disease, and that both his heart and liver were diseased). But we shall not

discuss these sorts of cases here.

5 It may, indeed, contain only one item, in which case there is no need for P3. For example: smoke is always

caused by ﬁre; therefore if we see smoke, then since we know that it is always caused by ﬁre, and never by

anything else, we can conclude immediately that the smoke we see is caused by a ﬁre. Such cases, of course, are

not very interesting.

the practice of argument-reconstruction 155

CAUSAL GENERALISATIONS

In the preceding examples we were concerned with causal relationships between particular

events or states of affairs. We were concerned, for example, with whether or not the

particular event in a car’s cooling system was caused by a particular fault. However

causal statements often appear as generalisations about types of events or states of affairs,

as in:

Powerful electric shocks cause the muscles to contract.

This sort of statement is relatively unproblematic. What it means, roughly, is that when-

ever powerful electric charges are applied to a living person’s body, the muscles contract

(unless there is something wrong with their nervous system). So it is a hard generalisation

about events. However, the word ‘cause’ does not always, or even typically, indicate a hard

generalisation of this kind. Consider:

Smoking causes cancer.

This is not a hard generalisation about events, persons or states of affairs. It does not mean,

for example, that every act of smoking causes an outbreak of cancer, or that everyone

who smokes gets cancer. It does not even mean that smoking usually causes cancer (since

it is not true that most smokers develop cancer). The following argument, then, is not

inductively forceful:

P1) Smoking causes cancer.

C) If you smoke, then, probably, you will get cancer.

What, then, does ‘Smoking causes cancer’ mean? Roughly, what it means is that each

person is more likely to develop cancer if they smoke than that person would be if they

did not smoke. Smoking raises the probability of getting cancer. So this argument is

deductively valid:

P1) Smoking causes cancer.

C) You will be more likely to get cancer if you smoke than if you don’t.

But note that the statement about smoking does not tell us to what degree smoking

raises the probability of getting cancer. In that respect it is vague. A more precise causal

generalisation would take the form: ‘Smoking raises the probability of cancer by such-and-

such per cent.’

the practice of argument-reconstruction156

This connects with another important issue regarding generalisations. Consider:

A recent study of primary school children has discovered a strong correlation

between diet and school performance: better diets were strongly linked to better test

marks. One of the simplest things we can do to improve performance in primary

schools, then, is simply to improve the foods on offer at school refectories.

To discover a ‘correlation’ between X and Y is to discover that the proportion of things

that exhibit the feature Y is higher among things that exhibit feature X than it is among

things that do not exhibit feature X. The arguer here seems to infer a causal relationship

from the correlation of better test marks with better diets. In the language to be intro-

duced in Chapter 7, this is the fallacy of confusing correlation with cause. The inference

goes like this:

P1) X is strongly correlated with Y.

C) X causes Y.

But this inference is no good. This can be seen easily by considering the following example

of the same pattern:

P1) High concentrations of bicycles are strongly correlated with air pollution.

C) High concentrations of bicycles cause air pollution.

P1 is actually true, since high concentrations of bicycles and high levels of air pollution

are typically found in the same place, namely large cities such as Paris or Bangkok. But

obviously C is false. This argument-pattern is evidently not valid, and not inductively

forceful either.

Usually, when there is a correlation between X and Y without causation, what is going on

is that some underlying factor causes both X and Y. In the case of bicycles and pollution, the

common underlying cause is the presence of a large and concentrated population of

human beings (the population density explains the presence of such sources of pollution as

cars, which in turn cause the pollution). As for the case of children and test scores, it is

certainly plausible to suppose that diet inﬂuences school performance, but there may be a

common underlying cause in that case, as well. For example, it might be that children from

better-educated households tend to be more intelligent (if only because intelligent people

are more likely to complete a university education), and that better-educated households

tend to eat better diets (perhaps because they tend to have more money, and hence can

afford a better diet). Or it might be that children from poor households tend to eat poorer

diets, and that poor households tend to suffer from other sorts of family problems that

tend to impair school performance. Thus the correlation is not sufﬁcient to establish the

causal relationship.

the practice of argument-reconstruction 157

Under what circumstances, then, can we legitimately infer the presence of a causal rela-

tionship? The answer should be evident from the rough-and-ready deﬁnition of causation

given above: In order to infer a causal relationship from a correlation between X and Y, we

need to know that the correlation holds, or would hold, even when other possible causes of

Y are absent or were absent.

In other words, we need to know that Y exists more frequently when X exists than when

it doesn’t, regardless of the circumstances in which we ﬁnd X. We need to rule out other

possible causes. So what we would need to know in the case of the children, for example, is

whether or not children from well-off households do worse at school if their diets are poor,

and likewise for children from less well-educated households, and similarly for other

alternative factors that might inﬂuence performance at school.

It is important to be aware of these issues, and especially to be able to point it out when a

causal relationship is wrongly inferred from a correlation. But it would take us too far

into the subject to give a general recipe for validly inferring causal relationships from

correlations; in the language of Chapter 1, the characterisation offered above tells only a

necessary condition, not a sufﬁcient condition. Probably the most important single lesson to

take away is that a causal relationship entails a correlation, but a correlation does not entail

a causal relationship.

A SHORT-CUT

Where an argument contains a conditional among its premises, we have, in order to infer

the consequent of the conditional, to write down its antecedent as a separate premise. This

means that we have to write a certain sentence down twice. This can be cumbersome, and

it often makes the structure of an argument more difﬁcult to see than it need be. Consider

again the ﬁrst sub-argument in the argument about the tuna industry:

P1) Tuna catches have been decreasing signiﬁcantly for the past nine years.

P2) If tuna catches have been decreasing signiﬁcantly for the past nine years, then,

if the tuna industry is not regulated more stringently, the tuna population will

vanish.

C1) If the tuna industry is not regulated more stringently, the tuna population

will vanish.

P2 is a conditional whose antecedent is P1. Instead of rewriting P1 out in full, we may

abbreviate it simply as ‘P1’. So we may rewrite the argument as follows:

P1) Tuna catches have been decreasing signiﬁcantly for the past nine years.

P2) If (P1), then, if the tuna industry is not regulated more stringently, the tuna

population will vanish.

C1) If the tuna industry is not regulated more stringently, the tuna population

will vanish.

the practice of argument-reconstruction158

This is easier to read, and it saves you having to write things out unnecessarily. Henceforth,

whenever an argument draws an inference from a conditional premise, feel free to

abbreviate in this way.

CHAPTER SUMMARY

This chapter was concerned to address some of the main logical problems encountered in

the reconstruction of arguments.

General aspects of this include defusing the rhetoric (rewriting so as to improve clarity by

eliminating rhetoric) and logical streamlining (clarifying logical connections by using

logically clear expressions such as ‘if–then’ for conditional relationships). In many cases,

one or more premises upon which a conclusion depends is left implicit by the arguer.

A necessary part of reconstruction is to make such premises explicit. Implicit premises

are usually, though not always, connecting premises: these are either conditionals or

generalisations. Where an argument contains a conditional among its premises, the con-

ditional is often regarded by the arguer as being supported by a covering generalisation. In

reconstruction, we should take care to include a suitable covering generalisation where

appropriate. Covering generalisations may be either hard or soft generalisations.

Not everything explicitly stated by an arguer is relevant to the argument. A proposition

asserted by an arguer may be completely irrelevant; that is, the arguer does not advance

that proposition as support for the conclusion. Such propositions should not be included

in the reconstruction. In other cases, a proposition explicitly stated does provide some

independent support for the conclusion, but is such that if it were ignored, the arguer

would still, by virtue of other propositions put forward, have given an argument for the

intended conclusion. In such a case, the proposition in question should be removed from

the argument. But if it is plausible to do so, it may be treated as a premise in a separate

argument for the same conclusion.

Where possible, ambiguity and vagueness should be coped with by removing them. If it is

possible to do so, the ambiguous or vague language should be replaced by language that is

not ambiguous or vague. If a word in a premise or conclusion is ambiguous (can be read

as expressing either of two meanings), and it is not clear which meaning is intended,

then two reconstructions of the argument should be given, each reﬂecting one of the two

meanings.

All generalisations in reconstructed arguments, whether hard or soft, should have explicit

quantiﬁers. Where a premise is a generalisation, the scope of a generalisation should

be as narrow as is needed to maximise its probability of being true, but not so narrow

that the inference to the conclusion is no longer valid (or inductively forceful, as the case

may be).

Practical reasoning, or means–end reasoning, is embodied in arguments that specify an

outcome as being either desirable or undesirable, along with an action said to be either

the practice of argument-reconstruction 159

necessary or sufﬁcient for bringing about that outcome. Such arguments can take any of

eight basic forms. In order to reconstruct such arguments as valid or inductively forceful,

we often have to add a premise stating that the proposed action is the most efﬁcient

means of bringing about the outcome, and a premise stating that the beneﬁt of the

outcome outweighs the cost of the action (or, in the negative case, that the cost of an action

would outweigh the beneﬁt of the outcome). But sometimes the outcomes of actions are

only probable. This may require us to calculate the expected value of an action, even if

our estimates of costs, beneﬁt and probabilities are vague or sketchy. The conclusions of

arguments based on expected value may be overridden by moral rules.

Arguments are distinct from explanations, but many arguments have explanations

as conclusions: such arguments attempt to establish which, of various possible causes

of a given fact or event, is the actual cause. Arguments that attempt to establish causal

generalisations present more difﬁculty. It is common to see causal generalisations

fallaciously inferred from mere correlations. Causal generalisations are not as informative

as one might be tempted to think: what they tell us is that one type of event or state of

affairs increases the probability of another type of event or state of affairs.

EXERCISES

1 As given, the arguments below are invalid. But each can plausibly be thought to

contain either a generalisation or conditional as an implicit premise – a proposition

that the arguer is assuming but has not explicitly stated. The arguments can easily be

made deductively valid by making the implicit premise explicit. (A) Identify the

conclusion and explicit premises, then add the premise needed to make the argument

valid. (B) Reconstruct the argument in standard form. Use a hard generalisation if

you can think of one that is plausible; otherwise settle for a conditional. You should

write all conditionals in the ‘if–then’ form.

a Mr Bean is an idiot. You should not marry him.

b All men are idiots. You should not marry one.

c Johnny will like the Blandings Castle books; he likes the Jeeves books.

d That fat man is going to sit in that chair! It’s going to break!

e Prices are not going to rise, because the savings rate is not decreasing.

f Massa won’t win unless Hamilton’s car breaks down. So Massa won’t win

unless Hamilton’s mechanic makes a major mistake.

g Verdi was greater than Rossini, so obviously Verdi was greater than Puccini.

h Since only democracies are just, no socialist countries are just.

i If he doesn’t accept the offer, then we will either withdraw the offer or raise

it. If we raise it, then we incur ﬁnancial risk. Therefore, if he doesn’t accept

the offer, then either we carry on with a second-rate manager, or we incur

ﬁnancial risk.

j Unless John brought wine, there isn’t any. John didn’t bring wine. So we’ll

drink beer.

the practice of argument-reconstruction160

k Cigarette advertisements don’t encourage people to smoke? Ha. I think it

safe to say that ads for chocolate encourage people to eat chocolates.

2 Rewrite the following in such a way as to defuse the rhetoric.

a The democratic candidate’s policy on the issues is that he jumps on the

winning bandwagon.

b The invasion of Iraq: the mother of all miscalculations.

c If they impose trade tariffs then we don’t have a level playing ﬁeld.

d She’s been raking it in since she switched to writing chick-lit.

e They can peddle that same ideology all they want, but we’re not buying.

f The Bio-tech shares offered by Ramsay? Just another fool’s gold.

g Our crusade against the junk-food mongers will not cease until the last

junk-food ad has disappeared from children’s television.

h Blundering doctors killed 40,000 patients this year.

3 Logical streamlining: rewrite the following as single sentences using simple logical

expressions such as ‘if–then’ and ‘every’.

a You threaten not to release prisoners? Then no cease-ﬁre.

b There is no way we’re going to win the election without increasing our

appeal to women.

c There are places in which the most offensive speech is always deemed

acceptable. They are called universities.

d A leaf-blower is louder than a rake.

e Embryo research is the thin end of the wedge towards human cloning.

f He who laughs last laughs longest.

g No pain, no gain.

4 Find appropriate covering generalisations for the following conditionals. Choose a

hard or soft generalisation as seems appropriate.

a If John is under 18, then he cannot legally purchase alcohol in the UK.

b If that is a scorpion, then it is poisonous.

c If that wine is not French, then it is probably not overpriced.

d That picture is not likely to be an oil painting, unless it was painted after

1500 or is Dutch or Flemish.

e He is probably good at analysing arguments, if he is a successful lawyer.

f If the patient is now haemorrhaging, then his blood pressure is decreasing.

g It is too dangerous for Annie to drive all the way from Thurso, if she’s only 17.

5 a Suppose you know that Doctor Bowes does not own or drive a Ferrari.

Reconstruct the argument in accordance with the principle of charity.

the practice of argument-reconstruction 161

Doctor Bowes, the candidate, owns a majority share in a large and

successful corporation. Furthermore, he drives a brand-new Ferrari. Of

course he is wealthy.

b The following passage includes the assertion that the defendant has been

addicted to cocaine for two years. Suppose you know this assertion to be

entirely false (the defendant has never used any illicit drug). Reconstruct the

argument in accordance with the principle of charity. In order to reconstruct

it, you will have to rephrase some of the sentences, ignore some material, and

also make implicit premises explicit. The conclusion is also implicit.

The evidence is very compelling. The defendant has been addicted to

cocaine for over two years. Her blood and ﬁngerprints were found on

the murder weapon. She was seen emerging from the victim’s ﬂat not

more than half an hour after the murder took place. She boarded a

ﬂight for Greece only twelve hours after the murder. And ﬁnally, the

victim had recently ended the sexual relationship between himself and

the accused.

6 We very frequently hear of claims or actions being criticised on the grounds that they

are politically motivated. Sometimes this is put by saying that someone is ‘playing

politics’ or using something as a ‘political football’. What does this mean? Why is it a

criticism? Find examples in the print media, and try to explain exactly what the point

is, in such cases, in calling something ‘political’.

7 Reconstruct the following arguments, taking care to eliminate vague or ambiguous

terms. You will have to rewrite sentences, ignore some material, and make implicit

propositions explicit.

a Ms Jones has demonstrated her commitment to feminism by supporting an

across-the-board pay rise for female academics. So no doubt she’ll support a

reduction of the evidential standard for rape convictions.

b Make no mistake: whatever their keepers say, these so-called ‘domesticated’

wolves are wild. Wild animals are too dangerous to be kept as pets.

c Researchers have found that heroin use in teenagers is linked to parents with

histories of depression. Parents under psychiatric care for depression should

therefore be told the symptoms of heroin use.

d The Mayor made San Francisco into a sanctuary for illegal aliens; he has no

appreciation whatsoever that San Francisco is a city within the United States,

not a ‘city-state’.

e Sarah Palin is clearly a socialist; she supported an across-the-board dividend

to all citizens of Alaska funded by oil revenue, which makes her the very

thing she criticised in Obama: one who favours taking legitimately created

wealth and ‘spreading it around’. And socialism is a godless doctrine. So don’t

tell me she’ll protect our American rights, i.e. to low taxes, gun ownership

and Christianity.

the practice of argument-reconstruction162

8 For this argument, reconstruct it twice: once retaining the vague term ‘political

correctness’, and once eliminating it.

When the Bunbury Women’s Group proposes that the City Council bar men

from the ‘Women’s Safe House’, we realise that we must not allow them to

have inﬂuence on the Council. For this makes it obvious that the virus of

‘political correctness’ has infected the women’s group, and we know what

‘political correctness’ stands for – they would promote such horrors as homo-

sexuality being taught in schools and legal prohibitions against language

deemed ‘incorrect’.

9 Reconstruct the following arguments, making implicit propositions explicit as

needed. If the argument is not deductively valid, increase its inductive force by

decreasing the scope of the generalisation. If the argument is deductively valid,

increase its chances of being sound by decreasing the scope of the generalisation.

a Of course your new horse can be trained without much difﬁculty. Most

horses can be.

b Most men marry. Therefore most men have, have had or will have a mother-

in-law.

c No primates can learn to talk. Bobo is a chimpanzee, hence a primate, there-

fore he cannot learn to talk.

d All countries can be attacked by sea. Thus all countries require a naval

defence.

10 Reconstruct the argument about compulsory military service discussed at the begin-

ning of this chapter (pp. 119–121). Take into account the advice given in the section

on practical reasoning (pp. 147–153).

11 Look at argument-pattern (1) in the section on practical reasoning (pp. 147–148). In

order for such arguments to be valid, we need to add two premises: ﬁrst, that the

beneﬁt of increasing the amount of chocolate outweighs the cost of performing

action X; second, that action X is the most efﬁcient way of increasing the amount of

chocolate. What similar premises are needed to make argument-patterns (3), (6) and

(8) valid?

12 Reconstruct the argument below. Some guidance: you will need to remove some

extraneous material and perhaps defuse some rhetoric. It is not easy to tell exactly

what the conclusion is, and it may be implicit. Once you have decided, you may

need to add implicit premises. You should also think about the role of the word

‘deviant’; is it vague or ambiguous? Should it be avoided in the reconstruction of the

argument?

Why has marriage always meant man and woman? Because other sexual

relationships are deviant. Obviously homosexual relationships are deviant;

that’s just biological fact. And that’s what the legalisation of same-sex

the practice of argument-reconstruction 163

marriage would mean: the legal protection of deviant sexual relationships –

the legal protection of all sexual relationships, of whatever kind. Why not

incest and bestiality too?

13 The following argument contains a fair amount of rhetoric, stage-setting and explan-

ation, but also a practical argument. Decide which of the eight patterns of practical

reasoning the central argument of the passage ﬁts, and reconstruct it. Don’t worry too

much about including every point that might be relevant; your main task should be

to get the central argument laid out before you (then you can add sub-arguments,

if you ﬁnd any). Part of the ﬁrst paragraph is concerned to reply to a point made by

the correspondent referred to; think carefully about whether, and in what way, this

contributes to the writer’s intended argument.

I despair of your correspondent who responded to the article on otters and

mink (Letters, 9 July). Mink are certainly not playful and delightful animals.

She must be confusing them with ferrets. While I agree it is no fault of their

own that they are with us, it is not a question of survival. Mink are in paradise

here in the wild: no harsh winter; no natural predators; a vast range of prey.

In the Mustelid family they have found a niche halfway between otters and

pine marten with the aquatic ability of the former and the natural aggression

of the latter. Mink are consequently able to reach nesting colonies of ducks

and seabirds, formerly secure from predation, wiping them out and rendering

the island sanctuaries untenable by birds. I would invite your correspondent to

come to Argyll and see for herself. Mink are a scourge on our environment and

should be eliminated at every opportunity.6

14 Another practical argument, this time giving you more practice identifying implicit

premises and conclusion. Reconstruct according to the instructions on practical

reasoning. The letter is humorous, but contains a serious (though implicit) argument.

Sir, having read your report on how the police plan to test drivers for drugs,

I and both my children in their early twenties attempted the tests described,

without having taken any illegal substances.

We consistently failed the second test (on one leg, head tilted back, eyes closed,

other leg off the ground, arms extended, touch nose with each index ﬁnger).

Swaying and giggling helplessly at each other’s attempts, we would have given

every appearance of intoxication.

We have therefore decided that, if we are stopped and invited to perform these

tests at the roadside, we will ﬁrst ask the ofﬁcer for a demonstration.7

6 Michael Murray, Independent, 16 July 2000.

7 John Tayler, The Times, 4 August 2000.

the practice of argument-reconstruction164

15 A friend offers you a wager: if you draw an ace out of a (normal) pack of playing

cards, he’ll give you £10. If you don’t, you pay him £1. What is the expected value of

accepting the wager? Should you do it?

16 The post ofﬁce is holding a sweepstakes draw: all you have to do is post a letter with

your name and address to the address given, and your name will go into the draw.

The lucky winner, drawn from a barrel containing 400,000 names, will receive

£100,000! Assuming that a second-class stamp costs 26p, what is the expected

(monetary) value of posting your letter, thereby entering the sweepstakes?

17 Criticize the following arguments.

a He cites the old shibboleth that nuclear power is already emission-free. In

fact there have always been signiﬁcant external energy inputs into the

nuclear cycle. Nuclear power is not the solution.

b The purpose of the National Lottery is to earn money for the Government.

Thus the amount collected from ticket sales exceeds the amount paid out in

prizes. Therefore the expected value of buying a lottery ticket is negative.

Therefore one should not buy lottery tickets.

18 The following passage contains an argument that can reasonably be construed as

balancing costs, beneﬁts and probabilities. Try to reconstruct it accordingly.

Elimination of global hunger, prevention of deﬁciency diseases and protection

of the world’s threatened environments are within reach as bio-tech and genet-

ically modiﬁed food research improves.

The debate over food production has swung in favour of new high-tech

methods. The beneﬁts to consumers, producers and the environment from

these new technologies are increasingly evident and vastly outweigh the risks.

Every year millions of lives are lost to malnutrition. Thousands of hectares of

precious habitat are sacriﬁced in the struggle to produce food using inefﬁcient

methods, namely conventional methods.

For example, vitamin A deﬁciency is a serious worldwide problem. So it is hard

to see the merit in eco-terrorists who destroy test crops of GM ‘golden rice’ –

which contains high levels of beta-carotene to help ﬁght rampant vitamin A

deﬁciency and resulting blindness in developing nations.

Meanwhile, too many people drastically overestimate the risks because they

don’t understand that GM crops are not essentially anything new. Genetic

improvement has a long and venerable history, and with the exception of wild

game, wild berries and the like, virtually all the foods in our diet are obtained

from organisms that have been genetically improved. Scientists worldwide

agree that adding genes to plants does not make them less safe either to the

environment or for humans to eat. Dozens of new plant varieties produced

through hybridisation and other traditional methods of genetic improvement

enter the marketplace each year without scientiﬁc review or scientiﬁc labelling.

the practice of argument-reconstruction 165

Many such products are plant varieties that do not and cannot exist in nature!

The scientiﬁc consensus is unequivocal: gene-splicing is more precise, con-

trollable and predictable than other, ‘traditional’ or conventional techniques.

For example, new insect-resistant varieties of grain crafted with gene-splicing

techniques have lower levels of contamination with toxic fungi and insect parts

than conventional grains. Thus, gene-spliced grain is not only cheaper to pro-

duce but is a potential boon to human health. Moreover, by reducing the need

for spraying chemical pesticides on crops, it is environmentally friendly.

Florence Wambubu, and agronomist from Kenya, described how all farming

there is ‘organic’ and has produced low yields and hungry people. She spent

three years at Monsanto, in the United States developing a genetically modiﬁed

sweet potato to help the farmers in her country, where the crop has been

nearly destroyed by a virus. The engineered sweet potato is virus-resistant, and

requires no pesticides. Wambugu is scornful of the environmental ‘hooligans’,

whom she sees as trying to tear down many years of work on behalf of romantic

notions and bad science.

19 The following are not simply explanations, but rather arguments that have

explanations as conclusions. Reconstruct them, eliminating extraneous material and

making implicit material explicit as needed.

a At your last visit I said that the pain in your abdomen is caused either by a

kidney infection, a musculoskeletal injury or cancer in the pancreas or liver.

But no indicators for a kidney infection showed up in the urinalysis, and if

it were musculoskeletal, the pain would have subsided, not grown, by now.

I’m afraid you have cancer.

b The stress of modern life is not because we work more than our parents

did – we don’t – but because we no longer go to church. Instead we shop:

the world’s most stressful activity.

c Nietzsche’s going irrevocably mad was caused either by his tortured

intellectual life – as romantically minded people would like to believe – or

by the syphilis he contracted as a young man. But if it were his intellectual

proclivities, then we should expect a great many other notable intellectuals

to have gone irrevocably mad. The truth – again contrary to romantic

fantasies – is that very few have.

d We read with horror that the age of the onset of puberty in girls is getting

younger. We don’t believe this has to do with artiﬁcial hormones in the

milk or anything like that – surely in these more environmentally aware

times, there are fewer artiﬁcial hormones and suchlike in our food than there

were, say, twenty years ago. The real reason is the unprecedented onslaught

of sexualised images to which children are now subjected, especially on

television.

e Mr Jenkins blames the high unemployment rate on Britain’s high interest

rates: these strengthen the pound, making British exports uncompetitive,

the practice of argument-reconstruction166

which in turn forces British manufacturers to cut costs by means of

redundancies. We blame it in the ease with which people out of work can go

on the dole. Jenkins’ argument assumes that the non-manufacturing sector

of the economy is not growing as fast as the manufacturing side shrinks.

Manifestly, it is.

f Mr Pettigrew says that greenhouse gases are mostly produced by trees, not by

industry. That makes perfect sense. Global warming is on the rise, and we all

see how, all over the world, people are busy planting trees and closing down

factories, getting rid of their cars, and so on. The world of our pre-industrial

ancestors must have been a real hothouse.

20 Review the section on causal generalisations. Every example below is a case either of

(1) assuming that a causal relation entails a hard generalisation or a generalisation of

the ‘most’ type; or (2) too readily inferring a causal relationship from a statistical

correlation. In a short paragraph, criticise the following arguments: say whether each

argument is a case of either (1) or (2) and explain your answer.

a It is just not true that prolonged exposure to the sun causes skin cancer. If it

did, then everyone who has ever had a suntan or a sunburn would get skin

cancer.

b I am so tired of hearing that social and economic deprivation ‘cause’ teenage

criminality. Plenty of teenagers suffer from social and economic deprivation

without turning to crime.

c Taking lots of vitamin C makes my colds go away. I always take vitamin C

when I get a cold, and it always goes away.

d A causal link between violent video games and juvenile violence has been

demonstrated. A study has shown that the incidence of violence is much

higher among teenage boys who play violent video games regularly than it is

among those who do not.

e Oxbridge representatives claim that their admission procedures are not

biased against students from poor backgrounds. How can they maintain this

obvious falsehood, when their own ﬁgures show that the proportion of

Oxbridge undergraduates from impoverished backgrounds is far lower than

the proportion of applicants from impoverished backgrounds? Oxbridge

continues to exclude the poor because they are poor.

21 (A) Draw tree-diagrams for the following arguments as written. (B) Reconstruct them

thoroughly, and draw tree-diagrams for the reconstructed versions. (C) Say whether

they are valid, inductively forceful or neither.

a The sharp increase in the death rate in ancient Antioch, in the year AD 364,

has been ascribed to many factors: to famine, to an inﬂux of disease

brought by soldiers returning from the Persian campaign, and to problems

with the city’s water supply. It was probably the water supply: if it were food

the practice of argument-reconstruction 167

shortages, it is unlikely both that no contemporary historian mentions it, and

that there should be no record of similar sufferings in the lesser towns of the

area or the surrounding countryside. And if the soldiers had contracted

disease in Mesopotamia, then, since they were seriously weakened by hunger

and the strain of a long and arduous campaign, they would have died of

disease in signiﬁcant numbers. And then it is certain that Ammanius, an

eyewitness, would have recorded those fatalities – so cruel after the humili-

ations and losses they had endured in battle – in his history. But he is silent

on the point.

b Jepsen’s Neural Syndrome – JNS – seems to be caused in dolphins by an

excessive intake of heavy metals. A genetic cause is ruled out, because if the

cause were genetic, then the correlation discovered between JNS and the

presence of abnormally high levels of heavy metals in dolphins would be

extremely unlikely. True, the correlation between JNS and abnormally high

levels of heavy metals is no greater than that of JNS with the consumption of

large amounts of squid. But squid, as we know, tend to retain, over time,

large concentrations of the trace heavy metals that pass through their bodies.

Dolphins tend to eat the larger, therefore older, squid. It is very probable that

if squid did not retain heavy metals, then the correlation between JNS and

squid consumption would not exist. Since there are no other signiﬁcant

correlations with JNS, the heavy metals diagnosis looks highly probable.

c If alcoholic behaviour in parents – as opposed to genetic predispositions

to alcoholism – caused alcoholism in children, then we would ﬁnd that

children whose parents are not alcoholic, and who are adopted at a very early

age by alcoholic parents, were signiﬁcantly more likely to become alcoholics.

But our study shows that they are not. Therefore mere heavy drinking in

parents does not, despite the well-known correlation, cause children to grow

up to be alcoholic.

the practice of argument-reconstruction168

issues in argument-

assessment

•Rational persuasiveness 169

•Some strategies for logical assessment 177

Arguments with conditionals or generalisations as conclusions –

conditional proof • Supposing the conclusion false

•Refutation by counterexample 180

•Engaging with the argument I: avoiding the ‘who is to say?’

criticism 183

•Engaging with the argument II: don’t merely label the position 184

•Argument commentary 185

•Complete examples 188

First argument: penalties for possession of cannabis • Second argument:

a criminal wins the lottery

•Commentary on the commentary 195

•Chapter summary 196

•Exercises 197

RATIONAL PERSUASIVENESS

It is plain common sense that the role of an argument is to give us reasons for accepting its

conclusion as true. The aim is to give an argument that the intended audience ought to be

persuaded by. But we have not quite deﬁned what it is, exactly, for an argument to do this.

You might think that we have done this with the notions of deductive and inductive

soundness, but that is not quite right. One reason is that, even if we have reconstructed an

argument perfectly, we cannot always tell whether or not the argument is sound. And that

is because a sound argument must have true premises. A deductively sound argument is

one that has true premises and which is deductively valid; an inductively sound argument

is one with true premises that is inductively forceful. Since we do not always know which

propositions are true and which false, we cannot always tell whether an argument is sound

or not.

Here is a very simple illustration. Suppose you are wondering whether or not you should

expect that interest rates will increase in the next year, and someone presents you with the

following argument:

P1) Interest rates will neither decrease nor remain unchanged in the next year.

C) Interest rates will increase in the next year.

Clearly this argument is of no use to you. It is deductively valid, but such an argument

could not persuade anyone of the conclusion who did not already accept it. For if you did

not know whether or not to expect interest rates to increase, then of course you didn’t

know whether to expect them to decrease, or to remain unchanged.

Here is another illustration. Suppose Bert drops a coin into a cup of coffee, and it settles to

the bottom ‘heads up’. But neither Bert nor Barney can see it, so neither knows that it

landed heads up. Neither has any idea which way the coin landed. Then Bert and Barney

consider the following argument:

P1) If the coin landed tails down, then it landed heads up.

P2) The coin landed tails down.

C) The coin landed heads up.

In the envisaged situation, the argument would be deductively sound, since it is deduc-

tively valid and the premises are true. But, although P2 is true, neither Bert nor Barney has

any reason think so. So, although the argument is deductively sound, and Bert and Barney

can see that it is deductively valid, it gets them no closer to knowing the truth-value of the

conclusion.

In such a situation, we say that the argument is rationally unpersuasive. More exactly we

must say it is rationally unpersuasive for Barney, and also for Bert. Why we must put it this

way – why we must relativise the notion of the rational persuasiveness of an argument –

can be seen from a variation of the story.

Suppose that Barney, but not Bert, knows that the coin is weighted in such a way that it

almost always ends up tails down. Then Barney, but not Bert, has a good reason to accept

P2. Therefore Barney has a good reason to accept that the argument is sound, but Bert does

not. Therefore the argument is rationally persuasive for Barney, but not for Bert.

issues in argument-assessment170

Now imagine a further variation on the story. Suppose that at a particular moment, Barney

tells Bert about the weighting of the coin. If Bert had considered the argument before

that moment, the argument would not have been rationally persuasive for him. But

if he considers it after that moment, then it is rationally persuasive for him, because

of Bert’s acquisition of the relevant information. So rational persuasiveness is doubly

relative: an argument is or is not rationally persuasive for a person at a particular

time. Since different people are in different states of information at different times, an

argument may be rationally persuasive for Barney but not for Bert, and it may be rationally

persuasive for Bert at one time but fail to be at another time. In what follows, we will

usually suppress this complication, but it is worth knowing that it can sometimes be

relevant.

Before we give our ofﬁcial deﬁnition of rational persuasiveness, there is one last complica-

tion to be discussed. Looking over the example just given, you might think that an

argument is rationally persuasive (for a person at a time) if (i) it is inductively forceful or

deductively valid and (ii) the person reasonably believes the premises (at the time). But

this is not quite right.

For consider now the following example:

P1) Almost all residents of Inverness, Scotland own at least one item of woollen

clothing.

P2) Fiona is a resident of Inverness.

C) Probably, Fiona owns at least one item of woollen clothing.

This is an inductively forceful argument. Suppose in fact you have good reason to accept

both P1 and P2. Indeed, suppose you know with certainty that they are both true. Does it

follow that you should accept C? Can you imagine a situation in which you know that P1

and P2 are true, but in which you could reasonably reject C? Yes. For suppose that, in

addition to your knowledge of P1 and P2, you knew Fiona personally, and with certainty

that C is in fact false (she is violently allergic to wool). Someone who knew the truth of P1

and P2, but nothing else about Fiona, could reasonably expect C to be true, but not you.

The argument would be rationally persuasive for them, but not for you.

What we say, in such a case, is that the argument is defeated for you by other evidence that

you have; in this case you have, in effect, two arguments: the argument as given, and also a

more compelling argument for the falsity of the ﬁrst argument’s conclusion.

In particular:

To say that an inductively forceful argument is

defeated

for a person is to say: The

person reasonably believes the premises, but, nevertheless, reasonably rejects

the conclusion.

issues in argument-assessment 171

An inductively forceful argument whose premises you have reason to accept is rationally

persuasive only if your total evidence does not defeat the argument for you (we will

say more about evidence in Chapter 8). Note that the above deﬁnition pertains only to

inductive arguments. The reason for this will be clear in a moment.

Thus our deﬁnition of rational persuasiveness:

To say that an argument is

rationally persuasive

for a person (at a time) is to say:

(i) the argument is either deductively valid or inductively forceful;

(ii) the person reasonably believes the argument’s premises (at the time); and

(iii) it is not an inductively forceful argument that is defeated for that person (at that

time).

There are seven further points to bear in mind as regards rational persuasiveness.

1 It is not possible for the conclusion of a deductively valid argument to be defeated

by a person’s total evidence – this is only possible for inductively forceful argu-

ments. Thus condition (iii) of the deﬁnition of rational persuasiveness only applies to

inductively forceful arguments. The reasons for this are:

a If you accept with good reason the premises of an argument that you

recognise to be deductively valid, then you must accept the conclusion as

well; for you know that if the premises are true, then the conclusion must

be true as well. If a person has good reason to accept the premises of a

deductively valid argument, then we may conclude that it is rationally

persuasive for that person without further ado. Any further consideration

that, for that person, casts doubt on the conclusion, must equally cast doubt

on the premises.

The reason for this comes from the deﬁnition of a valid argument: if its

premises are true, then its conclusion must be true. Remember from

Chapter 3 that validity has nothing to do with the actual truth of the

premises. Therefore, if the premises are true and the argument is valid – the

conclusion must necessarily (no exceptions) be true. So if you have reason to

accept the premises then those very same reasons are equally strong reasons

to accept the conclusion. The only way that a deductively valid argument can

fail to be rationally persuasive is if a person is without reason to accept the

truth of one or more of the premises (remember that since the argument is

deductively valid, condition (i) has already been fulﬁlled).

b The adverb ‘probably’ (or similar term) before the conclusion of an induct-

ively forceful argument allows the possibility that the premises are true and

the conclusion false. That is why such an argument may be defeated for a

issues in argument-assessment172

person: the person has evidence that prevents him or her from accepting the

conclusion even though (A) he or she reasonably accepts that the premises

are true and (B) the argument is inductively forceful.

2 It is not part of the deﬁnition that the argument be sound (either deductively or

inductively). The reason is simple: the notion of rational persuasiveness is intended to

capture what it is about an argument that constitutes its rational claim on a person. It

explains what it means to say: this person ought to accept the conclusion of this argument.

It is the notion of an argument’s giving a person good reason to accept its conclusion.

Indeed, an argument can have a false premise, and hence be unsound (neither

deductively nor inductively sound), yet be rationally persuasive for a person. To

illustrate, go back to the second version of the weighted coin. Suppose that on this

one rare occasion, the coin settles to the bottom of the cup heads down, so P2 is false.

Still, in that case, Barney would still be quite reasonable in thinking that P2 is true

(for he knows that the coin is weighted). So the argument would still be rationally

persuasive for Barney, despite its having a false premise, and thereby being unsound.

He would be quite right – in the sense of being rationally justiﬁed – to accept the

conclusion of the argument, even though, in fact, it is false.

This point about rational persuasiveness illustrates an important fact to which we

will return later in more detail: a person may reasonably believe a proposition that is,

as it happens, false. In other words, there is such a thing as a reasonable mistake. This

is an elementary point, but it is an easy one to forget – and hence, for example, you

might inappropriately blame people when they make a mistake of this nature.

Indeed, a useful way to put the point is to say that the word ‘mistake’ is ambiguous.

To say that someone is ‘mistaken’ could mean either (i) that they have accepted a

false conclusion, or (ii) that they have been persuaded by bad reasons – by an

argument which is not in fact rationally persuasive for them (or they have failed to be

persuaded by good reasons – by an argument that is rationally persuasive for them).

Clearly we are responsible for our mistakes of type (ii); we ought to be persuaded

by good reasons, and not by bad reasons. If we fail in this, then, typically, we are

blameworthy. But it is much less clear that we are always responsible for mistakes of

type (i). If someone believes a proposition on the basis of good reasons – on the basis

of arguments that are rationally persuasive for him or her – then it might just be bad

luck if the proposition turns out to be false. If so, then the person need not be to

blame for having made a ‘mistake’.

Suppose, for example, that you are a doctor. Suppose there is a drug X that you know

to have cured a certain dangerous disease every single time it has been used, in over a

million cases; furthermore, you know that it has never had a negative side effect, and

contains no substances known to be dangerous in any way. A patient has the disease

and you prescribe X. Unfortunately, instead of being cured by X, the patient is made

ill by it. Were you mistaken in believing that X would safely cure the disease? Not if

by ‘mistaken’ we mean a mistake of type (ii), and hence not in the sense required

if you are to be blameworthy. Indeed, you would have been open to criticism if you

issues in argument-assessment 173

had decided not to prescribe the drug, since you would have been going against a

massive body of evidence.

3 It should be appreciated why we have named rational persuasiveness as we have.

Remember that at the beginning we said that there are various kinds of attempts at

persuasion. This book is about trying to distinguish argumentative from non-

argumentative – especially rhetorical – attempts at persuasion, and learning to

evaluate them. An attempt at persuasion by argument is an attempt at rational

persuasion, as opposed to other kinds of persuasion, which do not appeal to your

reason (but rather to your emotions or prejudices). Directed at you, it is an attempt at

providing you with a rationally persuasive argument. Note, again, that this does not

mean that the argument must be a sound argument. The attempt depends upon

what you reasonably believe regardless of whether or not those reasonable beliefs are

in fact true.

4 Rational persuasiveness is a matter of degree; it is not all-or-nothing. This is evident

from (i) the fact that the reasonability with which one holds beliefs is a matter of

degree, and (ii) the fact that inductive force is a matter of degree.

5 ‘Rationally persuasive’ does not mean merely ‘persuasive’ or ‘convincing’. A rationally

persuasive argument may fail to persuade anyone. Whether or not an argument is

rationally persuasive for you does not depend upon whether you think it is. The crux

of the matter is to understand this: an argument may be rationally persuasive for you

even though you are not persuaded by it. This should not be regarded as paradoxical.

All it means is that there are cases where you ought to be persuaded by an argument,

but you are not. Likewise, there are cases where you are persuaded or convinced

by an argument, but where you should not be, because the argument is not actually

rationally persuasive for you. It is one task of rhetoric to cause people to overestimate

the rational persuasiveness of an argument – to convince or persuade people without

actually giving them good reasons.

To understand why this is so, examine Figure 6.1. You can see from this ﬁgure that

when we examine the relationships between sound arguments, rationally persuasive

arguments and the arguments that actually persuade people, it is possible for a given

argument to be one, two or all three of them. The important point you need to note

is that rational persuasiveness and soundness are properties that arguments can have

independently of whether an individual or group actually ﬁnds them persuasive.

Human beings are not always perfectly rational and part of the function of the

concept of rational persuasiveness as we have deﬁned it is to acknowledge this. If

rational persuasiveness were deﬁned so as to make all rationally persuasive arguments

ones that actually persuaded people, we would have no way of accounting for the fact

that sometimes people fail to be persuaded by arguments that they really should

be persuaded by, and are sometimes persuaded by arguments that they should not be

persuaded by.

There are three ways in which one can be mistaken about the rational persuasiveness

of an argument. Study them carefully, especially if the preceding paragraphs are

mysterious to you.

issues in argument-assessment174

First, we can make mistakes concerning whether or not an argument is valid or

inductively forceful. Especially in the case of a logically complex argument, we may,

for example, think the argument deductively valid or inductively forceful when it is

neither (for example, when the argument contains a fallacy that is also an effective

rhetorical ploy; see Chapters 2 and 7). If so, then even if we accept the truth of the

premises, and are perfectly justiﬁed or reasonable in doing so, we may think that the

argument is rationally persuasive for us when it is not. Equally, if we think an

argument invalid when it is valid, or think it inductively unforceful when it is

inductively forceful, it is possible to think an argument rationally unpersuasive for us

when in fact it is rationally persuasive for us.

Second, we can think we have good reason to accept a premise when we don’t, or vice

versa. For example, consider the following argument:

P1) Next summer will be a hot one.

P2) Hot weather is good for Cabernet Sauvignon grapes.

C) Probably, next year’s Cabernet Sauvignon harvest will be good.

This looks like an inductively forceful argument, and let us grant that P2 is true. Now

suppose Jane knows that P2 is true. She also thinks that P1 is true, but her reason is

that she has the superstitious belief that whenever it rains on winter solstice, the

following summer will be hot. In that case, assuming she knows it did rain on winter

solstice, she may think her belief in P1 is reasonable or well-founded, but it is not. So

in that case, having noticed its inductive forcefulness, she may well think that this

Figure 6.1

issues in argument-assessment 175

argument is rationally persuasive for her, but she would be wrong. She may be

persuaded, but she is not rationally persuaded.

Third, you can be mistaken about whether or not an argument is defeated for you.

On the one hand, you might accept an argument for a given conclusion – thereby

accepting the argument as rationally persuasive – without realising that you have

information sufﬁcient to construct another argument that defeats the conclusion of

the ﬁrst argument. You might, for example, accept an argument for the conclusion

that Mr Jones will attend the meeting, momentarily forgetting that Mr Jones had

scheduled a holiday today. On the other hand, you might think that an argument is

defeated for you when it isn’t. You might, that is, mistakenly think you have good

reasons to reject the conclusion of an argument that is inductively forceful and whose

premises you accept.

Obviously one can give arguments for various purposes, including deceitful ones. But

the rational, non-deceitful motivation for giving an argument is surely this: it is to give

a sound argument that is rationally persuasive for oneself, and for its intended audience.

Different arguments may be required for different audiences. We cannot always

know with certainty whether an argument is sound, but that is the human pre-

dicament. It is simply a consequence of the fact that we do not always know with

certainty which propositions are true and which false. If we did, we would never need

arguments.

6 Judgements about rational persuasiveness very frequently depend on estimates of

the legitimacy of the authority behind certain propositions. For example, an

ofﬁcial statement by the editor of the newspaper that such-and-such proposition

appearing in the newspaper was a mistake normally carries a good deal more

authority than the word of a random letter to the editor. A child would do better to

listen to his teacher on spelling than to her or his classmate. We will discuss this

more in Chapter 7, but in general it is perfectly normal and rational that one’s

credulity in certain propositions is proportional to our estimates of the authority

behind them.

7 In saying that an argument is rationally persuasive for a person only if the person

reasonably believes the premises, we are not requiring that the person have, at his or

her disposal, further arguments with those premises as conclusions. What we are

requiring is that the person be justiﬁed in accepting the premises. Justiﬁcation is a

wider concept than rational persuasiveness: if one has a rationally persuasive argu-

ment for a proposition then one is justiﬁed in accepting it, but one may be justiﬁed in

accepting it by means other than argument. In particular, some beliefs, especially

perceptual beliefs such as ‘I see a dog in front of me’, are often justiﬁed – reasonable

– even though they are not inferred from other beliefs. We will return to this in the

last chapter.

issues in argument-assessment176

SOME STRATEGIES FOR LOGICAL ASSESSMENT

Once we have an argument represented in standard form, we have to pronounce whether

or not the argument is valid, and if not, whether or not it is inductively forceful. To do

this, the basic technique is simple: ask yourself, can I imagine or conceive of a situation in

which the premises are true, but the conclusion false? If under no conceivable situation

could that be, then the argument is valid.

If you can think of ways in which the premises would be true but the conclusion false,

then you must determine to what degree, if any, the argument is inductively forceful.

What you do here is to imagine various situations in which all the premises are true. Of

these situations, which are more likely – the ones in which the conclusion is true, or the

ones in which it is false? If the situations in which the conclusion is true would be more

likely than those in which it is false, then the argument is inductively forceful; if not, not.

If it is forceful, it remains only to specify the degree to which it is so.

Here is an illustrative example:

P1) The diamond thief wore size ﬁve high heels.

C) The diamond thief was a woman.

This is not deductively valid, since it is not impossible that the thief was a man with very

small feet wearing high heels, or even a child. This is readily conceivable. Is the argument

inductively forceful? The premises themselves do not tell us that children seldom steal

diamonds and that men very seldom have such small feet. But these are items of general

knowledge that we can add as premises, thus making the inductive force of the argument

explicit:

P1) The diamond thief wore size ﬁve high heels.

P2) Very few men wear size ﬁve high heels.

P3) Very few children steal diamonds.

C1) Probably, the diamond thief was a woman.

Whenever we ﬁnd that an argument is not valid, we should always ask whether there are

premises that (1) the arguer could reasonably be expected to know, or which we know to

be true, and (2) would make the argument inductively forceful, if added.

Arguments with conditionals or generalisations as conclusions –

conditional proof

The process described above, where we ask ourselves whether there is a possible situation

in which an argument’s premises are true but its conclusion false, can be mentally

issues in argument-assessment 177

taxing, where the argument’s conclusion is a conditional or a generalisation. Recall the

argument from Chapter 5 concerning the tuna industry, rewritten to eliminate the use

of ‘unless’:

P1) Tuna catches have been decreasing signiﬁcantly for the past nine years.

P2) If tuna catches have been decreasing signiﬁcantly for the past nine years, then,

if the tuna industry is not regulated more stringently, the tuna population will

vanish.

C1) If the tuna industry is not regulated more stringently, then the tuna

population will vanish.

P3) If the tuna population vanishes, the tuna industry will collapse altogether.

C2) If the tuna industry is not regulated more stringently, it will collapse

altogether.

Concentrate on the argument from C1 and P3 to C2. It might be a bit difﬁcult to imagine

C1 and P3 true, and then ask whether C2 could be false in such a situation. But in fact,

when we considered this argument earlier, we used a method that makes it easier. We shall

now make this more explicit, as it is important when considering arguments that have as

much logical complexity as this argument (or more). Note that C2 is a conditional. What a

conditional asserts, roughly, is a certain relation between the antecedent and consequent –

that if the antecedent is true, then so is the consequent. So the question we want to answer

is this: If the premises of the argument were true, then would this purported relationship

hold? To answer this question we suppose, not only that the premises of the argument are

true, but that the antecedent of the argument’s conclusion is also true. And then what we want

to know is whether, under all those suppositions, the consequent of the argument’s con-

clusion would also have to be true. If that is so, then that conditional proposition does

follow from the premises.

We can illustrate the matter like this, using the arrow ‘→’ to indicate ‘if – then’ as we did

in Chapter 3. Suppose we have an argument that looks like this, with capital letters

standing in for sentences:

P1) . . .

P2) . . .

C) P → Q

Such an argument is valid only if the following is also valid, where P1 and P2 are the same

as before:

issues in argument-assessment178

P1) . . .

P2) . . .

P3) P

C) Q

That is to say, in order to determine whether P → Q follows from some premises, we ask

whether Q follows from those premises together with P. The technique is known as

conditional proof, since it provides a simpliﬁed means for proving a conditional.

So back to the tuna ﬁshing argument. Suppose C1 and P3 are true, and that the tuna

industry is not (going to be) regulated more stringently (this is the antecedent of C2). We

can now reason as follows: we have assumed that the tuna industry is not regulated more

stringently; therefore, according to C1, the tuna population will vanish. But in that case,

according to P3, the tuna industry will collapse altogether. But that is precisely what

the consequent of the C2 says. So we see that if C1 and P3 are true, then it does follow,

from the antecedent of C2’s being true, that the consequent of C2 is true also. So, by the

technique of conditional proof, the argument is valid.

The same sort of technique is useful where the conclusion of an argument is a generalisa-

tion. Consider this argument:

P1) Every midﬁelder on the Italian national side is a good defender.

P2) No one is a good defender who does not tackle well.

C) Every midﬁelder on the Italian national side tackles well.

Here, as before, we begin by supposing the premises true. But in this case the conclusion

is a generalisation. Now recall from Chapter 5 that generalisations can typically be

regarded as generalised conditionals. So the conclusion C can (somewhat awkwardly) be

re-worded as: ‘If someone is a midﬁelder on the Italian national side, then that person

tackles well.’ Thus suppose that P1 and P2 are true. What we do in this case is to suppose

that someone is a midﬁelder on the Italian national side; that is, we consider any mid-

ﬁelder on the Italian national side. What we now want to know is whether P1 and P2

force us to conclude that that person tackles well. They do: according to P1 this person

is a good defender; but then, according to P2, this person must tackle well. But this

was just any Italian midﬁelder, not any one in particular. So we can conclude that every

Italian midﬁelder tackles well (if P1 and P2 are true). Now consider a slightly different

argument:

P1) Every midﬁelder on the Italian national side is a good defender.

P2) Every player who tackles well is a good defender.

C) Every midﬁelder on the Italian national side tackles well.

issues in argument-assessment 179

If we imagine our Italian midﬁelder again, P1 entails that he is a good defender. But P2

does not entail that he tackles well. It says that every player who tackles well is a good

defender, but it does not tell us that if he is a good defender, then he tackles well. So P1

and P2, in this argument, do not allow us to conclude that our Italian midﬁelder tackles

well. The argument is invalid.

Supposing the conclusion false

Another way to assess the validity of an argument is suppose the premises are true but

the conclusion false. If we can see that this is impossible, then, according to the

deﬁnition of validity, the argument is valid; if we can see that this is possible, then we

know that the argument is invalid. So consider the ﬁrst argument about the Italian

footballers. To suppose the conclusion false is to suppose that there is at least one

Italian midﬁelder who does not tackle well. If he does not, then by P2 he is not a good

defender. But then he is an Italian midﬁelder who is not a good defender, which

contradicts P1. So if the conclusion is false, it is impossible for the premises to be true.

So the argument is valid.

Do the same with the second argument about the Italian footballers. We now imagine an

Italian midﬁelder who does not tackle well. According to P1, he must be a good defender.

But P2 does not force us, or enable us, to draw any further conclusion about this Italian

midﬁelder. It tells us that if he tackles well, then he is a good defender, but it does not tell

us anything about the case where he does not tackle well: it does not say that if he does not

tackle well then he is not a good defender. So the falsity of the conclusion is perfectly

consistent with the two premises being true. For all the premises say, our midﬁelder might

be a good defender for other reasons – he might be very quick and energetic, good at

clearances and so on. So the argument is invalid.

This method can be used on any argument, not just those whose conclusions are

conditionals or generalisations. But it is especially helpful in those cases.

REFUTATION BY COUNTEREXAMPLE

We move now to an important technique for showing that an argument is invalid or

inductively unforceful. Normally, you would use this when you have already determined

that the argument is not valid or inductively forceful, and, in an argument commentary,

when you wish to explain why the argument is not valid or inductively forceful. It is

grasped most easily by looking at an example. Consider this argument:

P1) Almost all heroin addicts were marijuana smokers before becoming heroin

addicts.

C) Marijuana smokers tend to become heroin addicts.

issues in argument-assessment180

This argument is sometimes given as a reason not to legalise marijuana (or cannabis). But it

is deﬁnitely a bad argument. This can be seen very readily by comparing it with this

argument:

P1) Almost all heroin addicts were milk drinkers before becoming heroin addicts.

C) Milk drinkers tend to become heroin addicts.

Obviously this argument would not give us a reason to outlaw the drinking of milk. Yet it

has a true premise, just as the ﬁrst argument, and more importantly, it embodies exactly

the same reasoning as the ﬁrst argument. In particular, both arguments assume that if

almost everyone who does X did Y beforehand, then having done Y makes them more

likely to do X (or, those who do Y tend to become people who do X). As the second

argument above illustrates, that is clearly wrong.

If you were given the ﬁrst argument, you could show that it is a bad argument by present-

ing the second as an example of the same reasoning. That is what we mean by refuting an

argument by means of a counterexample. The second example is a counterexample to the

belief in this form of reasoning.

Now in this case we have been able to lay bare the mistaken assumption upon which the

mistaken reasoning rested. This can often be very useful, and according to our general

policy of making everything explicit, we should make the assumption explicit, rendering

the two arguments thus:

P1) Almost all heroin addicts were marijuana smokers before becoming heroin

addicts.

P2) If almost everyone who does X did Y beforehand, then those who do Y tend to

become people who do X.

C) Marijuana smokers tend to become heroin addicts.

And:

P1) Almost all heroin addicts were milk drinkers before becoming heroin addicts.

P2) If almost everyone who does X did Y beforehand, then those who do Y tend to

become people who do X.

C) Milk drinkers tend to become heroin addicts.

In making this generalisation explicit, we make explicit exactly what is wrong with the

original argument. For we have now represented the argument as a deductively valid one.

But in this way we represent the argument as very obviously unsound, owing to the falsity

of P2. The second argument shows this, because it is valid, yet P1 is true and C is false.

According to the deﬁnition of validity, it follows that P2 is false.

issues in argument-assessment 181

The technique just discussed is this: if an argument is unsound due to an implicitly

assumed but false generalisation, ﬁrst make explicit the assumed generalisation, in such a

way that the argument becomes deductively valid (or inductively forceful). Then ﬁnd

a true premise and false conclusion that are suitably analogous to the premise and con-

clusion of the original argument, and substitute them (as we did with P1 and C of the

above argument).

Sometimes an arguer’s assumed, faulty generalisation is perfectly obvious, but they seem

not to notice that it is faulty. Here is an example:

The continuing carnage on our roads must be stopped. Since it will certainly reduce

the number of fatal road accidents, I propose that we immediately reduce all speed

limits by 25%.

We can reconstruct this, making the generalisation explicit, as follows:

P1) Reducing speed all limits by 25% would reduce the number of fatal road

accidents.

P2) Anything which will reduce the number of fatal road accidents should be done

immediately.

C) All speed limits should immediately be reduced by 25%.

This is deductively valid, but it can easily be refuted by counterexample:

P1) Banning all motor vehicles would reduce the number of fatal road accidents.

P2) Anything which will reduce the number of fatal road accidents should be done

immediately.

C) All motor vehicles should be banned immediately.

Since P1 is true and C false, and the argument is valid, P2 must be false. So the original

argument, since its P2 is the same, is unsound. Of course, this does not mean that nothing

should be done to reduce road fatalities. It means only that the fact that a given remedy

would reduce them is not sufﬁcient for carrying it out. As explained in the Chapter 5

section on practical arguments, we must, in such cases, show that the overall expected

value of the envisaged remedy would be positive (i.e. that it would not cause other, worse

problems), and also that no other remedy would have a higher expected value (no other

would be more practical and effective).

issues in argument-assessment182

ENGAGING WITH THE ARGUMENT I: AVOIDING THE

‘WHO IS TO SAY?’ CRITICISM

Sometimes an argument will contain a premise that no one would say can be known with

certainty. Sometimes these will have to do with what a particular person was thinking, or

with what motives people in certain circumstances are likely to have, or with the future,

such as whether unemployment will increase or the Labour Party will win the next

election. Consider this argument:

If they close down the factory – making over 500 workers redundant – then

unemployment in our town will immediately double, at the very least. This will

surely lead to increases in family tensions, hence in domestic violence. Studies have

found this happening in every case where there is such an abrupt and dramatic

increase in unemployment.

The conclusion is that if the factory closes, domestic violence will increase. Without

bothering to reconstruct further, you can well imagine someone reacting to this argument

with:

Well, who is to say what will happen? You don’t know that increased domestic

violence would result; you can’t just assume that the people in our town are as bad as

that.

But this is an empty criticism of the argument. The critic has given no reason to suppose

that the people of the town in question are different from other people. The critic is just

ignoring the argument, not analysing it. Assuming the premises to be true, the evidence

that an increase in domestic violence tends to follow large increases in unemployment is

very strong. Perhaps this sort of thing cannot be absolutely certain until it happens, but

that is the nature of inductive inferences. Where an argument is inductively forceful, the

person who says ‘who is to say’ that the conclusion is true is either repeating what nobody

doubts – that the argument is not deductively valid – or expressing a seemingly unreason-

able scepticism, like a person who refuses to believe that past observation supports the

hypothesis that spring will follow winter.

Another variety of the ‘who is to say?’ response is illustrated in the following example:

P1) Our ﬁnest works of art are irreplaceable cultural assets.

P2) It is the Government’s responsibility to protect our irreplaceable cultural

assets.

C) It is the Government’s responsibility to protect our ﬁnest works of art.

Now the phrase ‘ﬁnest work of art’ is a vague term; no doubt the boundary between the

ﬁnest works and the not-so-ﬁne works is not clear. It is also what is sometimes called a

issues in argument-assessment 183

‘value-laden’ term, since what makes something a ﬁne work of art depends at least partly

upon whether, in fact, people do value it (more generally, a value-laden term is one whose

application to things depends in some way upon our attitudes towards those things; for

example, the word ‘weed’ is value-laden, since whether or not something is a weed depends

on whether we like or tolerate it in gardens or among crops). So now suppose some

opponent of the conclusion responds to this argument with:

Well, who is to say what are our ﬁnest works of art? It’s a matter of opinion.

This is not an effective criticism of the argument. It may well be that there is some

difﬁculty in achieving unanimity on such a question. But in order effectively to criticise

an argument – in order to engage with it – one must either (i) show that the argument

is neither valid nor inductively forceful; or (ii) show or argue that there is no reason

to believe one or more of the premises, or that one or more of them is false; or (iii) show,

if it is an inductive argument, that it is defeated by some other argument. Merely

pointing out that a term occurring in the argument is vague or value-laden is not sufﬁcient.

Certainly remarking the presence of vagueness is not sufﬁcient. For example, ‘bald’ is a

vague term, yet it is inductively forceful to argue ‘Robin is female, therefore it is unlikely

that Robin is bald’. Nor is remarking the presence of a value-laden term sufﬁcient as a

criticism.

To make this vivid, consider this argument:

P1) Killing innocent children is immoral.

P2) One should not do what is immoral.

C) One should not kill innocent children.

This argument contains the words ‘immoral’, and ‘innocent’, which are certainly value-

laden. It would certainly be possible for someone to say: ‘Who is to say what is immoral, or

what is innocent?’ But the fact that these terms can present problems of application does

not detract from the evident soundness of this argument.

Of course, it might be that if the Government policy suggested by the argument about

works of art were enacted, it would be very difﬁcult to apply it, owing to the difﬁculty of

identifying ‘our ﬁnest’ works of art. That might even constitute an argument against such a

policy. But in order actually to engage with the argument, the critic must actually produce

such arguments; merely to point out that an argument contains a problematic or vague

term like ‘ﬁne work of art’ is not enough, as shown by the murder example.

ENGAGING WITH THE ARGUMENT II: DON’T MERELY

LABEL THE POSITION

Here is a typical example of what we mean by this:

issues in argument-assessment184

Freiberg argues that rape victims are ‘peculiarly vulnerable’ to emotional distress and

therefore should be given special protections when questioned by defence lawyers.

This is the usual ‘politically correct’ stance that gives every break to women or so-

called ‘minorities’.

It should be clear that whatever Freiberg’s argument was, the writer has not engaged with

it. The writer has not given a reason to think that the argument is not sound: they have not

criticised either its reasoning or its premises. What the writer has done, in calling Freiberg’s

position ‘politically correct’, is indulge in a certain kind of prejudicial labelling. Used in

this way, the label invites the reader to think that Freiberg is merely biased in certain ways,

subscribing unreﬂectively to a certain perceived orthodoxy. Similar things happen when

positions or arguments are labelled ‘conservative’, ‘liberal’ and the like.

ARGUMENT COMMENTARY

We have now completed our survey of our basic concepts and procedures of argument

analysis. By ‘argument analysis’ we mean a two-stage process; comprising ﬁrst the

reconstruction, then the assessment of the argument. At this point, we need to say a bit

more about the ﬁnal product of this process. When the analysis of an argument is under-

taken, you may sometimes want to produce a piece of written work that summarises the

analysis you have made. This should consist of three parts:

1 The argument (or arguments) as originally expressed.

2 The argument(s) expressed in standard form.

3A commentary on the argument(s), written in ordinary prose.

Generating 2 out of 1 is the stage of argument-reconstruction; most of what was said in

Chapter 5 of this book is addressed to various sorts of difﬁculties commonly encountered

in making that step. The concepts discussed in Chapters 3 and 4 also bear systematically

upon the step from 1 to 2, because, as explained earlier, the principle of charity enjoins us

to reconstruct the argument in the most favourable way, and we need those concepts in

order to determine exactly what that means.

What we have not yet discussed explicitly is step 3. What this comes to is simply a written

piece of work that covers the following points (either all of them, or as many as seems

relevant in the particular case):

(i) A general discussion of the argument, explaining, as appropriate: (1) The context in

which the argument is given, that is, whatever facts a reader would need to know in

order to understand the point of the argument. Often this will include a description

of what the arguer’s opponents are saying or arguing, especially when the arguer’s

primary intention is to rebut those arguments. (2) If needed, some discussion of the

structure of what the arguer has written or said. For example, if the arguer gives

issues in argument-assessment 185

several arguments, or devotes a great deal of space to explanation or rhetoric rather

than argument, then it may be useful to explain this.

(ii) A discussion of how and why the standard-form reconstruction was derived as it was,

focusing especially on any problems encountered in the process. In particular:

•The exclusion of extraneous material should be explained.

•Any rhetorical ploys should be pointed out, explained, and eliminated.

•If any implicit premises (or any implicit conclusions) have been added, it should

be explained why.

•If the conclusion or any premises have been re-worded, it should be explained

why (for example, it should be explained why an ambiguous sentence has been

rewritten, why a vague or highly rhetorical term has been replaced, etc.).

•It may also be useful to explain meanings of important words that appear in the

reconstruction.

In general, this section should ideally include everything necessary to justify the given

reconstruction. You have to explain why you have reconstructed the argument in the

way that you have (but there is no need to state points which are simply obvious).

Frequently, this will mention the likely intentions of the author of the original

argument, and the context in which the argument was given.

(iii) A discussion of the validity or degree of inductive force of the argument. You

have ﬁrst to pronounce whether or not the argument is deductively valid. If it is not,

you should explain why it is not (here, for example, you might use the method

of refutation by counterexample). And if it is not, you should pronounce and

explain to what degree, if any, the argument is inductively forceful. If the argument

commits a fallacy, then you may identify it at this point, especially if the fallacy is a

formal one.

(iv) If the argument is either valid or inductively forceful, a discussion and verdict con-

cerning the truth-values of the premises. This will amount to a verdict regarding the

soundness of the argument. It should be explained in detail which premises are most

debatable, and why. Except where it is more or less obvious, these explanations must

be substantive; actual reasons for accepting or doubting particular premises must be

given. One should avoid the ‘who is to say?’ criticism, for example. If the argument

commits a substantial fallacy (see Chapter 7, pp. 207–228), then you would explain

this here.

(v) In the case of an inductively sound argument, you should also say whether or not the

argument is defeated for you. An argument’s being defeated for you is a fact about

your relation to the argument, not a fact directly about the argument itself. By

contrast, an argument’s validity or inductive force (or lack of it), and its soundness (or

lack of it), are matters concerning which there is a single right answer, a fact about the

argument which is independent of the state of knowledge of particular people.

Nevertheless, when our ultimate concern is with the truth-value of the conclusion

of an argument, it is obviously relevant, when the argument is defeated for you, to

point this out in your argument commentary. In other cases, however, we may be

issues in argument-assessment186

interested, not so much in the truth of the conclusion, but in the merits of the

argument as given by the arguer. For example, Napoleon may have advanced an

inductively sound argument for the conclusion that his army would prevail at Water-

loo. That argument would be defeated for us, since we know that his army did not

win. But if our concern were to assess Napoleon’s reasoning, then we would not fault

it on the grounds that his argument is defeated for us.

We might rest with showing that the argument was inductively sound. Still, this

leaves open whether the argument was rationally persuasive for Napoleon. In order to

ﬁnd this out, we would need to know more about what Napoleon knew or might

have known. As historians or military strategists, we might be interested in this

question. And depending on the answer, we might ﬁnd Napoleon open to criticism in

either of two ways. First, even if the argument was inductively sound and rationally

persuasive for Napoleon, its degree of inductive force may not have been sufﬁcient to

risk the battle. In other words, the expected value of ﬁghting the battle may have

been negative, or insufﬁcient to justify the risk. Second, the argument may have been

defeated for Napoleon, and hence not rationally persuasive for him despite being

inductively sound. That is, the argument may have been defeated by some fact that

he knew but failed to take into account.

If an argument is defeated for you, you may be perfectly justiﬁed in saying: the

conclusion is false. For if an argument for a conclusion is defeated for you by a more

powerful argument against that conclusion, then you have a good reason for asserting

that the conclusion is false. In that case, you can say something stronger than ‘this

argument is defeated for me’; you can say: ‘the conclusion of this argument is false’.

We cannot always reach a deﬁnite verdict concerning a valid or inductively forceful

argument. In some cases your belief in the premises may not be strong enough for

you to pronounce conﬁdently that the argument is sound. In such a case you would

say that you think that the argument is probably sound. In other cases we fail to have

a belief either way with respect to an argument’s premises. What we should do in

such a case, rather than arbitrarily committing ourselves to a soundness verdict, is to

say that we cannot determine it because we are too ignorant of the truth-values of the

premises (note that one is in such a case showing that one ﬁnds the argument

rationally unpersuasive). We should also explain, if we can, what we would need to

ﬁnd out in order to alleviate that ignorance.

Ideally, it is helpful to keep the discussions (i)–(v) separate. However, this is not always

practical. For example, we may justify a given reconstruction on the grounds that it is

inductively more forceful than another possible reconstruction (following the principle of

charity). So we would be jumping ahead to (iv) in the midst of (ii). That is all right. The

main thing is to ensure that all three tasks are completed, with as much clarity as possible.

issues in argument-assessment 187

COMPLETE EXAMPLES

What follows are two complete reconstructions with commentaries of arguments

appearing in the newspapers – one relatively easy to reconstruct and the other relatively

more difﬁcult.

First argument: penalties for possession of cannabis

‘Class A’ drugs in the UK include heroin and cocaine; ‘class B’ includes oral amphetamine;

‘class C’ includes tranquillisers and certain painkillers. Cannabis (marijuana or hashish) is

presently a class C drug in the UK, downgraded from Class B in 2004 (class C means it

is roughly equivalent to a US-style misdemeanour to possess a small amount for personal

use; in practice it means at most a ﬁne, not imprisonment). The argument is given by Dr

Evan Harris MP, co-signed by an impressive team of experts in the area.1 We have assigned

letters to paragraphs and numbered sentences within in order to facilitate discussion, but

this is not always necessary, provided that you can clearly indicate which parts of the

argument as originally presented you are talking about.

Part 1 The arguments as presented

(A) 1 Today the House of Lords debates the proposal from the Home Ofﬁce to

reclassify cannabis from class C to class B. 2 In recommending this change to

parliament, the government has rejected the explicit advice of its appointed

experts, the Advisory Council on the Misuse of Drugs, for the ﬁrst time in nearly

30 years. 3 In its last report, produced at the request of the Home Secretary, the

ACMD clearly recommended – for the third time in the last six years – that cannabis

remains a class C drug, and did so after examining all the available and latest

evidence on short- and long-term health risks, as well as social harms, public

attitudes and policing priorities.

1 Dr Evan Harris: MP Lib Dem science spokesman; David King: former government chief scientiﬁc adviser;

Prof Michael Rawlins: Chair, ACMD 1998–2008; (Lord) Robert May: former government chief scientiﬁc

adviser; Phil Willis MP: Chair, Science select committee; Prof Gabriel Horne: Chair, Academy of Medical

Science working group on addiction; Prof Colin Blakemore: Member, UK Drug Policy Commission, former

director, Medical Research Council; Tracey Brown: Director, Sense about Science, Dr Leslie King: member,

ACMD; Ruth Runciman: former member, ACMD; Prof Ian Gilmore: President, Royal College of Physicians

and member, Academy of Medical Sciences Working Group on Brain Science, Addiction and Drugs; Prof Roger

Brownsword: Professor of Law at King’s College London and member, Academy of Medical Sciences Working

Group on Brain Science, Addiction and Drugs, Prof Bill Deakin: Professor of Psychiatry, Manchester University

and member, Academy of Medical Sciences Working Group on Brain Science, Addiction and Drugs; Prof

Trevor Robbins: Professor of Cognitive Neuroscience, University of Cambridge, member, Academy of Medical

Sciences Working Group on Brain Science, Addiction and Drugs. The letter is from the Guardian, Thursday

25 November 2008; it has been abridged.

issues in argument-assessment188

(B) 1 The impact of parliament agreeing to the government’s policy could be very

damaging. 2 Cannabis use has fallen in recent years, especially following its

downgrading to class C in 2004, and it is obviously unwise to risk reversing that

trend. 3 The classiﬁcation system must be credible – reclassiﬁcation would

send out an ambiguous message about the dangers of current class B drugs.

4Even more importantly, the move would be a sad departure from the welcome

trend – established after the Phillips report into the BSE disaster – of public policy

following expert scientiﬁc advice unless there is new evidence.

Part 2 The arguments reconstructed

Argument 1

P1) The ACMD’s position on drug classiﬁcation is the position of the

government’s own team of experts, and takes account of short- and long-

term health risks, social harms, public attitude and policing priorities.

P2) If (P1), then the ACMD’s position on drug classiﬁcation should not be

rejected by the government.

C1) The government should not reject the ACMD’s advice on drug

classiﬁcation.

P3) If the government reclassiﬁes cannabis from class C to class B, the

government will have rejected the explicit and repeated advice of the

ACMD.

C2) The government should not reclassify cannabis from Class C to

Class B.

Argument 2

P1) If the government reclassiﬁes cannabis from class C to class B, it risks

reversing the decline of cannabis use in the UK since it became a class C

drug in 2004.

P2) A reversal of the decline in cannabis use in the UK since it became a class C

drug in 2004 should not be risked.

C) The government should not reclassify cannabis from class C to class B.

Argument 3

P1) The government, in matters of public policy, should follow expert scientiﬁc

advice.

P2) If the government reclassiﬁes cannabis from class C to class B, the

government would be contradicting expert scientiﬁc advice on a matter of

public policy.

C) The government should not reclassify cannabis from class C to class B.

issues in argument-assessment 189

Argument 4

P1) The classiﬁcation system must be credible.

P2) If the government reclassiﬁes cannabis from class C to class B, the

classiﬁcation system will not be credible.

C) The government should not reclassify cannabis from class C to class B.

Part 3 Commentary

With connecting premises added, all four arguments seem to me to be valid, and

they all have the same conclusion. Sentence 1 from paragraph 1 is factual stage-

setting, and plays no argumentative role. Sentences 2 and 3, paragraph 1, make it

clear that Harris represents a formidable body of experts. Thus arguments 1 (from

paragraph 1, sentences 2 and 3) and 3 (paragraph 2, sentence 4) are straight-

forward arguments by appeals to authority, which in these cases appear to be

legitimate. In argument 1, I have represented Harris as ﬁrst arguing that authorities

are indeed legitimate, and

then

arguing that to upgrade cannabis from C to B

would amount to rejecting their advice. I ﬁnd argument 1 much more persuasive

than argument 3: (P1) of argument 3 is extremely sweeping; it entails, for example,

that scientiﬁc advice the only relevant consideration in setting the laws covering

abortion; that is at best contentious. Even if it were so, it does not seem relevant to

the issue here. In fact argument 3 is perhaps merely argument 1 but with a wider

scope in the generalisation, and hence the generalisation is more likely to have

counterexamples. Argument 1 is much more focused on the relevant issue.

Argument 2 is rather weak (straightforwardly derived from paragraph 2, sentences

1 and 2). The argument appears to claim that it is probable that a decline in cannabis

use since 2004 has been

caused

by its being downgraded at that time, but no

evidence is provided that this is not a mere

correlation

. Argument 4 (paragraph 2,

sentence 3) is also rather unpersuasive because of P2: If the government

reclassiﬁes cannabis, I don’t think it will mean that the credibility of the classiﬁcation

system would be undermined. At least, I would need far more information that what

is provided here, and it is unclear that the author is a relevant authority. It is the one

place where the rhetoric gets in the way: what is it, in this context, to ‘send out an

ambiguous message about the dangers of current class B drugs’? Presumably it

means that to lump cannabis with current class B drugs would be unwarranted,

since cannabis is not as bad as those. But that is the very point at issue; it would be

a case of begging the question. Perhaps Harris meant to point to the dangers of

the appearance of a governmental ‘ﬂip-ﬂop’ – the downgrade in 2004 followed by

an upgrade in 2008 – but I’m not sure exactly what he meant.

I think that Argument 1 is sound and very persuasive; argument 2 is almost

deﬁnitely unsound and not all persuasive; arguments 3 and 4 are of doubtful

soundness and unpersuasive. Since Argument 1 is

deductively

sound, the

conclusion is established.

issues in argument-assessment190

Second argument: a criminal wins the lottery

These are some arguments appearing in a London Times editorial piece by Mick Hume.

Many members of the public, and some tabloid newspapers, had expressed outrage that a

convicted rapist who had served ﬁfteen years of his sentence had won £7 million in the UK

National Lottery, having purchased a ticket while out on weekend furlough (he was due to

be released the following year).

Part 1 The arguments as presented

(A) 1 LIFE, they say, is a lottery. 2 But life has taught me that some things, other

than death and taxes, are dead certainties. 3 It seems a safe bet, for instance,

that as soon as newspapers stir up public outrage over something, the Home

Secretary will promise a law to ban it. 4 When it comes to new legislation, David

Blunkett’s knee jerks so fast and often that his guide dog might need to wear a

riot helmet.

(B) 1 Mr Blunkett’s latest example of made-to-order law and order is a pledge to

stop prisoners who win the National Lottery beneﬁting from their winnings in jail,

and make them pay compensation to the ofﬁcial victims’ fund. 2 This comes after

the public uproar over Iorworth Hoare, a convicted rapist serving a life sentence,

who won £7 million while on release from an open prison.

The Sun

promising to ‘ﬁnd a way to stop this happening again’. 2 Given that it

has never happened before, there seems no reason to imagine that it ever will.

3Yet Mr Blunkett’s article protests that ‘this is not a knee-jerk reaction’.

(D) 1 Hoare is obviously a horrible specimen deserving of public contempt, and I

could not care less about his ‘human right’ to buy a Lotto ticket. 2 I am worried,

however, about this irrational outburst of national outrage.

(E) 1 Everybody seems to be up in arms about such a bad man enjoying such good

fortune. ‘And he’s not the only undeserving winner’, moans one newspaper.

2Indeed he is not. 3 I am also an undeserving lottery winner. 4 And if, like me, you

have picked up the occasional tenner, then you are one, too. 5 As Clint Eastwood

tells Gene Hackman in

Unforgiven

, ‘Deserves got nothin’ to do with it’. 6 Life may or

may not be a lottery, but Lotto deﬁnitely is. 7 To win it, nobody has to prove his moral

worth, simply that he has the price of the ticket.

(F) 1 Some complain that they are outraged by Hoare’s windfall because they play

the lottery to give money to good causes. 2 Come off it. 3 When I buy a ticket it is no

more an act of charity than when I bet on the dogs or football. 4 It gives me (and my

young daughters who pick the numbers) a quick frisson of excitement on a

Saturday evening. 5 But when we don’t win, what difference can it make to us who

does?

issues in argument-assessment 191

(G) 1 Now Mr Blunkett says that ‘there’s no justice’ if Hoare can win the lottery

while his victims suffer. 2 Since when, Home Secretary, has criminal justice had

anything to do with who wins a rafﬂe? 3 I always thought justice involved criminals

paying their debt to society, not repaying their lottery winnings to the Home Ofﬁce.

4 That is why Hoare was sent to prison. 5 No doubt there is an argument to be had

about whether he should have been on release. 6 But the widespread suggestion

that his victims should start suing him for compensation is likely to make matters

worse. 7 What price do you put on a rape that happened 20 years ago, anyway?

8 It is entirely understandable that the women he attacked in the seventies and

eighties should feel aggrieved at this turn of events. 9 But exactly how are they

supposed to beneﬁt from seeing their past ordeals dragged across the national

media today?

(H) 1 Lotto can be neither a force for good nor evil in society, whether that

overblown rafﬂe is won by a convicted rapist or a conviction politician. 2 And there

cannot be a new law to ban everything that we don’t like in life.

Part 2 The arguments reconstructed

Argument 1

P1) Something should not be banned if it is unlikely to happen.

P2) It is unlikely that another imprisoned criminal will win the lottery.

C) Imprisoned criminals should not be banned from winning the lottery.

Argument 2

P1) Very few lottery winners deserve their winnings.

P2) Most lottery winners are entitled to collect their winnings.

C1) Some lottery winners who do not deserve their winnings are entitled to

their winnings.

C2) In order to be entitled to lottery winnings, it is not necessary to deserve

them.

Argument 3

P1) Most people, when playing the lottery, are not motivated primarily by the

desire to support good causes.

P2) Most lottery winners are entitled to collect their winnings.

C1) Some lottery winners who are not motivated by the desire to support

good causes are entitled to their winnings.

C2) In order to be entitled to lottery winnings, it is not necessary that one’s

playing the lottery should be primarily motivated by the desire to

support good causes.

issues in argument-assessment192

Argument 4

P1) If a someone convicted of a crime has served the sentence prescribed for

that crime, then, if the sentence was sufﬁcient for the crime, the person has

been sufﬁciently punished for the crime.

P2) Mr Hoare has served the sentence prescribed for the crime for which he was

convicted.

C) Either Mr Hoare’s sentence was not sufﬁcient for the crime, or he has

been sufﬁciently punished for it.

Part 3 Commentary

Iorworth Hoare, a convicted rapist, purchased a lottey ticket while on weekend

furlough from prison. he has served 15 years and is due to be released shortly.

The ticket was the winning ticket for a prize of £7 million. The author, Mick Hume,

appears to be responding to claims that Hoare should not be given the money,

which seem to be supported by arguments based on the following premises. First,

that imprisoned criminals should be banned from winning the lottery. Second, that

only people who ‘deserve’ to win the lottery are entitled to lottery winnings. Third,

that only people who play the lottery with the intention to contribute to ‘good

causes’ (the causes funded by lottery ticket sales) can be entitled to lottery

winnings. Hoare is an imprisoned criminal, is not a ‘deserving’ person, and

presumably did not play with the intention of contributing to good causes. Thus if

these premises are true, then we have three sound arguments for the conclusion

that Hoare is not entitled to the £7 million. Hume provides a further argument

whose relevance will be explained below.

Paragraph D, sentence 1 makes it clear that Hume is not contesting that Hoare is a

‘horrible specimen’. Sentence 2 expresses a vague worry about an ‘irrational

outburst of national outrage’, but it is never made clear what this worry is.

Argument 1 is derived from paragraph C. Paragraphs A and B are largely stage-

setting and rhetoric. Hume also criticises Home Secretary2 David Blunkett.

Argument 2 is derived from paragraph E. Some people, Hume says, complain

that Hoare is an ‘undeserving’ lottery winner, and therefore that he should not be

entitled to collect the prize. However, Hume says that he too is an ‘undeserving

lottery winner’. By this, as sentences 4–5 make clear, he means to present himself

as a

typical

case. The typical lottery winner does not ‘deserve’ the money they win;

thus, as represented in the reconstruction, very few winners ‘deserve’ the money.

The word ‘deserve’ is important here. To

deserve

something does not simply mean

2 In the British system of government, the Home Secretary is a member of the Prime Minister’s cabinet who is

responsible for various domestic matters, especially law and order and immigration policy. Blunkett was Home

Secretary in 2004, when this argument was given.

issues in argument-assessment 193

that one is

entitled

to it. For example, a person who merely ﬁnds a pound (or a

dollar) on the street does not thereby

deserve

it even though he or she is entitled to

keep it. On the other hand a person who does appropriate labour may have earned

the money and thereby deserve it. We also say, for example, that a man who has

worked hard for several months in succession ‘deserves’ a holiday. In general,

‘deserves it’ seems to mean ‘is owed it’, or ‘has earned it, by virtue of work or other

valuable actions’. So in this sense (P1) very few lottery winners

deserve

their

winnings. Yet we do accept that most winners are entitled to them: typically, if your

ticket is the winner, you have the right to collect. C1 of argument 2 thus follows. In

fact, it is probably true and accepted by most people that all but a few winners are

entitled to the prize, in which case it would follow that

most

lottery winners do not

deserve their prize but are entitled to it. But all we need here is the weaker P2 as

written. C2 follows from C1, which establishes Hume’s point: one cannot argue that

Hoare is not entitled to the lottery prize from the premise that he is undeserving.

For the needed premise, that winners are entitled to the prize only if they deserve

it, is false.

Argument 3, derived from paragraph F, is similar to argument 2. Again, some

people claim that those who do not play the lottery with the intention of

contributing to good causes by purchasing lottery tickets are not entitled to the

prize. Since Hoare is a bad person, they reason, he cannot have had that intention,

so he is not entitled to the prize. Hume contests the ﬁrst premise of that argument.

Hume points out that he and his daughters are not motivated in this way when they

play, and again assumes that he and his daughters are typical in this respect.

Hence P1. P2 is as in argument 2; from these follow C1, from which follows C2,

contradicting the idea that only those who intend to support good causes by

purchasing lottery tickets are entitled to collect winnings.

Argument 4 is directed against the quoted claim by David Blunkett that ‘there’s no

justice’ if a criminal such as Hoare wins the lottery. Hume interprets this as

meaning that if the criminal wins the lottery, then the requirements of

criminal

justice will not have been satisﬁed. That is to say, it will not be the case that the

criminal has received a legal punishment appropriate to the crime. As against this,

Hume poses what is written in the reconstruction as P1, and which seems to be

what is expressed by sentences 2–4. The condition ‘if the sentence was sufﬁcient

for the crime’ seems necessary. For suppose we wrote simply ‘if someone

convicted of a crime has served the sentence prescribed for that crime, then the

person has been sufﬁciently punished for the crime’. This is surely not true, since

at least some prescribed sentences are too lenient. Hume’s point seems to be that

it is the purpose of penal sentences to satisfy the demands of criminal justice.

Provided that the sentence ﬁts the crime, a criminal who has served the prescribed

sentence has satisﬁed the demands of criminal justice. Although Hume does not

do so, it might be added that it is

wrong

to punish a criminal further, when the

criminal has already satisﬁed the demands of criminal justice, and thus it would be

inappropriate to deprive him of money (the lottery winnings) that would otherwise

issues in argument-assessment194

legally be his. Since Hume does not assert that Hoare’s sentence was appropriate

to the crime, and I do not know whether it was, I have stated Hume’s conclusion

(which is only implicit in his presentation of the argument) as a disjunction: ‘Either

Mr Hoare’s sentence was not sufﬁcient for the crime, or he has been sufﬁciently

punished for it.’

All four of the arguments are valid, and arguments 2–4 seem to me to be sound.

Argument 1 does not seem to me to be sound because P1 seems to me to be false.

If something is highly unlikely, then still it might be that it should be banned,

especially if its consequences would be extremely bad. Also, it is not clear whether

P2 is true. Perhaps it is not likely that

another

prisoner will win £7 million, but if it

has happened once, it cannot be so unlikely that we can assume it won’t happen

again. Also, it is not so unlikely that prisoners will win smaller prizes, which would

raise the same issue.

Finally, some mention should be made of paragraph H. Hume’s opponents think

that something is morally wrong if bad people win the lottery. Hume’s main point

seems to be that it is the whole purpose of the lottery that the winner should be

determined by pure luck – not moral considerations or anything of that sort. So

argument 2 seems to be the most important one. Since it is sound, I conclude that

Hume has been successful in his main task.

COMMENTARY ON THE COMMENTARY

In work of this kind, there is always the question of how much detail to go into. In this case

we have included quite a lot of detail, largely in order to be highly illustrative. Still, we

could have gone into a lot more. In other cases – especially where it seems important or

interesting to do so – even more detail may be appropriate; more likely, less detail may be

appropriate. Also you should bear in mind that this case only illustrates a handful of the

techniques and issues that have been raised in this book; no one case is going to illustrate

very many of them, and every argument presents its own problems of interpretation and

reconstruction. There is certainly no need to copy the style of the foregoing commentary

slavishly – what is important is that the reconstruction be explained and justiﬁed in a way

that it is informative, clear, non-rhetorical and balanced (that is, you should aim to be

judicious and disinterested, in the sense of being neutral or unbiased). Any technique,

style or approach that serves these aims may be appropriate. Note also that, although the

ability to analyse arguments is a highly transferable skill – that is, it can be exercised on

arguments on any subject, and does not typically require specialised knowledge of the

subject – knowledge of the subject is often helpful, especially for understanding the context

in which the argument is given. This is often crucial, since so many key components of

arguments are often only implicit.

issues in argument-assessment 195

CHAPTER SUMMARY

A rationally persuasive argument must be either deductively valid or inductively forceful.

A deductively valid argument is rationally persuasive for you (at a time) if you have good

reason to accept its premises (at that time). An inductively forceful argument is rationally

persuasive for you (at a time) provided that you have good reason to accept the premises

(at that time), and the argument is not defeated for you (at that time). An inductively

forceful argument is defeated for you (at a time) if you have some other argument

for rejecting the conclusion that is more rationally persuasive for you than the one in

question.

Unlike validity, inductive force and soundness, rational persuasiveness is not a feature of

arguments in themselves. It is also a matter of a given person’s relationship to an argument

(at a time). An argument may be rationally persuasive for one person but not for another,

and for a person at a given time but not for the same person at another time. An argument

may be sound but not rationally persuasive for you, for the premises might be true even

though you lack good reasons to accept them, or you may accept the premises of an

argument that you recognise to be inductively sound, yet the argument is defeated for

you. Moreover, an argument may be rationally persuasive for you but not sound. For you

may have good reasons for accepting a set of premises, even when one of the premises

is false. But the question of whether or not an argument is rationally persuasive for you

is not simply the question of whether or not you ﬁnd it persuasive, or whether you are

in fact persuaded by it. For unlike the question of whether we are actually persuaded

by an argument, we can be mistaken about rational persuasiveness: an argument may

be rationally persuasive for you even when you think it isn’t, and fail to be when you

think it is. The importance of the concept of rational persuasiveness is that it captures

what arguments are intended to do: the distinctive aim of persuasion by argument is to

persuade people rationally, that is, by actually giving them good reasons to accept a given

conclusion, and not just seeming to. The person ought to accept the conclusion, even if

they do not.

There are various informal methods of logical assessment, and of demonstrating that an

argument is not valid or inductively forceful. The principal task is simply to apply the

deﬁnitions of deductive validity and inductive force, but there are some strategies to

facilitate this in more difﬁcult cases. One strategy that is almost always pertinent is to

suppose the conclusion of the argument to be false, and then to ask whether it would still

be possible for all the premises to be true. Another strategy, where the conclusion of an

argument is a conditional, is to suppose that the antecedent of that conditional is true, and

then to determine whether the remaining premises force one to conclude that the con-

sequent would also be true. If the conclusion of an argument is a generalisation, an

analogous strategy is to suppose that the antecedent of an arbitrary instance of the general-

isation is true. Finally, an effective way of demonstrating that an argument is invalid, or

inductively unforceful, is the method of refutation by counterexample. This involves

giving an argument that employs the same type of inference as the one in question, but

which is obviously invalid or unforceful.

issues in argument-assessment196

It is important to avoid the ‘who is to say?’ criticism. One form this takes is to complain

that the conclusion of an inductively forceful argument has not been ‘proven’, that it

‘might’ be false. Another is to object to an argument on the grounds that it contains a

value-laden term. It should be clear that these are not genuine criticisms from a rational

point of view. One must also avoid merely labelling an argument of position, for example,

as ‘politically correct’, ‘socialist’ or whatever; the applicability of such a label does not in

itself show why the argument or position should be rejected or accepted.

EXERCISES

1 For questions a–i, consider this argument:

P1) If Rangers won the match then the pub will sell pints for £1 tonight.

P2) Whenever Rangers are ahead at half-time of a Scottish Premiership

match, they almost always win the match.

P3) Rangers were ahead at half-time, and this is a Scottish Premiership match.

C) Very probably, the pub will sell pints for £1 tonight.

Suppose that the premises are true. Suppose that both Andrew and James know that

the premises are true (they have both seen the sign in the pub window about the £1

pints, they both saw the half-time score of 1–0 in favour of Rangers announced on

television, and both know that Rangers have won every Scottish Premiership match

in the past three years when leading at half-time). Andrew has no other information

relevant to the truth of the conclusion; but, unlike Andrew, James saw on television

that the opposing side scored twice in the second half to win the match 2–1.

a Is the argument deductively valid?

b Is the argument deductively sound?

c Is the argument inductively forceful?

d Is the argument inductively sound?

e Is the argument rationally persuasive for Andrew?

f Is the argument rationally persuasive for James?

g Should Andrew be persuaded by the argument?

h Should James be persuaded by the argument?

i If the argument is not rationally persuasive for either Andrew or James,

explain why.

2 Now consider this argument:

P1) The majority of well-educated Germans speak English.

P2) Jacob is a well-educated German.

C) Probably, Jacob speaks English.

issues in argument-assessment 197

Assume this time that P1 is true and that the conclusion is true; but assume that P2 is

false: Jacob is Austrian, and not very well-educated either. Still, he did learn English

quite well from his American mother. Assume that Catherine, Jane, Mary and Anna

all know that P1 is true. Catherine believes P2 is true because her friend David told

her it is; David is a reliable person who knows Jacob, and Catherine has no reason to

doubt him. In fact David’s mistake was quite reasonable: Jacob lied to him, telling

him he completed a university degree in history; further, it was reasonable for David

to infer, from Jacob’s accent, that Jacob is German. For, although German is the

national language of Austria, the vast majority of native German speakers are Ger-

man. Catherine knows nothing else about Jacob, and accepts C. Jane also believes P2,

but for different reasons: she fancies Jacob, having seen him, at a distance, at a party,

and thinks he’s well-educated because she saw Jacob wearing glasses and a tie. Jane

also accepts C, but has no other information relevant to the truth of C. Mary believes

both P1 and P2, for the same reasons as Catherine; but she does not accept C, because

she heard Jacob speaking German to David at the party, and inferred, quite reason-

ably, that Jacob does not speak English. She has no other information relevant to the

truth of C. Anna does not believe P2. She heard what David said to Catherine, and

believes that David is always sincere and well-informed; but Jacob is athletic and

handsome and she has a stupid irrational prejudice according to which athletic,

handsome men are almost always stupid, and therefore not well-educated. She has no

other information relevant to the truth of C.

a Is the argument inductively forceful?

b Is the argument inductively sound?

c Is the argument rationally persuasive for Catherine? Why or why not?

d Is the argument rationally persuasive for Jane? Why or why not?

e Is the argument rationally persuasive for Mary? Why or why not?

f Is the argument rationally persuasive for Anna? Why or why not?

3 Consider the following argument:

George W. Bush’s apparent obsession with Saddam Hussein may have the

appearance of paranoid schizophrenia: the fear that someone is out to get us

(paranoia) and the belief that only we can save the world (grandiosity). But

Bush’s beliefs wander into dangerous mental territory only if they’re wrong.

If he’s right about the danger presented by Saddam and our role in ending

that danger, then he’s perfectly rational.

Harry Sorenson, San Francisco Chronicle, 17 March 2003

(i) The last two sentences embody a serious confusion. Explain this confusion in

terms of the distinction between the rational persuasiveness of an argument and

truth of an argument’s conclusion.

(ii) What do you suppose is the intended conclusion of the argument? Reconstruct

the argument. Is it sound? Why not?

issues in argument-assessment198

4 The conclusions of the following arguments are conditionals or generalisations.

Reconstruct them. Then, using the technique discussed earlier of supposing the

antecedent of a conditional conclusion to be true, explain why the argument is, or is

not, valid. (In h, the conclusion is a generalisation; trying supposing ‘X is a Roman’,

whatever X may be.)

Example

This man is either a Russian spy or a criminal. No Russian spy wears a Rolex.

Everyone who enters this repair shop wears a Rolex. Therefore, if this man

enters this repair shop, then he is a criminal.

✎P1) No Russian spy wears a Rolex.

P2) Everyone who enters this repair shop wears a Rolex.

P3) If this man is not a Russian spy, then he is a criminal.

C) If this man enters this repair shop, then he is a criminal.

Suppose the man enters the repair shop. Then according to P2, he wears a Rolex.

Then according to P1, he is not a Russian spy. Then according to P3, he is a criminal.

So if he enters the repair shop, then he is a criminal.

a If the Lena is polluted, then the Ob is polluted. But if the Ob is polluted,

then the Dnieper is polluted. Therefore if the Lena is polluted, then so is the

Dnieper.

b The Lena is longer than the Ob. Therefore if the Danube is longer than the

Lena, it is longer than the Ob.

c Every Russian spy wears a Rolex. Everyone who enters this repair shop wears

a Rolex. Therefore if this man enters the repair shop, then he is a Russian

spy.

d If this man is not a spy, then he is a detective. But all detectives wear trench

coats, and he is not wearing one. If he is a spy, then either he is Russian or

American. But no American spy knows how to order dessert wines, unless he

is from New York. But all spies from New York wear trench coats. Therefore,

if this man knows how to order dessert wine, then he is a Russian spy.

e If the ancient Allemani wre both vicious and loyal, then the Romans would

have purchased their allegiance. If they had done so, then the Franks would

never have challenged the Allemani. But they certainly did. Therefore, if the

Allemani were vicious, they were not loyal.

f All Roman citizens were literate. Therefore if some ancient Visigoths were

literate, then some ancient Visigoths were Roman citizens.

g All Roman citizens were literate. Therefore if some ancient Visigoths were

Roman citizens, then some ancient Visigoths were literate.

h Every educated Roman knew Homer. But anyone who knows Homer knows

the story of Achilles. Therefore all Romans knew the story of Achilles.

issues in argument-assessment 199

i If God is unwilling to prevent evil, then God is not good. If God is unable to

prevent evil, then God is not omnipotent. God exists only if God is both

good and omnipotent. If God is willing and able to prevent evil, then evil

does not exist. Therefore if evil exists, then God does not exist.

j If God is unwilling to prevent evil, then God is not good. If God is unable to

prevent evil, then God is not omnipotent. If God exists, then God is good

and omnipotent. If God is willing and able to prevent evil, then evil does not

exist. Therefore if evil does not exist, then God exists.

5 The conclusions of the arguments in Exercise 3, a–e and i–j are conditionals. Split

them into two statements: antecedent and consequent. Now add the antecedent to

the premises, regard the consequent as the conclusion of the argument, and rewrite

the argument accordingly in standard form.

Example

P1) All Roman citizens were literate.

C) Therefore if some ancient Visigoths were Roman citizens, then some

ancient Visigoths were literate.

✎P1) All Roman citizens were literate.

P2) Some ancient Visigoths were Roman citizens.

C) Some ancient Visigoths were literate.

6 Reconstruct the following arguments, then refute them by counterexample – that is,

by giving arguments that embody the same pattern, but which have true premises

and false conclusions. It may help to extract the logical form of the argument (as

according to Chapter 3, pp. 78–81).

a A signiﬁcant increase in the rabbit population would bring about an

increase in the number of foxes. And sure enough, the number of foxes

has increased lately. This must, therefore, be due to an increase in the rabbit

population.

b If free will is impossible, then the concept of responsibility is nonsense. If so,

then the existing justice system is legitimate. Therefore if free will is possible,

then the existing justice system is legitimate.

c Many people have tried to prove that Nessie does not exist. But they have

failed. You should by now admit it. Nessie is real.

d You admit that the Loch Ness monster has not been seen in recent years.

If so, then it must be very secretive. But if it is secretive, then, obviously, it

exists. Therefore you have admitted that Nessie exists.

e Why don’t we do what we know will stop these evils? We should give drug-

dealers and paedophiles life prison sentences.

issues in argument-assessment200

7 For Exercise 3, a and c–j, extract the logical form. Use capital letters for sentences or

general terms. (See Chapter 3, pp. 78–81.) Some are difﬁcult! It may help to choose

letters that remind you of what you’re replacing them for. For example, in d, you

could use S for ‘spy’, D for ‘detective’, T for ‘trench coat wearer’, R for ‘Russian’, A

for ‘American’ and Y for ‘from New York’.

8 Draw tree-diagrams for the arguments in Exercise 3.

9 List the explicit premises and the conclusions of the arguments in Exercises 16, 18

and 19 of Chapter 5. Draw tree-diagrams for these, including only the explicit prem-

ises. Now add the needed implicit premises to the list, and draw new tree-diagrams

for the complete arguments.

10 Could one give an argument that (i) one knows to be sound, (ii) is rationally per-

suasive for its audience and (iii) is not rationally persuasive for oneself ? If not, why

not? If so, would that be deceitful, or otherwise naughty in any way? Why or why

not? Make up an example.

issues in argument-assessment 201

pseudo-reasoning

•Fallacies 202

Formal fallacies • Substantive fallacies

•Faulty argument techniques 228

Equivocation • Red herring • Slippery slope • Straw man • Begging the

question • False dilemma

•Too much maths! 235

Confusing absolute and relative difference • Margin of error

•Chapter summary 237

•Exercises 239

FALLACIES

Fallacies are arguments in the sense that ﬁts our deﬁnition of a set of propositions,

some of which are premises, one of which is a conclusion, the latter intended to follow

from the former. But in one way or another, they are bad arguments. Strictly speaking,

a fallacy is a mistake in reasoning. One commits a fallacy when the reasons advanced or

accepted in support of a claim fail to justify its acceptance. A fallacy can be committed

either when one is deciding whether to accept a claim on the basis of a fallacious

argument with which one has been presented, or when one is presenting the fallacious

argument oneself.

A fallacious argument or inference is one in which there is an inappropriate connection

between premises and conclusion. Almost all fallacies fall under one of the following two

types:

•Formal fallacies. Sometimes the inappropriate connections are failures of logical con-

nection, for example, in the case of the fallacy (below) of afﬁrming the consequent;

here the argument or inference is neither deductively valid nor inductively forceful,

even where all implicit premises have been made explicit. It is simply a logical mistake.

•Substantive fallacies. Sometimes the inappropriate connections involve reliance on

some very general unjustiﬁed assumptions or inferences. We need only make these

premises explicit in order to see that they are false and unjustiﬁed. What distinguishes

a fallacious argument of this kind from an ordinary unsound argument is that the

implicit, false or dubious premise will be of a very general nature, having nothing

speciﬁcally to do with the subject-matter of the argument. What this means will

become apparent when we turn to examples.

The vast majority of fallacies that we encounter in everyday texts and speech are substan-

tive fallacies, but some are formal fallacies. Arguments embodying formal or substantive

fallacies are necessarily unsound, but not all fallacious arguments are actually unsound.

Since fallacies are many and various in this way, it would be tedious and distracting to

formulate a precise deﬁnition. We will simply take fallacies to be mistakes in reasoning

that arise because of inappropriate connections between premises and conclusions; we

will identify the most commonly encountered fallacies, and we will demonstrate different

strategies for dealing with them.

It is important at the outset to note the general point, however, that a fallacious argu-

ment can have true or false premises: simply having false premises does not make an

argument fallacious. Nor does having true premises guarantee that an argument is not

fallacious.

Furthermore, a proposition accepted on the basis of a fallacious argument may turn out to

be true as a matter of actual fact. Suppose that someone reasons as follows:

There is blood on the candelabra. And if Colonel Mustard killed the victim with the

candelabra, then there would be. So Colonel Mustard must be the murderer.

Laid out in standard form the argument is thus:

P1) If Colonel Mustard killed the victim with the candelabra, then there is blood on

the candelabra.

P2) There is blood on the candelabra.

C) Colonel Mustard killed the victim.

Now suppose that, in fact, the conclusion is true: Colonel Mustard is the murderer. Still,

the reasoning that takes us to that conclusion is fallacious (the fallacy is the fallacy of

afﬁrming the consequent, which we discuss shortly). It is not legitimate to infer on the

basis of P1 and P2 that Colonel Mustard is the murderer. Even if both premises were true,

it would be possible for the conclusion to be false: for example, someone else could have

killed the victim with the candelabra. Knowledge of the truth of those premises, just by

themselves, would not be sufﬁcient to infer the conclusion, even if that conclusion were

actually true. If you were to be fooled by such an argument, you would end up with a true

belief, but for mistaken reasons.

pseudo-reasoning 203

Like linguistic phenomena and rhetorical ploys, the best way to become acquainted with

the different types of fallacies considered in this chapter is to practise identifying and

analysing them. As they are attempts to persuade by argument, you need to reconstruct

them in standard form and then use techniques of argument analysis and assessment to

demonstrate the ways in which they are fallacious.

And one last thing to bear in mind before we work through speciﬁc types of fallacies: many

types of fallacious argument are effective as rhetorical ploys. Someone might be aware that

their argument commits a fallacy, but will use it to try to persuade us because they are

aware of its rhetorical power: they are aware, that is, that it does tend to persuade people.

Fallacies tend to be effective as attempts to persuade because the psychological effect of

their rhetorical power means that we often ﬁnd them persuasive even though we ought

not to. Common examples include uses of ad hominem, majority belief and slippery slope

arguments to rhetorical effect.

Formal fallacies

The ﬁrst group of fallacies we want to discuss here are strictly formal fallacies; these are

patterns of argument whose reasoning makes purely logical mistakes. Each type of fallacy

constitutes an invalid argument and once you are familiar with the patterns, the fallacies

will be recognised by the presence of the particular invalid pattern.

Afﬁrming the consequent of a conditional

Or ‘afﬁrming the consequent’ for short. This occurs when we argue from the conditional

premise that if P (the antecedent), then Q (the consequent) together with the premise that

Q to the conclusion that P, as in the following example:

If someone is a philosopher then they are wise. Jon is wise, so Jon is a philosopher.

Reconstruction of the argument reveals its invalidity:

P1) If someone is a philosopher (P), then they are wise (Q).

P2) Jon is wise (Q).

C) Jon is a philosopher (P).

If the premises were true, the conclusion would not have to be true. There are plenty

of people who are wise and are not philosophers. So the fact that someone is wise is

insufﬁcient for us to draw the conclusion that they are a philosopher. That the inference

is fallacious is obvious if we consider a true conditional such as ‘If it is raining, then there

are clouds’; it certainly does not follow, from this and the premise ‘there are clouds’, that it

is raining.

Notice that afﬁrming the antecedent of a conditional premise does not make for an invalid

argument:

pseudo-reasoning204

P1) If someone is a philosopher (P), then they are wise (Q).

P2) Jon is a philosopher (P).

C) Jon is wise (Q).

This is of course valid because the conditional gives one condition under which someone is

wise and P2 asserts that the condition is met; so it is legitimate to conclude that the person

in question is wise.

Denying the antecedent of a conditional

Or ‘denying the antecedent’ for short. This is the fallacy that occurs when we argue from a

conditional premise (if P then Q) together with the negation of its antecedent (not-P) for

the conclusion that the consequent is also negated (not-Q). The invalidity of this pattern

can be seen clearly using a version of the example above:

P1) If someone is a philosopher (P), then they are wise (Q).

P2) Jon is not a philosopher (not P).

C) Jon is not wise (not Q).

The invalidity here has similar grounds to that of the fallacy of afﬁrming the consequent.

There are conditions other than being a philosopher under which someone could be wise,

so the fact that someone is not a philosopher does not give us sufﬁcient grounds for

concluding that they are not wise; other factors may mean that they are wise. Or again:

from ‘If it is raining then there are clouds’ and ‘it is not raining’, it does not follow that

there are no clouds.

Fallacy of deriving ‘ought’ from ‘is’

The Scottish philosopher David Hume famously argued that an ‘ought’ cannot be derived

from an ‘is’. The claim can be understood in two ways: ﬁrst, as a claim about motivations

to act or refrain from acting. The fact that something is thus-and-so, argued Hume, is

insufﬁcient as a reason for thinking that one ought to act in such-and-such a way. The fact

that torturing animals causes them suffering is not, according to this argument, sufﬁcient

reason to refrain from torturing animals. An additional motivating force – a desire to

avoid harm to animals – must also play a role in our motivation to act in such cases.

Although an interesting and controversial thesis, this way of interpreting Hume’s claim is

not the one that interests us here.1 Rather, we are interested in Hume’s claim under-

stood as the claim that a prescriptive conclusion cannot be validly derived from purely

descriptive premises, such an inference is fallacious. Thus the fallacy of deriving an ‘ought’

1 For a detailed discussion of this debate see J. L. Mackie, Ethics: Inventing Right and Wrong (Harmondsworth:

Penguin, 1977).

pseudo-reasoning 205

from an ‘is’ occurs when a prescriptive conclusion – a conclusion making a claim about

something that should or ought to be done or avoided or believed or not believed – is

deduced solely on the basis of descriptive, fact-stating, premises. Inferences from descrip-

tive to prescriptive propositions are considered fallacious because the fact that something

happens to be the case, or happens not to be the case, is insufﬁcient grounds for concluding

that it ought or ought not to be the case. If we want to make a valid argument for a

prescriptive conclusion, we must always do so from premises at least one of which is

prescriptive. Thus the following commits the fallacy of deriving ‘ought’ from ‘is’:

How can anyone claim that the monarchy should be abolished? The monarchy

as we know it has been central to British life for nearly a thousand years, arguably

longer.

Although it is not expressed as such, the conclusion of this argument is really a prescriptive

one – that the British monarchy should be retained – but the conclusion is arrived at

purely on the basis of the premise that it exists, and has done so for a long time. As such,

the argument is plainly invalid:

C) The British monarchy should be retained.

In this particular case we can make the argument valid by adding a prescriptive premise as

follows:

P1) The British monarchy has existed for nearly a thousand years.

P2) Anything that has existed for nearly a thousand years should be retained.

C) The British monarchy should be retained.

But the argument is clearly deductively unsound: poverty has existed for at least a

thousand years, but it is surely false to claim that it should be retained. Note that P2 does

not become more plausible if we make it into a soft generalisation. Thus the argument

cannot be saved by attempting to make it inductively forceful and inductively sound.

The base rate fallacy

This fallacy has already been mentioned in Chapter 4 (see pp. 103–104). It is committed

when an argument takes the following form: the proportion of one group that has a certain

feature is higher than the proportion of another group that has that feature. Therefore,

some X that has that feature is more likely to be from the ﬁrst group than the second.

Suppose someone reasons, for example: Rex is either a rat or a cat, 75 per cent of cats are

black whereas only 45 per cent of rats are black, Rex is black, therefore Rex is probably

a cat. The inference is mistaken because the number of black rats may still be larger

than the number of black cats. In fact it surely is: the overall number of rats in the

world is far greater than the number of cats, so even if blackness is more common among

pseudo-reasoning206

cats than rats, the number of black rats can still be much higher than the number of

black cats.

The fallacy commonly occurs when arguers resort to gender or racial stereotypes to make a

point. Suppose that Ringons are a minority group outnumbered by non-Ringons by ten to

one and someone argues:

P1) Most Ringons have a criminal record.

P2) Few non-Ringons have a criminal record.

P3) Apex has a criminal record.

C) Probably Apex is a Ringon.

Even though there is a high incidence of criminality among Ringons, there are so many

more non-Ringons than Ringons that someone with a criminal record is still more likely

to be a non-Ringon than they are to be a Ringon. Since the argument tells you nothing

about the total number of Ringons as compared with non-Ringons, the argument is not

inductively forceful: P1–P3 do not give you a reason to infer the conclusion. In fact, if you

did know that non-Ringons outnumber Ringons ten to one, then, given P1–P3 and asked

to guess whether Apex is a Ringon or a non-Ringon, ‘non-Ringon’ would be the better

guess.

Substantive fallacies

The ﬁrst two substantive fallacies that we consider involve an illegitimate inference from

the prevalence of a belief or an action to its acceptability. As with all of the substantive

fallacies we’ll discuss, we can expose the fallacy by making explicit the hidden assumption

that generates the illegitimate inference.

The fallacy of majority belief

This is the fallacy of concluding, on the basis of the fact that the majority believe a certain

proposition, that the proposition is true. The following reasoning commits it:

Of course the Government must crack down on identify theft, after all that’s what

most reasonable, law-abiding people believe.

The only reason the arguer gives for a government crack-down is that most people think

such a crack-down would be a good thing. We can see this more clearly by laying out the

argument in standard form:

P1) Most reasonable, law-abiding people believe that the Government should

crack down on identity theft.

C) The Government should crack down on identity theft.

pseudo-reasoning 207

So rendered, the argument is invalid. But we can make the cause of the faulty reasoning

clearer by making the hidden assumption explicit thus:

P1) Most reasonable, law-abiding people believe that the Government should

crack down on identity theft.

P2) Any belief shared by most reasonable, law-abiding people is true.

C) The Government should crack down on identity theft.

Once we add the implicit premise, the argument becomes valid; but we can now see that

the assumption underlying the argument, expressed by the hard generalisation P2, is false

and that the argument is therefore unsound. Even if a majority of people do believe a

proposition and even if they are of sound character, etc. their believing it is not sufﬁcient

to make it true. Imagine, for example, if most reasonable, law-abiding people believed that

the Earth was ﬂat, that would not establish that it is! More controversially, if a majority

of reasonable, law-abiding people believe that capital punishment should be restored as a

sentence for murder, the fact that it is a majority belief is not sufﬁcient to make it true.2

Even though the claim that the Government should take measures to prevent and punish

identity theft is uncontroversial, the fact remains that the fact that a majority of people

agree that this is so does not give us grounds to accept it. We are owed some justiﬁcation

for the claim that is independent of what anyone might believe. Here we have demon-

strated the principal strategy for dealing with substantive fallacies; by exposing the hidden

assumption generating the fallacy, we reveal that the same (or a very similar) false

proposition, usually a generalisation, ﬁgures in all instances of a particular fallacy.

The fallacy of majority belief often places us in an apparent dilemma when we have to take

decisions on behalf of others. Suppose you are a member of the jury in an important and

high-proﬁle trial that has received a great deal of pre-courtroom publicity. On that basis

you know that most people believe that the defendant was the victim of a conspiracy

on the part of the investigating police ofﬁcers; nevertheless, the evidence presented in

court gives you good reasons to believe that he is guilty. Thus you might be tempted into

reasoning as follows:

P1) Most people believe that the defendant was set up and is not guilty of the crime

he is alleged to have committed.

C) The defendant is innocent.

Such reasoning would commit the fallacy of majority belief and should be avoided as a

basis for a juror’s decision. Again we can make the faulty reasoning clear by exposing the

hidden false assumption, which will be a very similar generalisation to that which ﬁgured

in the previous example, thus:

2 We consider the relationship between truth and belief in more detail in Chapter 8.

pseudo-reasoning208

P1) Most people believe that the defendant was set up and is not guilty.

P2) Any belief held by the majority is true.

C) The defendant is innocent.

So the argument is valid but not sound.

The fallacy of majority belief is similar to the rhetorical ploy of appeal to popularity,

because both use the fact of something’s popularity or commonality to attempt to per-

suade us to do or believe it. Sometimes, the very act of presenting an argument that

commits the fallacy of majority belief is at the same time an example of the rhetorical ploy

of appealing to popularity. Still these are distinct things: again, to call it a (substantive)

fallacy is to say that the argument presented implicitly embodies a certain sort of unjusti-

ﬁed assumption; to call it a rhetorical ploy is to say that it attempts causally to induce us

to accept a certain belief by activating our social instincts, desires and fears. Some cases

exemplify the fallacy without exemplifying the rhetorical ploy: someone might, for

example, be quite sincere in thinking that if something is believed by the majority it must

be true, and accept a conclusion on that basis. On the other hand, some cases exemplify

the rhetorical ploy without exemplifying the fallacy: an advertisement, for example, that

shows someone being humiliated because they are the only person not drinking a certain

brand of cola is clearly trying to inﬂuence us by way of our social instincts and feelings, not

by presenting an argument.

Common practice

This is the tactic of attempting to persuade someone to do something they shouldn’t do

by giving them the justiﬁcation that ‘everyone does it’. The implication of this faulty

reasoning is that if everyone does X, X must be acceptable. We often use this tactic to

provide justiﬁcation to ourselves for doing things we ought not to do. For example: ‘I feel

like a day off today. It won’t hurt to call in sick, everyone does it once or twice a year.’ Like

the fallacy of majority belief, the common practice fallacy is driven by a false assumption

concerning the connection between what is commonly believed or done and what it is

morally, socially or rationally acceptable to believe or do. The following reasoning is an

instance of the common practice fallacy:

Of course it’s OK to cheat on your expenses once in a while, everyone does.

This standard form rendition of the argument shows it to be invalid because there is no

appropriate connection between the premise and the conclusion:

P1) Everyone falsiﬁes their expenses occasionally.

C) It is acceptable to cheat on one’s expenses occasionally.

Once again, exposing the false assumption produces the following argument, the

unsoundness of which rests on the actual falsity of both P1 and P2:

pseudo-reasoning 209

P1) Everyone cheats on their expenses occasionally.

P2) Any act that everyone occasionally performs is acceptable.

C) Cheating on one’s expenses is acceptable.

Surely there are some people who have never cheated when making a claim for expenses

from their employer; and we can think of actions – meting out violence to an innocent

stranger, for example – which, if performed occasionally by everyone, would still be

unacceptable. Even if the quantiﬁer in P1 and P2 was qualiﬁed by ‘almost’, making the

argument inductive rather than deductive, although P1 might be true, it becomes even less

plausible that P2 is true.

The next group of fallacies involve using alleged facts about the person(s) putting forward

an argument as the basis for inferring a conclusion that their argument should not be

accepted. In each case the fact about the person is irrelevant to the issue of whether or

not we should accept their argument. As critical thinkers we are only interested in the

argument, not in the character of the person giving it. It is also helpful to remember this

if we feel uncomfortable criticising arguments put forward by people we like, respect, fear

or want to impress. If the argument is a good one, it makes no difference by whom it was

given, likewise if it is a bad one.

Ad hominem

This fallacy (the name derives from the Latin, meaning ‘to the man’) can be committed in

two ways: either by responding to someone’s argument by making an attack upon the

person, rather than addressing the argument itself, or by rejecting a claim because of

disapproval of or dislike for the person who makes it. An example of the latter use of the

ad hominem fallacy is provided by the following reasoning which commits this fallacy by

citing a claim about a politician’s political allegiance as a reason for rejecting the legislation

they propose to prevent physical punishment of children:

Jill Goodwin says we should ban smacking, but what does she know, she’s a

representative of the bleeding heart, do-gooding, lentil eating, sandal-wearing Green

Party, for heaven’s sake!!

To reconstruct we need ﬁrst to defuse the rhetoric used to ridicule the person making the

proposal with which the arguer disagrees. This initial reconstruction displays the argument

as invalid:

P1) Jill Goodwin wants to legislate to ban smacking.

P2) Jill Goodwin is a representative of the Green Party.

C) We should not ban smacking.

pseudo-reasoning210

Our strategy of exposing the crucial underlying assumption results in the following argu-

ment, which is unsound because P3 is false:

P1) Jill Goodwin wants to legislate to ban smacking.

P2) Jill Goodwin is a member of the Green Party.

P3) We should never pass legislation proposed by Green Party MPs.

C) We should not legislate to ban smacking.

All instances of the ad hominem fallacy will depend upon similar underlying general

assumptions referring to certain characteristics or beliefs of arguers.

Ad hominem

circumstantial

This is a sub-species of the ad hominem fallacy and occurs when someone’s argument in

favour of doing or believing something is discounted on the grounds that they would

allegedly beneﬁt from our doing or believing it. Someone would be committing the ad

hominem circumstantial fallacy if they were to argue:

Of course academics argue in favour of the proposed expansion of university

education: the more aspiring graduates there are, the more job opportunities there

are for people like them.

Notice that the conclusion of this argument is left implicit, but given the arguer’s tone,

it is reasonable to conclude that they do not agree with the expansion proposal. When

reconstructing we need to add the conclusion for ourselves:

P1) Academics argue in favour of the proposed expansion of university education.

P2) They would beneﬁt from such an expansion.

C) We should reject academics’ arguments in favour of the proposal to

expand university education.

The result, however, is an argument that is neither valid nor inductively forceful. Once

again, we can see the true shape of the reasoning that constitutes this fallacy by exposing

the hidden assumption thus:

P1) Academics argue in favour of the proposed expansion of university education.

P2) They would beneﬁt from such an expansion.

P3) Whenever someone would beneﬁt from something they propose, we should

reject their arguments in favour of it.

C) We should reject academics’ arguments in favour of the proposal to

expand university education.

pseudo-reasoning 211

Note that P3 is really quite ludicrous: if it were true, then one could never hope to argue

successfully for what one wants! Normally, that is exactly what we do, and there is nothing

intrinsically illegitimate about it. So it is unreasonable to reject an argument because the

arguer desires or would beneﬁt from the truth of the conclusion. What matters is the

strength of the reasons given for the claim, irrespective of the arguer’s motives for making

the claim. Reason places no strictures on arguing in favour of things from which one

would beneﬁt.

However, this is not to say that the issue of a speaker’s or a writer’s character is entirely

irrelevant in matters of argument analysis and evaluation. A person’s character and actions

are certainly relevant to their credibility: the degree to which someone’s having said

something constitutes a reason to think it true. We should, for example, be on our guard

against believing the claims of people whom we know to be dishonest. Even those who are

not habitually dishonest are more likely to attempt deception if they are arguing for

something that is strongly in their own interest. There is certainly a higher probability

that someone who is not disinterested will deliberately resort to techniques of faulty

reasoning in their attempts to persuade us of the truth of their claims; for they have more

to lose if their arguments are not accepted. This probability increases with the degree to

which the person is unscrupulous. In such cases we should check the reasoning carefully,

and we should not take their having advanced a premise as a reason, in itself, to think it

true. This is not, however, to say that we should positively assume their reasoning to be

faulty or their premises false. That would be committing the ad hominem fallacy. We

should never lose sight of the need to assess the argument on its own account. If the

argument is found to be valid or inductively forceful, or the premises true, the character

of the arguer is irrelevant. As we have seen, considerations about the character of an

arguer do come into play when we consider whether or not an argument is rationally

persuasive for us. Whether or not the source of the claim that forms a premise of an

argument is a reliable source is a factor we should bring to bear in consideration of

whether we have reasons to accept an argument’s premises. Note that this is a matter of

assessment of our cognitive relationship to the premises, rather than a question of the

truth-values of those premises.

There is one ﬁnal observation to make concerning the relationship between people’s

characters and reputations and the strength of their arguments. This point does not

directly concern a type of fallacious reasoning, but is relevant to considerations about the

credibility of arguers and their arguments: sometimes we are tempted to ignore or reject

criticism of a person’s arguments because of the way in which they have been labelled or

treated by the media. The sorts of cases we have in mind are those in which someone has

received racist, sexist or homophobic treatment in the media and this has been given as a

reason for avoiding criticism of or for accepting their views. An example was provided by

arguments that it was acceptable to allow the convicted rapist and former heavyweight

boxing champion Mike Tyson into the UK on the grounds that much of the media

coverage of the case was racist. It may well be the case that a good deal of what was written

and said about Mr Tyson was racist and also that there were good reasons to grant him

entry. It is crucial to recognise, however, that the existence of the racist discourse was

pseudo-reasoning212

irrelevant to the strength or weakness of arguments that he should or shouldn’t have been

granted leave to enter the UK.

Tu quoque

In common with ad hominem fallacies, the tu quoque (‘you too’) fallacy occurs when we

make unwarranted connections between a person’s alleged lack of credibility and the

strength of their argument. Here the alleged lack of credibility ensues speciﬁcally from

their being hypocritical; from a perceived inconsistency between the arguer’s actions and

their claims. The fallacy is committed when we reject a person’s claim that a behaviour or

proposal should be refrained from or discarded on the grounds that they themselves

practise that behaviour; or when we reject a person’s claim that a behaviour or proposal

should be adopted on the grounds that they fail to follow it themselves. Consider the

following argument:

My Dad’s always telling me not to talk on my mobile phone while I’m driving, but

why should I take any notice of him? He’s always taking calls when he’s driving.

An initial reconstruction yields an invalid argument:

P1) My Dad says one shouldn’t talk on the mobile phone while driving.

P2) My Dad talks on his mobile phone while he’s driving.

C) It is OK to talk on the mobile phone while driving.

Exposing the hidden false assumption demonstrates that the argument is unsound due to

the falsity of P3):

P1) My Dad says one shouldn’t talk on the mobile phone while driving.

P2) My Dad talks on his mobile phone while he’s driving.

P3) Whenever someone’s behaviour is inconsistent with their advice, that advice is

false.

C) It is OK to talk on the mobile phone while driving.

The tu quoque fallacy occurs frequently in discussions of the gaps between politicians’

policy and private decisions.

Suppose someone were to argue the following:

The Government’s transport policy is a joke. How can we take them seriously when

they tell us to leave the car at home and use public transport when they themselves

go everywhere in chauffeur-driven limousines?

An initial reconstruction yields an invalid argument:

pseudo-reasoning 213

P1) The Government tells the public to use public transport.

P2) Members of the Government use cars instead of public transport.

C) We should not take the Government’s transport policy seriously.

Exposing the hidden false assumption (P3) demonstrates that the argument is

unsound:

P1) The Government tells the public to use public transport.

P2) Members of the Government use cars instead of public transport.

P3) Whenever someone’s behaviour is inconsistent with their policies, we should

not take those policies seriously.

C) We should not take Labour’s transport policy seriously.

The arguer has spotted the inconsistency between what the Government does and what it

says, but that inconsistency does not render false the Government’s views about public

transport and it does not provide a reason to reject the policies in question. Whether it

would be a good idea for more people to use public transport instead of private cars does

not depend on whether or not the members of the Government use public transport

themselves. When we commit this fallacy we are going against the old adage: ‘Don’t do as

I do, do as I say.’ We might well think that people ought to follow their own advice and

principles; in fact in most cases it is irrational for them not to do so, but it is equally

irrational of us to discount their arguments solely on the grounds that they themselves

don’t heed the conclusions of those arguments. Of course, the fact that someone in the

public arena behaves inconsistently or hypocritically does undermine their credibility and

may lead us to withdraw our trust and respect, but it is not in itself a reason to reject their

arguments. What seems to happen in such cases is that someone gives advice or expounds

a policy that they believe applies to their audience, but apparently not to themselves. We

suspect they delude themselves into thinking that they represent an exception to the

prescriptive claim that they are making. For instance, in the ﬁrst case above, Dad might

delude himself into thinking that he’s such an experienced and safe driver that when he

talks on his mobile phone while driving, he is not a danger to himself and to others and so

need not desist from doing it.

Appeal to authority

This fallacy also involves mistaken assumptions about the people mentioned by an

argument. It is committed when an argument makes an unjustiﬁed appeal to an alleged

authority. This can occur either because the authority appealed to is not in fact authorita-

tive on the matter in hand or because there is good reason to doubt that the claimed

authority is adequately informed of the facts of the matter. Often the alleged authority

will have some association with the matter in hand, but that association is not of a type to

make them an authority on the question on which they pronounce. For instance:

pseudo-reasoning214

Angus McKay, whisky blender for MacDonald’s distillery for 30 years, called today

for alcohol education to be introduced for children as young as ﬁve. With all those

years in the industry, Mr McKay must know what he’s talking about.

An initial reconstruction shows the argument to be valid:

P1) Mr McKay says that alcohol education should be introduced for ﬁve year

olds.

P2) Mr McKay has 30 years’ experience as a whisky blender.

P3) If someone has 30 years’ experience as a whisky blender, they must be an

expert on alcohol education.

P4) If someone is an expert on a subject, we have good reason to accept their

opinion on that subject.

C) Alcohol education should be introduced for ﬁve year olds.

It is unsound, however, because of the falsity of the conditional P3. The fact that someone

is very experienced, and expert, at making whisky is not sufﬁcient reason to think that

they are knowledgeable about everything to do with alcohol. We should be aware of the

risk of making unjustiﬁed appeals to authority when using the internet as a source of

information. The fact that an internet site states that something is the case should not

automatically be taken to mean that it is authoritative. We should take care to check the

source of the material and use the techniques introduced in this book to determine

whether we have good reason to accept the claims made.

This does not mean, of course, that all appeals to authority are fallacious; only those

that are mistaken about someone’s claim to be authoritative about the matter in hand.

Whisky blenders can claim authority on those matters on which they are best qualiﬁed to

speak. If Mr McKay were to say that the best way to make a single malt whisky is to use the

purest possible ingredients, then one might accept that claim on the basis of his evident

expertise in such matters. An argument incorporating such an appeal to authority might

look thus:

P1) Mr McKay says that the best way to make a single malt whisky is to use the

purest possible ingredients.

P2) Mr McKay has 30 years’ experience as a whisky blender.

P3) If someone has 30 years’ experience as a whisky blender, they must be an

expert on whisky blending

P4) If someone is an expert on a subject, we have good reason to accept their

opinion on that subject.

C) The best way to make a single malt whisky is to use the purest possible

ingredients.

pseudo-reasoning 215

Notice that, although the premises of the second argument are almost identical to those of

the fallacious one, it is valid and sound.3

The appeal to authority can also function as a rhetorical ploy; the pull of the alleged

authority being used to lure us into accepting the proposition argued for. A common

example of this use of the appeal to authority is the use of celebrity endorsement to sell

things. Although one might take Andy Murray’s endorsement of a brand of tennis rackets

as a good reason for buying that brand, one ought to be more wary about taking him to be

an authority on makes of car, for example, whereas Lewis Hamilton’s endorsement of a car

would be authoritative but his recommendation of a particular brand of golf clubs would

not.

The perfectionist fallacy

This fallacy occurs when we place excessive demands on an idea or a proposal and then

reject it purely on the grounds that it will not completely solve a problem. Someone would

commit the perfectionist fallacy if they were to argue or to accept the argument that:

World leaders should give up their plans to spend billions of dollars on rescuing

ﬁnancial markets. It would take trillions of dollars to ﬁx this mess, the amount they

are talking about will only partially solve the serious problems we face.

An initial reconstruction shows that the argument is invalid:

P1) World leaders’ plans to spend billions of dollars to rescue ﬁnancial markets will

not solve the economic problems completely.

C) The plans should be abandoned.

The assumption driving this instance of the perfectionist fallacy is that solutions should

only be pursued if they will completely solve the problems they are intended to solve;

more generally, the perfectionist assumption is that no measure aimed at solving or

reducing a problem is justiﬁed unless it solves or reduces it completely. This is really quite

silly if you think about it. It is obvious that many measures are intended to reduce a

problem, not completely eradicate it, and are justiﬁed if they do reduce the problem

sufﬁciently. For example, fences are put around cow pastures to keep the cows in; once in a

while a cow escapes, but no one would say that the occasional escape shows that the fences

are unjustiﬁed.

When we include the perfectionist premise in the argument, in this case expressed as a

conditional, we see that it is deductively unsound because the perfectionist premise is

false:

3 Our judgement that the argument is sound, however, is fallible. We might still be mistaken about the truth-

value of P3) or P4). Notice also that the argument could plausibly be interpreted as an inductive argument the

premises of which claim that we usually or almost always have good reason to accept the opinions of experts.

pseudo-reasoning216

P1) World leaders’ plans to spend billions of dollars to rescue ﬁnancial markets will

not solve the economic problems completely.

P2) If a proposed solution will not completely solve the problem it is intended to

solve, it should be abandoned.

C) Plans for rescuing ﬁnancial markets should be abandoned.

Conﬂation of morality with legality

This is the mistake of assuming that anything legal must be moral or, conversely, that

anything illegal must be immoral. For something to be legal within the boundaries of a

given political entity (nation, city, district, the United Nations) is to say that there is no law

in the statutes of that entity that prohibits it. However, the fact that something is legal

does not automatically make it morally acceptable. For example, it is not illegal to cheat on

your lover, or to be rude to a shy person at a party just out of cruelty, but these things are

immoral. More gravely, in some countries, slavery, though obviously immoral, was legal

until the nineteenth century. In other countries, even today, people may legally be denied

human and civil rights because of their race, ethnicity, gender or religious belief.

In some cases the laws ought to be changed in order to reﬂect what is morally right. Indeed,

it is tempting to argue that what is legal should include only what is moral. But to try to

outlaw everything immoral would be unworkable, and indeed it would overstep what are

generally considered to be the proper bounds of governmental authority. Some aspects of

behaviour that we ﬁnd morally unacceptable are not necessarily appropriate subjects for

legislation – conduct in personal relationships, for example. We would not want it to be

against the law to tell a lie, break a promise, make fun of someone or fail to show up for a

date. Conversely, the fact that something is illegal does not automatically make it immoral.

In some countries, Australia for example, it is illegal not to cast a vote in elections, but it is

not obvious that there is a moral issue at stake here. Similarly, you are breaking the law

when you park in a no-parking zone, but it is arguable whether or not you are doing

anything immoral. And sometimes laws that are meant to legislate against immorality are

mistaken; throughout the ages there have been laws against all manner of things, thought

by the authorities of the time to be immoral, that in retrospect we think are not immoral,

and that never were – the worship or non-worship of certain gods, the education of

women, the wearing of certain clothes. Indeed, to think that everything legal is moral is to

nullify the possibility of criticising existing laws on moral grounds.

Consider this example:

I don’t see why people are so hard on Donald Mirving. After all, he’s done nothing

wrong; in this country there’s no law against denying the Holocaust.

The ‘there’s no law against it, so it’s acceptable’ argument is an extremely common

instance of the fallacy of conﬂating legality and morality. The ﬁrst reconstruction shows

that the argument is invalid without the conﬂating assumption; the second shows that it is

pseudo-reasoning 217

valid but unsound with it because P3), which is made explicit in the second argument, is,

as the counterexamples discussed above demonstrate, clearly false:4

P1) Donald Mirving has denied the extent and facts of the Holocaust.

P2) It is not illegal to do this in the UK.

C) Donald Mirving’s denial of the extent and facts of the Holocaust was not

morally wrong.

P1) Donald Mirving has denied the extent and facts of the Holocaust.

P2) It is not illegal to do this in the UK.

P3) Anything legal is moral.

C) Donald Mirving’s denial of the Holocaust was not morally wrong.

So, pointing out that the act in question is not against the law does not show that it is not

wrong. Of course, many of the questions surrounding whether or not an issue is a moral

one are controversial (the examples given above are by no means clear-cut); they may

require reﬂection and argument in their own right.

Weak analogy

Analogies are often interesting and may be illustrative of points one wishes to make, but

arguing on the basis of analogy is often unsuccessful and turns out to be fallacious either

because the analogy is too weak to sustain the argument or because the analogy itself has

not been argued for. (This makes the argument question-begging. We discuss arguments

that beg the question later in this chapter.) In the case of the fallacy of weak analogy, it will

be helpful ﬁrst to see the form that instances usually take, and then to consider an

example. The fallacy of weak analogy usually proceeds on the basis of a proposition that

because one thing is similar to another in one respect, it is, therefore, similar in a further

respect. This mistaken inference is based on the false assumption that if something is

similar to another thing in one respect, it is similar in all respects. Hence we construct an

argument of the following valid but unsound form:

P1) An object X is similar to an object Y in respect of characteristic A.

P2) Whenever an object X is similar to an object Y in one respect, it is similar in all

respects.

P3) Y has characteristic B.

C) X has characteristic B.

4 We could, of course, use the technique of refutation by counterexample (see Chapter 6) to demonstrate the

weakness of this argument.

pseudo-reasoning218

An instance of this fallacy occurs frequently in debates about legislation to control the

ownership and use of ﬁrearms. So let’s take such an instance as our example:

I don’t see what all the fuss is about guns. Of course gun ownership shouldn’t be

prohibited, you can kill someone with a hockey stick, but no one proposes to ban

ownership of hockey sticks.

A reconstruction demonstrates that this argument takes the form characteristic of the

fallacy of weak analogy, except that to render the arguer’s reasoning fully, we have to add

a further premise to the effect that things that are the same should always be treated the

same:

P1) Guns are like hockey sticks in that both can be used to kill people.

P2) Whenever an object X is similar to an object Y in one respect, it is similar in all

respects.

P3) Objects that are similar to each other in all respects should be treated identically.

P4) We would not ban ownership of hockey sticks.

C) We should not ban ownership of guns.

The argument is unsound because it is obviously false to assume that similarity in one

respect implies similarity in all respects. While it is of course true that hockey sticks and

guns have some shared similarities, those similarities are not sufﬁcient for the analogy to

hold. The dissimilarities – hockey sticks have a different primary purpose; it is difﬁcult

to commit mass murder with a hockey stick, and so on – outweigh the similarities (indeed,

one can kill a person with just about any solid, heavy object, such as a television; it is

unreasonable to argue that since we don’t ban those potential murder weapons, we

shouldn’t ban ﬁrearms!)

The fact that arguments from analogy frequently turn out to be fallacious does not mean

that they are universally unsuccessful. For an analogy to be effective in giving us a reason to

accept a conclusion, an arguer must ﬁrst present an argument for the claim that the objects

that are allegedly analogous (hockey sticks and guns in the case under consideration) are

sufﬁciently similar in the relevant respects. Once established, this conclusion would

become a premise of a subsequent argument for the claim that gun ownership should

not be banned. For example, suppose that having offered an effective argument for the

conclusion that Britain and Sweden are sufﬁciently similar in the relevant respects,

someone were to argue thus:

The claim that the Government’s proposed legislation to target those who buy sex

from trafﬁcked women is ‘unworkable’ (Letters Nov 21st) must be robustly chal-

lenged. In Sweden, where such legislation was introduced in 1999, the number of

trafﬁcked women has dropped from about 2,500 to 500 per year. Our Government

should be applauded [for its proposals.]

June Purvis, Portsmouth, Guardian, 22/11/08

pseudo-reasoning 219

The letter writer is arguing in favour of the British Government’s proposed legislation

to make it a criminal offence to buy sex from trafﬁcked women working as sex workers. To

support her conclusion that the Government should be commended for its proposals,

she draws on a comparison with similar legislation in Sweden that has been successful in

reducing the number of trafﬁcked women. The argument can be reconstructed thus

(remember we are assuming that P1) has been satisfactorily argued for):5

P1) The British Government is proposing legislation to make buying sex from

trafﬁcked women a criminal offence.

P2) A similar law has been in force in Sweden since 1999.

P3) The Swedish law has been effective in signiﬁcantly reducing the number of

trafﬁcked women.

P4) Britain is sufﬁciently similar to Sweden in all the relevant respects.

P5) If P4), then it is likely that similar legislation would be effective in Britain.

P6) Governments that propose legislation that is likely to be effective should be

commended.

C) Probably, the British Government should be commended for its

proposed legislation to make it a criminal offence to buy sex from

trafﬁcked women.

Causal fallacies

These fallacies are committed when we make mistaken inferences about the cause(s) of

something. Three types can be distinguished:

•Post hoc ergo propter hoc (from the Latin, meaning ‘after that, this, therefore this because

of that);

•fallacy of mistaking correlation for cause; and

•inversion of cause and effect.

Post hoc ergo propter hoc

This fallacy occurs when we mistakenly infer that an event X caused an event Y merely on

the basis that Y occurred after X. In the following example, the fallacy is committed twice.

We can tell that the argument includes a causal claim because the proposition expressed

by the conclusion states that one event – making a will – makes another event happen –

living longer:

Making a will makes you live longer. That’s the conclusion reached by legacy

specialists Live and Let Live, who compared the mortality ﬁgures of those who had

5 We should note that, although a theory may be in principle provable, it may remain neither proved nor

unproved indeﬁnitely because there is insufﬁcient evidence to prove or disprove it conclusively.

pseudo-reasoning220

made a will with those who hadn’t. The average age of death for people who hadn’t

made a will was 72 years, 6 months. However, bequeath your personal possessions

on paper and life expectancy shoots up to 80 years, 5 months. Want to live even

longer? Leave some cash to charity; generous donors lasted until the ripe old age of

83 years.

As with previous cases, we can ﬁrst represent causal fallacies as neither invalid nor induc-

tively forceful arguments, then, to demonstrate that they are driven by a false assumption,

make the argument valid or inductively forceful but unsound:

P1) Generally, people who make a will live longer than those who don’t.

C) Probably, making a will causes people to live longer.

Adding the implicit general assumption and making explicit a further implicit

premise, needed to make the argument inductively forceful, gives the following, which

is inductively forceful but unsound due to the falsity of P2:

P1) Generally people who make a will live longer than those who don’t.

P2) Whenever one event (Y) occurs after another event (X), Y is caused by X.

P3) Living longer (not dying) occurs after making a will.

C) Probably, making a will causes people to live longer.

The post hoc ergo propter hoc fallacy is frequently committed in public discourse when

arguers are attempting to persuade people of the merits of a recently introduced policy or

piece of legislation. Thus, tougher sentencing policies might be fallaciously inferred to be

the cause of a drop in the crime rate, or a teachers’ pay increase to be the cause of better

examination marks in schools. Where the second event is alleged to be causally linked to

the ﬁrst solely on the basis that it occurred after the ﬁrst, the argument is almost deﬁnitely

fallacious. This is not to say that tougher sentencing couldn’t be a cause of a drop in the

crime rate; it’s just that we need to be given stronger reasons to accept the causal claim

than simply the fact that one event occurred before the other.

Fallacy of mistaking correlation for cause

Whereas the fallacy of post hoc ergo propter hoc occurs because the temporal priority of one

event over another is mistakenly assumed to be sufﬁcient to establish a causal relationship

between those events, this fallacy is committed when the fact that one type of event or

state of affairs is always or usually found in conjunction with another type of event or state

of affairs is mistakenly taken to be sufﬁcient to establish that events or states of affairs of

the one type cause the other. In short, the fallacy is committed when a statistical correl-

ation is assumed, without any further justiﬁcation, to establish a causal relation. So, for

instance, someone who argues:

pseudo-reasoning 221

You only have to look at the statistics to see that poverty is the obvious cause of

educational under-achievement. Eighty per cent of those who leave school with no

qualiﬁcations come from homes whose income is at least 50 per cent below the

national average.

commits the fallacy of mistaking correlation for cause. Our point here is not that it is

completely mistaken to think that there is a link between poverty and educational under-

achievement. Indeed, there is plenty of credible research establishing a relationship

between them. And certainly a statistical correlation is necessary for a causal relation: if

there is no statistical correlation, then there cannot be a causal relation. What is crucial,

though, is that we resist making the mistaken inferential leap from the fact of their

statistical correlation to the alleged fact of a causal relationship between them. There

may well be such a relationship, but correlation alone is not sufﬁcient to conclude

that the relationship is causal, as we see when we reconstruct the argument in standard

form:

P1) There is a statistical correlation between poverty and educational under-

achievement.

C) Poverty causes educational under-achievement.

Making explicit the hidden assumption, we derive the following valid but unsound

argument:

P1) There is a statistical correlation between poverty and educational under-

achievement.

P2) Whenever two phenomena X and Y are correlated, X is the cause of Y.

C) Poverty causes educational under-achievement.

That P2 is false can be made obvious by considering certain counterexamples. Creatures

that wear clothes, for example, tend to be more intelligent than those that do not. These

things are statistically correlated. But wearing clothes does not cause intelligence. In cases

where there is correlation between two or more events or phenomena and they are in

fact causally related, it is often difﬁcult to distinguish which is cause and which is effect.

Poverty and ill health tend to go together, but which causes which? It is probable that in

many cases they are mutually causally efﬁcacious.

Inversion of cause and effect

Here one mistakenly infers that if X causes Y, an absence of X will prevent Y:

Research carried out by a team of researchers shows that vitamin E may be the

key to the secret of everlasting youth. The team believe that the vitamin may be

pseudo-reasoning222

at work normally in humans to prevent ageing. Experiments carried out on

laboratory rats have enabled the scientists to discover that animals deprived of

vitamin E seem to age faster and even become senile. Their spokesperson, Dr Young,

said that although the ageing process remains mysterious, these experiments have

demonstrated an ‘interesting causal relationship’ between vitamin E and the ageing

process.

It is not warranted to infer from the fact that vitamin E deﬁciency seems to hasten ageing

to the claim that vitamin E is the secret of everlasting youth (i.e. that it prevents ageing).

The proposition that a lack of something (vitamin E) causes X (hastened ageing) does not

entail the proposition that the presence of that thing (vitamin E) causes the opposite of X

(slowed ageing). We can use a reconstruction to expose the mistaken causal assumption

driving this fallacy:

P1) Vitamin E deprivation causes hastened ageing.

P2) If a lack of something X is the cause of a phenomenon Y, the presence of X will

cause of the opposite of Y.

C) Vitamin E causes the ageing process to slow.

Sometimes we encounter the inversion fallacy and the fallacy of mistaking correlation

for cause committed simultaneously. The following reasoning fallaciously infers a causal

relation between eating certain foods and eating disorders from a correlation between

those things (in this case the correlation is anecdotal rather than statistical), but also

commits the inversion fallacy by mistakenly inverting that causal relationship:

Contrary to what the healthy eating lobby dictates, traditional British cooking is

good for you. Remember the good old days when we ate bacon, eggs, sausages, fried

tomatoes, potatoes, toast and marmalade? And that was just for breakfast. Well, in

those days, people didn’t succumb to anorexia or bulimia and the incidence of

obesity was much lower. Seems the ‘experts’ have got it wrong again.

This argument seems to conclude not only that eating traditional British cooking

protects people from anorexia, bulimia and obesity, but that not eating it causes those

illnesses. To expose the fallacies, we can reconstruct the entire argument as an extended

argument:

P1) When we ate traditional foods (X) there was a signiﬁcantly lower incidence of

anorexia, bulimia and obesity (lack of Y).

P2) Whenever two phenomena (X) and (Y) are correlated, X is the cause of Y.

C1) Eating traditional foods (X) causes a low incidence of anorexia, etc.

(lack of Y).

pseudo-reasoning 223

P3) Now we don’t eat those foods (lack of X) and the incidence of anorexia, etc. is

much higher (Y).

P4) Whenever X causes a lack of Y, a lack of X causes Y.

C2) Not eating traditional foods (lack of X) causes a higher incidence of

anorexia, bulimia and obesity (Y).

The fallacy of mistaking correlation for cause is signalled by P2. The mistaken inversion is

signalled by P4, which is false. Some causal relationships can be inverted, but it is certainly

not true of causal relationships in general that they can be. For example, drinking milk

causes us not to be thirsty. But it is not true that not drinking milk causes us to be thirsty!

The next two fallacies that we consider are committed when we make unwarranted

inferences from what is known, believed or proven.

Epistemic fallacies

Appeal to ignorance

This is the fallacy of concluding either that because a claim has not been proven it must be

false (the negative form), or that because it has not been disproved it must be true (the

positive form). It is often used when defending a belief in something that remains

unproven such as astrology or the existence of a deity. The following commits the negative

form of the fallacy:

As no one has proved that UFOs exist, it’s reasonable to assume that they don’t.

whereas this equally fallacious argument commits the positive form:

No one has managed to prove that UFOs don’t exist, so we can reasonably conclude

that they do.

As we see when we reconstruct the arguments, each fallacious and unsound argument is

driven either by the false assumption that absence of proof means a proposition is false or

that absence of disproof means a proposition is true. Notice that in reconstructing this

argument, we omit the indicator phrase ‘it is reasonable to conclude that’:

P1) No one has proved that UFOs exist.

P2) All unproved propositions are false.

C) UFOs do not exist.

P1) No one has proved that UFOs don’t exist.

P2) All propositions that have not been disproved are true.

C) UFOs do exist.

pseudo-reasoning224

Of course, in cases where efforts to prove something have been sufﬁciently strenuous, it

may be reasonable to infer the falsity of the proposition. For example, repeated efforts have

been made, using sophisticated scientiﬁc equipment, to ﬁnd the Loch Ness monster (to

prove the proposition that Nessie exists); but to no avail. It is reasonable on that basis to

conclude, alas, that Nessie doesn’t exist. But that is because we know that if Nessie did

exist, then she probably would have been detected by those efforts. The mere fact that a

proposition hasn’t been proved, just by itself, is no reason to think it false. Likewise,

the mere fact that a proposition hasn’t been disproved, just by itself, is no reason to think

it true.

‘Proof’ connotes certainty, and part of the faulty reasoning driving this fallacy is that

people sometimes think that if a claim is not certain, then it can reasonably be denied. But

that is not how things are, as should be reasonably clear from Chapter 4. Where we know

we have an inductively very forceful argument with true premises, then, despite not

having perfect certainty, it would be unreasonable to deny the conclusion (with certain

exceptions, as explained in Chapter 6). Some claims and theories provide the most

probable explanations of the phenomena they concern even though they remain neither

proved nor disproved. The theory of natural selection is one such example. The arguments

in favour of it have a great deal of inductive force, but as yet no one has managed to prove

it. Reasons why it should be considered the most plausible explanation of the evolution

of species ought to be incorporated into relevant arguments; whether or not it has been

proved is not essential to the question of whether we ought to believe it.

Epistemic fallacy

This fallacy (from the Greek episteme, meaning ‘knowledge’) arises because of the tricky

nature of knowledge and belief, and the difﬁculty of discerning from the third-personal

point of view what someone believes or knows. It is committed when we make a fallacious

inference from the fact that someone believes that P that they must also believe that Q

on the grounds that P and Q are about the same thing or person, even though the way

in which they refer to that thing or person is different. The following provides a simple

instance of the epistemic fallacy:

Chris believes that the US President enjoys basketball. Barack Obama is the US

President, so Chris believes that Barack Obama likes basketball.

A reconstruction gives us:

P1) Chris believes that the US President enjoys basketball.

P2) Barack Obama is the US President.

C) Chris believes that Barack Obama enjoys basketball.

pseudo-reasoning 225

The inference is incorrect and the argument invalid because the arguer has assumed that,

in addition to having beliefs about the President’s preferred leisure pursuits, Chris also

knows that Barack Obama is the President. But the arguer has given no grounds for this

assumption. Chris may only have a belief about the President but not know who is the

President. If so, then C might be false. Another way of putting this is to say that Chris may

not know that ‘the US President’ and ‘Barack Obama’ refer to the same person. Thus, if

Chris is indeed ignorant of Barack Obama’s being US President, the following argument,

though valid, would be unsound due to the falsity of P3 and of C:

P1) Chris believes that the US President enjoys basketball.

P2) Barack Obama is the US President.

P3) Chris knows that Barack Obama is the US President.

C) Chris believes that Barack Obama enjoys basketball.

It is important to note that similar inferences made in different contexts are warranted and

the arguments containing them valid. Consider the following:

P1) The British Prime Minister is a world champion darts player.

P2) Gordon Brown is the British Prime Minister.

C) Gordon Brown is a world champion darts player.

Inferences such as this are sanctioned by an apparently indubitable logical principle known

as Leibniz’s Law (after the seventeenth-century German philosopher and mathematician,

Gottfried Leibniz). This law holds that if one thing is the same identical thing as another,

then what is true of one must be true of the other. For example, if Superman has blond

hair and Superman and Clark Kent are the same person, then Clark Kent must have

blond hair. Sentences about people’s beliefs or knowledge, such as our example about

Barack Obama and basketball, are exceptions to Leibniz’s Law. If Chris believes that X is

thus-and-so, even if X and Y are the same thing, it does not follow that Chris believes Y to

be thus-and-so because we do not know whether or not Chris knows that X and Y are the

same thing. The inference would only be warranted if the arguer knew that Chris knew

this. How to make sense of these sorts of cases is a famous philosophical puzzle, but we

need not let that worry us here.6

The epistemic fallacy is often used knowingly to discredit someone’s opinion. For example:

Mr Smith believes that the cultivation and use of cannabis should remain a criminal

offence in this country. But cannabis is the most effective anti-nausea drug for

6 The most famous discussion is ‘On sense and reference’, by Gottlob Frege, reprinted in Meaning and

Reference, ed. A. W. Moore (Oxford: Oxford University Press, 1993).

pseudo-reasoning226

chemotherapy patients. So Mr Smith believes that it should remain a criminal

offence to produce or use the most effective anti-nausea drug for chemotherapy

patients.

An initial reconstruction of the argument gives us the following valid argument:

P1) Mr Smith believes that it should be a criminal offence to produce or to use

cannabis.

P2) Cannabis is the most effective anti-nausea drug for chemotherapy patients.

C) Mr Smith believes that it should be a criminal offence to produce or to use

the most effective anti-nausea drug for chemotherapy patients.

If we add an implicit premise of the same form as P3 in the previous example, we see that

we cannot conclude that the argument is sound unless we have some grounds for saying

that P3 (and hence C) are true:

P1) Mr Smith believes that it should be a criminal offence to produce or to use

cannabis.

P2) Cannabis is the most effective anti-nausea drug for chemotherapy patients.

P3) Mr Smith knows that the most effective anti-nausea drug for chemotherapy

patients is cannabis.

C) Mr Smith believes that it should be a criminal offence to produce or to use

the most effective anti-nausea drug for chemotherapy patients.

We are unjustiﬁed in making this knowledge attribution if we don’t know whether Mr

Smith is aware of the anti-nausea properties of cannabis. It is possible that Smith is

unaware that cannabis is the best anti-nausea drug for chemotherapy patients. Indeed, it

might well be that Smith believes that the best remedy for nausea ought to be made

available to chemotherapy patients, and so long as he is genuinely ignorant that cannabis

is the best such remedy, he would not be inconsistent in making this claim. The danger

of epistemic fallacies, then, is that they may attribute beliefs to persons that they do not

really hold.

Notice that the familiar ‘if you’re not with us you’re against us’ type of argument is an

instance of the epistemic fallacy. By claiming that a non-supporter takes an opposing

position, the arguer makes an unwarranted assumption about the non-supporter’s beliefs

when, in fact, the non-supporter may hold a view that does not amount to an opposing

one, or she may simply not have a view on the issue in question.7 Here’s an example:

7 The ‘if you’re not with us, you’re against us’ argument can also be an instance of the false dilemma fallacy.

The arguer implies that there are only two positions available on the issue in question – their own and one that

is in direct opposition to it.

pseudo-reasoning 227

The President has made it perfectly clear: we know who the terrorists are, and we are

going to hunt them down. Now Senator Routman wants to set limits on the pursuit

of these killers, by opposing covert overseas invasions by Special Forces. So he thinks

we should simply let them go?

The fact that the Senator opposes a particular means of pursuing terrorists is not sufﬁcient

to warrant the claim that he believes that terrorists shouldn’t be pursued at all. In all

likelihood he does believe they should be pursued, but by some means other than covert

overseas operations. Notice that the use of the epistemic fallacy in this way has a strong

rhetorical pull – the view attributed to the non-supporter is often a much stronger

position (a straightforward negation of the arguer’s position) than that which she actually

holds on the issue in question. The rhetorical effect of using the fallacy in this way is to

make opponents’ positions appear more extreme than they actually are and, hence, to

undermine the credibility of and support for that position. These examples turn on verbs

such as ‘knows’, ‘believes’ and ‘wants’. Philosophers and linguists call verbs such as these

propositional attitude verbs. If we reﬂect upon how these verbs are used, we see that

we say someone believes that . . ., where the blank is ﬁlled by the expression of some

proposition or other. A propositional attitude, then, expresses the fact that someone holds

some attitude towards a speciﬁc proposition. Smith believes that such-and-such is the case;

Jones wants such-and-such to happen; Brown knows that such-and-such is the case. Other

examples are ‘desires’, ‘hopes’, ‘prays’ and ‘wishes’.

FAULTY ARGUMENT TECHNIQUES

As we have seen both formal and substantial fallacies make for unsound arguments;

they are either irremediably invalid, or depend on some very general, but false, implicit

assumption. We turn now, to a different group of arguments. These are sometimes

labelled as fallacies, but not every instance of them will be invalid, or inductively unforce-

ful, or even unsound. However, they are all poor techniques at argument; they should be

criticised when we analyse arguments, and avoided in our own attempts to persuade by

argument. Many of them, however, are useful for non-rational persuasion: they are

frequently used to avoid engagement with an opponent, or to trump an opponent in the

knowledge that their premises do not actually give good reason to accept their conclusions.

In many cases they do have persuasive power, but it is not rational persuasive power and

we make an error in reasoning if we are persuaded by them.

Although reconstruction will be helpful in analysing instances of these argument tech-

niques, they cannot be exposed by making explicit a false assumption that drives all

instances of the technique in question. This is because there is no single false assumption

(expressed as a generalisation or a conditional) that underlies all instances of each of these

techniques. So, while we should, in order to expose their faulty reasoning, continue the

practice of reconstructing arguments that we suspect of employing these techniques, it is

not so easy to give a straightforward method for detecting them.

pseudo-reasoning228

Equivocation

The rhetorical ploy of trading on an equivocation is the ploy whereby we deliberately use a

word or form of words with the intention to confuse the audience; one hopes that the

audience will conﬂate the two or more possible interpretations. A single unsupported

claim, rather than an argument, may be the instrument of the ploy. To fall prey to an

argument that employs equivocation, by contrast, is to fail to notice an ambiguity, or in

some cases an instance of vagueness, thereby accepting the conclusion of an argument, when

one should not have. Silly but clear examples are easy to come by – for example, ‘In the

Philosophy department, someone broke one of the chair’s legs; therefore one of the

Philosophy department’s professors has a broken leg’ (equivocation on the word ‘chair’).

Such a case is simple and amusing but no one would actually be taken in by it. In the more

interesting cases, explaining the faulty reasoning can be a subtle conceptual task. For

example:

Some conservatives claim moral universal truths; they claim that throughout

history, in all times and places, people fundamentally have the same rights. This

displays a lamentable ignorance of history, and – characteristically of conservatives

– of other cultures. It is a plain fact that at other times in history, and in other parts

of the world today, human beings do not have the same rights. In some countries,

for example, a man has the right forcibly to conﬁne his wife to the home if he sees

ﬁt; not so in our culture. The conservative claim of universal rights is plainly false.

The arguer wishes to conclude that, contrary to certain conservatives who believe in

universal moral truths, whether or not a human being possesses a given right depends on

what culture they are in. Thus ignoring some irrelevant material, we may reconstruct it as

a very simple argument:

P1) In some countries, men have the right to conﬁne their wives forcibly; in other

countries they do not.

C1) It is not the case that human beings have the same rights in all places and

at all times.

C2) The conservative claim – that throughout history, in all times and places,

people fundamentally have the same rights – is false.

The argument equivocates on the word ‘right’, however. Both senses are established items

in our language, but they are close together in meaning. In one sense of the word, to

possess a ‘right’ is be allowed, by the culture or other social environment one is in (often,

but not always, this a system of laws), to perform a certain action. Call this the ‘con-

ventional’ sense of the word. In the other sense, to possess a ‘right’ is to be such that one

ought, whatever culture or other social environment one is in, to be allowed to perform a

certain action – even if one is not in fact allowed to. Call this the ‘philosophical’ sense of

pseudo-reasoning 229

the word. Thus one may possess rights in the philosophical sense that are not rights in the

conventional sense. The trouble with the argument is that it uses both senses: if we keep to

the conventional sense of the word, P1 is true, C1 is true, and the inference from P1 to C1

is valid. The inference to C2 would be valid if the conservative claim were intended in the

conventional sense. But the conservative claim, no doubt, was that rights are invariant in

the philosophical sense of the word. In that case C2 cannot be inferred from C1; the

inference would be no better than the silly one about the broken chair.

Red herring

So-named after the practice of dragging a smelly, salt-cured (and therefore reddish)

herring across the trail of an animal tracked by dogs, the red herring technique is used to

throw someone off the scent of one’s argument by distracting them with an irrelevance.

The rhetorical ploy of the smokescreen constitutes a similar tactic. However, where an

irrelevant premise(s) is given as a reason for accepting the conclusion being advanced, a

faulty argument is being used. For example:

The judge should rule against the charge of false accounting against the Chief

Executive of Utilicorp. The CEO is very popular with shareholders, and presides over

an extremely healthy company.

The arguer seems to advance the CEO’s popularity and success at running her company as

a reason to rule against the charge of ﬁnancial corruption. If we make the reasonable

assumption that the judge should rule strictly on the basis of the accused’s guilt or inno-

cence, then the CEO’s popularity and business acumen is utterly irrelevant.

Reconstructed, the argument looks like this:

P1) The CEO is very popular with shareholders, and presides over an extremely

healthy company.

P2) If the CEO is very popular with shareholders, and presides over an extremely

healthy company, then the judge should rule against the charge of false

accounting.

C) The court should rule against the charge of false accounting.

In general, the red herring fallacy is that of inferring a conclusion from a premise that is

strictly irrelevant to it, but in a way that has the potential to fool the audience into

accepting the inference. Normally this is accomplished by a premise that tends to instil

some sort of positive attitude towards the conclusion. In this case, the premise is intended

to make the audience feel supportive towards the CEO and to think that she is successful

in her role as CEO, thus unreceptive to the idea that she should be convicted of

misconduct.

Note that, although red herring arguments can easily be represented as valid (as in the

example above), red herring is not a substantive fallacy. P2 is obviously false, but our

pseudo-reasoning230

ability to recognise this depends on our knowledge of what is and what is not relevant to

the establishment of guilt in a court of law. More generally, what is and what is not

relevant to a conclusion will depend on the conclusion’s particular subject-matter. So there

is not going to be one characteristic premise that red herring arguments assume, in the

way that there is, for example, in the case of inverting cause and effect. So red herring,

according to our categories, is not a substantive fallacy, but it is a faulty argument

technique.

A common example of the red herring technique occurs when someone argues, in

response to criticism of their own approach to some problem or other, that because the

critic offers no solution to the problem, their criticism is wrong. Politicians often use this

technique when trying to score points from each other in debate. Of course, whether or

not your opponent is offering a solution to the problem at hand is irrelevant to whether or

not their criticism of your position is justiﬁed. It might be relevant to the question of their

credibility with respect to the issue under discussion, but that is a question about the

arguer, not the argument. Like many of the fallacies and faulty argument techniques

we discuss here, the red herring technique is certainly effective rhetorically, pulling an

audience’s attention away from the matter in hand towards some other issue.

It is worth re-emphasising, ﬁnally, that to say that someone has been taken in by a red

herring argument is to say that they have been fooled. The ability to recognise red herring

arguments varies depending on our knowledge of the subject-matter of the argument. But

if X honestly believes, for example, that cancer is always caused by thinking morally bad

thoughts, then, although having developed cancer is irrelevant to the question of the moral

character of their thoughts, X does not commit red herring if X infers, from the fact Y has

cancer, that Y must have been thinking bad thoughts. X is just badly informed. The point

of distinguishing red herring as an argument trading on irrelevance is to single out the

cases where one is fooled by an irrelevance, where one ought to have known better. Every

minimally educated person knows, for example, that guilt or innocence in a court of law

is properly established only by the preponderance of evidence; because of this, one who

advances or accepts the argument given above has been fooled by an irrelevance, and has

thus committed red herring.

Slippery slope

This technique is employed when an arguer wrongly assumes that to permit or forbid a

course of action will inevitably lead to the occurrence of further related and undesirable

events, without providing good reasons to suppose that the further events will indeed

inevitably follow; and thus to allow the ﬁrst is to tread on a slippery slope down which we

will slide to the other events. Since its rhetorical power is derived from fear or dislike of the

undesirable events, it is from a rhetorical point of view closely related to the appeal to fear.

Slippery slope arguments are sometimes used to justify particularly harsh laws or penal

sentences and occur frequently in debates about the liberalisation or toughening of laws or

constraints on behaviour, as in the following example about the decriminalisation of

cannabis use:

pseudo-reasoning 231

The decriminalisation of cannabis would be just the start. It would lead to a down-

ward spiral into widespread abuse of harder drugs like heroin and cocaine.

The implicit conclusion is that cannabis should not be decriminalised. The only explicit

premise is that if cannabis were decriminalised then the use of hard drugs would increase.

So an initial reconstruction represents the argument as invalid:

P1) If cannabis were to be decriminalised, the use of hard drugs would increase.

C) Cannabis should not be decriminalised.

Notice that as it stands the argument also commits the fallacy of deriving ‘ought’ from ‘is’.

To correct this, we need to add a premise to make good the connection between the non-

prescriptive premise and the prescriptive conclusion, thus ending up with the following

argument:

P1) If cannabis use were decriminalised, the use of hard drugs would increase.

P2) Anything that leads to increased use of harder drugs should be avoided.

C) Cannabis should not be decriminalised.

The immediate problem is that we have not been given a reason to think that P1 is true;

that is, no reason to think that decriminalisation of cannabis will unavoidably be the

beginning of a slippery slope to an increase in the use of hard drugs. Of course, some slopes

really are slippery; even in this case, it might be possible to give such reasons and they

might form part of an extended argument for the same conclusion. But as it stands the

argument remains faulty, because the arguer has not given a reason for supposing that it is

inevitable that allowing the ﬁrst event will precipitate a slide into even worse events. (This

form of argument is sometimes called ﬂoodgates – the arguer alleges without evidence that

allowing X will inevitably open the ﬂoodgates to Y and Z.) Occasionally, the appeal to a

slippery slope is legitimate – there is good reason to believe that some event X will

inexorably lead to some other event Y, which is undesirable. If this is so, however, the

reasons for believing that X is highly likely to lead to Y should be made explicit in an

argument.

Straw man

This is the technique used when an arguer ignores their opponent’s real position on an

issue and sets up a weaker version of that position by misrepresentation, exaggeration,

distortion or simpliﬁcation. This makes it easier to defeat; thereby creating the impression

that the real argument has been refuted. The straw man argument, like the straw man

himself, is easier to knock down than the real thing. Suppose that Jones is an advocate of

the legalisation of voluntary euthanasia; that is, Jones believes that terminally ill patients

should have the legal right to choose to have their life ended if their suffering has greatly

pseudo-reasoning232

diminished their quality of life, and doctors agree that the patient’s mental state is

sufﬁciently sound to make the decision rationally. Smith, Jones’ opponent, responds as

follows:

How can you support giving doctors the right to end a person’s life just because they

decide that the person’s life is no longer worth living; no one should have that power

over another person’s life, and doctors should not kill patients.

According to Smith, Jones advocates that doctors should unilaterally have the power to

end a patient’s life, if they think that the patient’s life is not worth living. That would be a

very controversial position. But it is not Jones’ position. Jones’ position is that patients

should have the choice of euthanasia, so long as that choice is approved by doctors. Of

course the doctor administers the lethal drug, but, as Jones envisages things, only at the

behest of the patient. Smith thus fails to engage with Jones’ actual position and instead

misrepresents it as a more extreme and therefore weaker position that (as far as we know)

Jones does not advocate.

Begging the question

An argument commits the fallacy of begging the question when the truth of its conclusion

is assumed by one or more of its premises, and the truth of the premises depend for their

justiﬁcation on the truth of the conclusion. Thus the premises ask the audience to grant

the conclusion even before the argument is given. Contrary to the way in which the phrase

is sometimes used in ordinary language, ‘begging the question’ does not mean raising the

question without offering an argument. By way of example, imagine the following

scenario:

Three thieves pull off a successful heist and steal four diamonds, but they can’t

decide how to divide their haul. Eventually the ﬁrst thief says: ‘I should get two

diamonds, and you two should get one each, because I’m the leader.’ The second

thief says: ‘Wait a minute, who says you’re the leader?’ The ﬁrst thief replies: ‘I must

be the leader, I’m getting the largest share of the haul.’

A reconstruction enables us to see clearly the way in which the ﬁrst thief’s reasoning begs

the question. Initially thief number one appears to argue from the proposition that he’s the

leader together with the implicit premise that leaders should always get the biggest haul to

the conclusion that he should get the biggest share:

P1) I’m the leader of the gang.

P2) Gang leaders should always get the biggest share of their gang’s haul.

C) I should get the biggest share of the haul.

But when requested by thief number two to justify P1, he argues as follows:

pseudo-reasoning 233

P1) I’m getting the biggest share of the haul.

P2) Whoever gets the biggest share of the haul is the leader of the gang.

C1) I must be the leader of the gang.

Once we put the two steps of the argument together to form a complex argument, we see

that it begs the question of who should get the biggest share:

P1) I’m getting the biggest share of the haul.

P2) Whomever receives the biggest share of the haul is the leader of the gang.

C1) I must be the leader of the gang.

P3) Gang leaders always receive the biggest share of their gang’s haul.

C2) I’m getting the biggest share of the haul.

Thief number one is guilty of begging the question (in addition to armed robbery) because

P1, which he uses to reach C2, expresses the same proposition as that expressed by C2. So

the conclusion – that thief number one gets the biggest share – is already assumed by the

premises. Notice that each inference stage passes our test for validity. If the premises

were true, the conclusion would have to be true, but the argument is a clear instance of

the fallacy of begging the question of who should get the biggest share of the proceeds

of the robbery.

An argument’s premise(s) and conclusion need not express a proposition in precisely the

same way (as they do in the previous example) in order for it to count as an instance

of begging the question. It is sufﬁcient that the premise be a version of, or rely upon, the

claim made by the conclusion. If someone were to argue from the premise that newspaper

editors claim that their publications are better than any other medium for ﬁnding out

about global affairs, to the conclusion that newspapers are the best source of international

news, their argument would still beg the question. For obvious reasons, arguments that beg

the question are often referred to as ‘circular reasoning’.

False dilemma

This is the technique of limiting consideration of positions on an issue to fewer alterna-

tives than are actually available to be considered. Typically, the arguer pretends that there

are only two options, when in fact there are more: the arguer sets up a dilemma where

none really exists by misrepresenting the possible positions on an issue, so that there

appears to be a straight choice between their own and its opposite. The technique is

employed by a politician who argues as follows:

There is a tough choice facing the Government and the nation: either we cut

taxes and increase everyone’s spending power, thereby providing much needed

pseudo-reasoning234

stimulation to the economy, or we increase spending on health and education. It is

impossible to do both; and without a tax cut the economy will remain weak. So

increased spending on health and education will have to wait.

As the reconstruction shows, the argument is valid, it is driven by the false assumption

that cutting taxes and increasing public spending on health and education preclude each

other.

P1) We should stimulate the economy.

P2) The only way to stimulate the economy is by cutting taxes.

C1) We should cut taxes.

P3) We cannot both cut taxes and increase public spending on health and

education.

C2) We should not increase public spending on health and education.

The assumption in P3 is not true because (a) if a tax cut does improve the economy, then

even if the Government takes a smaller proportion of the Gross National Product it might

take more in absolute terms (because the GNP will be larger); (b) expenditure on health

and education might be increased by diverting Government funds from other areas such as

defence; (c) the Government might be able to sustain a period of decreased tax revenues

and increased overall expenditure by increasing its debt (or decreasing its surplus, as the

case may be).

The false dilemma technique is often used to make the false assumption that if someone

does not agree with X, they must be anti-X, whereas they may hold some intermediate

position or be undecided. For example, suppose someone asks you if you are in favour of

positive discrimination towards under-represented groups in the award of promotion to

higher grades of a profession (afﬁrmative action). You reply that you are not and, employ-

ing a fallacious inference, they accuse you of being against afﬁrmative action, when in fact

you may just be undecided, neither for nor against it. Or, worse, perhaps they retort that

you support discrimination against under-represented groups, and therefore are racist,

ageist and misogynist (among other things).

TOO MUCH MATHS!

We will end this chapter on poor reasoning with a brief discussion of ways in which we

sometimes fail properly to take account of statistical material. This constitutes faulty

reasoning because misinterpretation of statistics can lead us draw unwarranted con-

clusions about what we should do or believe. Here we consider two common occurrences

of this type of mistake.

pseudo-reasoning 235

Confusing absolute and relative difference

This confusion is often seen in discussion of the results of trials of new medication; of the

likely effects of consuming/not consuming some or other foodstuff or the effects of using

some product or other, often cosmetic or domestic cleaning products. In some cases media

reports apparently deliberately gloss over the difference between absolute and relative risk,

perhaps because they feel the distinction is too complex for their audience to grasp or

because discussion of relative risk has more headline-grabbing appeal than that of absolute

risk. Consider the following:

Researchers are excited about new wonder drug Roccastatin. Trials revealed a

dramatic decrease in risks of cardio-related illnesses, with risk of heart attack

lowered by 54%, and risk of stroke lowered by 48%.

Headlines such as these refer to the reduction in relative risk of developing a condition or

experiencing an adverse event. Relative risk is a measure of the difference in risk between

someone taking the medication that’s being trialled and someone who’s not taking it. If

we are told that the risk of heart attack reduces by 54 per cent if the medication in

question is used, then we might be inclined to believe that taking the drug would make a

big difference to our life expectancy and ask our doctor to prescribe the drug. However, in

order properly to understand the likely effects on our life expectancy of taking the medica-

tion, we need to know the absolute risk because the relative risk reduction ﬁgure is

actually a percentage of the absolute risk. So if trials of Roccastatin are reported to reduce

the risk of heart attack by 54 per cent, we should understand this as a 54 per cent

reduction in the absolute risk. Suppose that risk is 0.5 per cent, then taking the new

medication would reduce that risk to 0.27 per cent. Now the effects of the medication

seem much less ‘dramatic’ and, assuming one’s absolute risk were not elevated by other

factors, one might feel less inclined to start taking the drug.

A (possibly deliberate) conﬂation of the distinction between relative and absolute dif-

ference occurs in advertising. Consider the following:

Perfectskin is the total solution to skin ageing. In tests, 9 out of 10 women reported

an 80% improvement in ﬁne lines and wrinkles compared with their usual skin care

routine.

If you were a lady of a certain age worried about your appearance, an advertisement such as

this might incline you to try out the new cream. Indeed, an 80 per cent improvement in

the skin’s appearance seems a pretty impressive result. However, 80 per cent represents the

difference between how the skin appeared using the new product and how skin appeared

when the testers used their regular face cream. So, although the new cream affords an

80 per cent improvement, that improvement is 80 per cent of whatever improvement they

saw when using their usual cream. That ﬁgure will most likely vary depending on the

tester and the cream used (so the advertisement is misleading in glossing over those

differences, as well), but let’s suppose that testers regularly using some other cream

generally see an improvement in their skin of approximately 20 per cent, then, according

pseudo-reasoning236

to the results of the clinical tests, using the new cream affords an absolute improvement of

36 per cent. Perhaps impressive enough for one to give it a try, but nothing like the

promise held out by the original 80 per cent ﬁgure.

As you can see, the rhetorical effects of the conﬂation of relative and absolute risk should

not be underestimated. Notice also that appeals to scientiﬁc and clinical evidence are

increasingly used rhetorically to give the impression of a product that has been subject to

rigorous scientiﬁc investigation, thereby leading us to form the belief that the product in

question is safe, effective and of top quality.

Often relative and absolute difference are confused simply because the language used

to explain the data in question is insufﬁciently precise to capture the distinction. It is

common for the language used by media writers in reporting scientiﬁc matters to the

general public to be insufﬁciently precise. For instance, in reporting a correlation between

screening for a certain type of cancer and detection of that cancer, a journalist may report

that ‘the incidence of cancer has risen in every country with screening’ but the information

that should be communicated is that detection of cancer has risen in every county with

screening. Clearly there is a correlation between increased screening and increased detec-

tion (indeed, achieving such a correlation is one of the secondary aims of introducing

screening), but it would be incorrect, and misleading, to claim a correlation between

screening and incidence of cancer. A further frequently encountered case is the mis-

representation of the margin of error involved in interpreting opinion poll data.

Margin of error

The notion of margin of error is associated with the interpretation of opinion poll data,

such as that gathered in pre-election polling. If we are told that a poll has a margin of error

of n percentage points, then we are being told that the poll predicts the actual percentage

within n percentage points with 95 per cent probability of being correct. There is no less

complex way of putting it. Often, impatient with the actual meaning of ‘margin of error’

(or uncomprehending of it), people assume something simpler and in doing so distort the

facts, as happens in the following case:

A recent CNN poll, conducted by the Opinion Research Corp., shows Clinton 3

percentage points ahead of McCain, 50–47, in a hypothetical matchup. That’s

within the poll’s margin of error, so it’s a tie.

Ruben Navarrette Jr8

CHAPTER SUMMARY

Fallacies can be grouped together according to certain shared features. Formal fallacies are

simply mistaken inferences – inferences of certain characteristic kinds that are often

8 From the CNN website, at http://www.cnn.com/2008/POLITICS/02/11/navarrette/index.html

pseudo-reasoning 237

mistakenly thought to be valid or inductively forceful. These include: the fallacies of

afﬁrming the consequent (of a conditional proposition) and denying the antecedent (of a

conditional proposition); the fallacy of deriving ‘ought’ from ‘is’, which is committed by

any argument that attempts to move from solely descriptive premises to a prescriptive

conclusion; and the base rate fallacy.

Substantive fallacies are committed by arguments that tacitly assume some very general

principle of a characteristic kind that it may be tempting to rely upon, but which is false,

and which can easily be seen to be false the moment it is brought to light. The fallacies of

majority belief and common practice make illegitimate inferences from the commonality

of a belief or an action to its acceptability. The ad hominem fallacy and the tu quoque

fallacy use facts about the person(s) putting forward a position as grounds for rejecting it.

The appeal to authority makes a mistaken appeal to the opinion of someone who is not

qualiﬁed (or under-qualiﬁed) on the matter in hand. The perfectionist fallacy is com-

mitted when excessive demands are placed on an idea or proposal; the fallacy of conﬂating

morality with legality occurs when we mistakenly assume that anything that is legal

must also be moral or that anything that is illegal must be immoral. The fallacy of weak

analogy arises when an argument employs an unsustainable or an unjustiﬁed analogy.

Causal fallacies are committed when we make mistaken inferences about the cause of a

phenomenon or an event. There are three types of causal fallacy: post hoc ergo propter hoc

– the fallacy of assuming that the temporal priority of X over Y makes X the cause of Y;

the fallacy of mistaking correlation for cause – falsely assuming that the simultaneous

occurrence of X and Y makes one the cause of the other; and the fallacy of causal inversion

– the mistaken inference that if X causes Y, an absence of X will prevent Y. Epistemic

fallacies and the fallacy of appeal to ignorance occur because of unwarranted inferences

from what is known, believed or proven to additional knowledge, beliefs or proof of which

the arguer has no independent evidence.

Substantive fallacies can be exposed by careful argument-reconstruction. An initial

reconstruction will demonstrate that the argument, as stated, is either invalid or lacking

inductive force. A second reconstruction can be used to reveal the false assumption that

drives the fallacious reasoning, thereby demonstrating that the (amended) argument is

unsound. For each substantive fallacy, all instances of the fallacy will be driven by the same

or a very similar assumption.

Some common argument techniques are not fallacies according to our account, but they

are faulty argument techniques. Not all instances of these techniques are invalid, non-

inductively forceful or unsound even when carefully reconstructed. A deductively sound,

hence valid, argument may beg the question, for example. While the method of exposing

hidden assumptions will prove helpful for some instances, there is no single false assump-

tion that underlies all instances of each of these faulty argument techniques. The red

herring fallacy occurs when irrelevant premises are given as a reason for accepting a

conclusion. Slippery slope arguments occur when an arguer assumes without justiﬁcation

that to permit or forbid a course of action will inevitably cause a chain of undesirable

events. The straw man is deliberately set up as a target that will be easier to defeat than

pseudo-reasoning238

an opponent’s real argument. An argument begs the question when the truth of its

conclusion is assumed by its premise(s). The false dilemma technique is employed when

an argument limits consideration of positions on an issue to two mutually exclusive ones,

thereby setting up an apparent dilemma, when there are other positions that could be

considered.

EXERCISES

1 Name the fallacy committed by the following arguments. If no fallacy is committed,

write ‘N/F’.

Example

No one has ever been able to prove the existence of extrasensory perception.

We must therefore conclude that extrasensory perception is a myth.

✎Appeal to ignorance.

a Of course the monarchy shouldn’t be abolished; we’ve had a monarchy in

this country for centuries.

b A few minutes after the minister made his speech to the City of London, a

devastating explosion occurred. For the safety of the people who live and

work in the city, it is imperative that the minister makes no more speeches

here.

c Publishing these vile criminals’ names and addresses in our paper was

deﬁnitely the right thing to do. We have been inundated with calls and faxes

from readers who support our stance.

d If she doesn’t ﬁnish her assignment on time, she will fail the course. She has

failed the course, so obviously she didn’t ﬁnish her assignment on time.

e If the Bank of England lowers interest rates, the pound will lose value against

the US dollar. The Bank of England has not put interest rates down, so the

pound will not lose value against the US dollar.

f As my client has pointed out, tax avoidance is not illegal, so she has done

nothing immoral.

g The Japanese diet is low in dairy products and certain cancers have a very low

incidence in Japan. So if you want to avoid cancer, give up drinking mild and

eating milk products.

h Teachers say their job is becoming harder and harder and that they deserve

better pay and conditions. But the Government should ignore them; they’re

just a bunch of whingeing liberals.

i It’s all very well for a TV chef to tell people how they should feed their

families on a budget, but there he is, a multi-millionaire driving around in a

ﬂash SUV. What right has he got to tell real working people how to live their

lives?

pseudo-reasoning 239

j Given the evidence that so many students are plagiarising their assignments,

assessment by coursework should be abandoned in favour of examinations.

2 (i) Name the fallacy committed by each of the following arguments and (ii)

reconstruct the argument to demonstrate its fallaciousness.

Example

Democracy is the best system of government. Most people in the world believe

in the superiority of democratic systems.

✎(i) Fallacy of majority belief.

✎(ii) P1) Most people believe that democratic systems are superior systems

of government.

✎P2) Any belief held by the majority is true.

C) Democracy is the best system of government.

a Our lecturers are always extolling the virtues of critical thinking, but they

would, wouldn’t they? They only keep their jobs if they’ve got students to

teach.

b It’s not illegal for me to exaggerate my skills on my curriculum vitae, so it

can’t be immoral either.

c My doctor says that wearing high heels is bad for your knees and I shouldn’t

wear them, but she wears high heels, so I don’t think they really are.

d Smoking causes cancer, so if you don’t smoke, you won’t get cancer.

e Whenever the cherry trees blossom, the weather begins to get warmer. So

cherry blossom makes the weather warmer.

f David Beckham is the best midﬁelder ever to play for England and he says

that Arbarmi jeans are his favourite. They must be the best.

g There’s nothing wrong with getting drunk once in a while; everyone I know

tends to have a few too many every now and then.

h There’s no point in implementing harsh penalties for drunk drivers because

there will always be some people who are going to drive drunk no matter

what penalties are in place.

i Jo knows that Bono is the lead singer of U2, so she also knows that Paul

Hewson is the lead singer of U2.

j If a car breaks down on the road, no one thinks that a passing mechanic is

obligated to render emergency road service. So why expect doctors and

nurses to render emergency medical assistance to all and sundry when they

are off duty?

3 Identify the faulty argument technique employed in each of the following:

a Our employees have asked us to provide lounge areas where they can spend

their breaks. We will have to refuse. If we give them lounges, next they’ll be

pseudo-reasoning240

asking for a ﬁtness centre, then it’ll be a swimming pool and sauna, tennis

courts, basketball courts...

b That’s the trouble with her: it’s always her way or the highway, no

compromise.

c Of course he’s not a liar: he swore to me that he always tells the truth.

d David’s criticism of our plan for the company re-branding is simply wrong.

After all, he’s not offering any alternative.

e The minister says he will cut public services in order to cut taxes for middle-

income families. He’s like a reverse Robin Hood, giving to the rich and taking

from the poor.

4 Provide an example of each of the following fallacies and faulty argument techniques.

Try to make your example appreciably different from those already provided for you.

Example

Denying the antecedent

✎If he took all of his medication, he should be feeling better by now. He

ﬂushed half of his medication down the lavatory so he can’t be feeling

any better.

a Begging the question

b Red herring

c Straw man

d Mistaking correlation for cause

e Perfectionist fallacy

fAd hominem

g Deriving ‘ought’ from ‘is’

h Weak analogy

i Base rate fallacy

jTu quoque

k Appeal to authority

l Equivocation

m False dilemma

n Slippery slope

o Epistemic fallacy

5 Without looking back at the relevant section, write a paragraph explaining the

difference between relative difference and absolute difference. Try to ﬁnd an

example of a media report in which relative and absolute difference are confused.

Hint: such reports often concern the likely beneﬁts of new medications, cosmetic

products or domestic cleaning products.

6 Without looking back at the relevant section, write a paragraph explaining what

‘margin of error’ means with respect to an opinion poll. Explain what is meant by

saying that a poll has a margin of error of ‘plus or minus 4 per cent’.

pseudo-reasoning 241

truth, knowledge

and belief

•Truth and relativity 243

•True for me, true for you 248

•Truth, value and morality 251

•Theories 252

•Belief, justiﬁcation and truth 253

•Justiﬁcation without arguments 255

•Knowledge 256

•Justiﬁcation failure 257

Insufﬁciency • Mistakes about justiﬁcation

•Knowledge and rational persuasiveness 259

•Philosophical directions 261

Foundationalism vs coherentism • Internal vs external justiﬁcation •

Probability and justiﬁcation

•Chapter summary 264

•Exercises 264

In this ﬁnal chapter we will delve deeper into some of the philosophical issues underlying

the principles of good critical thinking. We begin the chapter by extending the discussion

of truth that appears in Chapters 1 and 3 and attempting to dispel what in our experience

is a deep-seated myth – that what is true depends on nothing more than personal opinion

or taste. As we will explain, this is the myth that all truth is relative. Later we examine the

relationship between believing that something is the case and knowing that it is the case.

These relationships are important for critical thinking because they are concerned with the

adequacy of evidence for beliefs. Thus they are at the root of our determinations of

whether or not premises are true, whether or not the conclusion of an inductively forceful

argument is defeated for a person, and whether or not an argument is rationally persuasive

for a person. Further, the concepts of truth, knowledge and evidence are such frequent

sources of confusion in argumentative contexts that clarity about them is extremely

valuable in its own right.

TRUTH AND RELATIVITY

When we claim something such as ‘The kettle has boiled’, we assert something; we

express a belief. A belief is an attitude we take towards a proposition: to believe a

proposition is to accept it as true. Assertion is a truth-claim, and belief is a truth-attitude.

Assertion, belief and truth are internally related in this way. From the outset we have

been working with an intuitive understanding of truth such that to say that a claim is true

is simply to say that things are as the claim says they are: to assert that a proposition is true is

equivalent to asserting that very same proposition. What this means is that a pair of sentences

such as the following:

•Serena Williams was the Wimbledon Women’s Singles Champion in 2008.

•It is true that Serena Williams was the Wimbledon Women’s Singles Champion

in 2008.

must have the same truth value; if one of them is true, then so is the other. This necessary

equivalence is the fundamental fact about the ordinary meaning of the word ‘true’.

Suppose, then, that Julie says that Serena Williams was the Wimbledon Women’s Singles

Champion in 2008. To say that Julie’s claim is true, at bottom, is just to say that Serena

Williams did win the Women’s Singles at Wimbledon in 2008. Thus, although truth is a

feature of claims that people make (of some claims, of course, not of all of them), whether

or not a claim is true has nothing at all to do with the person who makes it; nor with that

person’s beliefs, culture or language (except when the proposition is explicitly about those

things). Whether or not Julie’s claim about Serena Williams is true depends only on

whether or not Serena Williams won the Women’s Singles at Wimbledon in 2008, and

does not depend in any way on anything about Julie. In particular, the mere fact that Julie

believes, and has claimed, that Serena Williams won Wimbledon, has nothing to do with

whether or not her belief or claim is true.

Notice also the following consequence of the equivalence noted above. If John responds

to Julie’s claim by saying, ‘That’s true’, then what he does, in effect, is to assert the very

same thing that Julie did. He agrees with her. Her claim is true if Serena Williams won

Wimbledon and false otherwise; likewise with John’s.

These points are quite straightforward, but they can be easy to lose sight of in other

contexts, and these contexts can create confusion about truth generally. In order to dispel

truth, knowledge and belief 243

the myth that truth is relative, we ﬁrst explain the concepts of indexicals and implicit

speaker-relativity. Consider the following sets of claims:

1•Bill Clinton was the US President immediately before George W. Bush.

•Water is H2O.

•Neptune is larger than Venus.

•La Paz is the capital of Bolivia.

2•It’s raining here.

•She’s 35 years old.

•That book is too expensive for most students to afford.

•The boss is visiting our ofﬁce today.

3•Algebra is hard.

•Chocolate ice cream tastes better than vanilla ice cream.

•George Clooney is more handsome than Brad Pitt.

•Gone with the Wind is a highly entertaining ﬁlm.

•It is more fun to play Monopoly than it is to play football.

The claims in each of the three sets are expressed using the same assertoric form.

Assertoric form is generally used to express a belief that such-and-such is true (except

when someone is lying or play-acting); but the fact that someone has made an assertion

does not establish that the assertion is true, only that the speaker believes it to be so. Thus,

if someone asserts ‘Neptune is larger than Venus’, they express their belief that one planet

is larger than another, that it is fact that the one is larger than the other. But whether or

not the assertion is true depends only on whether or not Neptune really is larger than

Venus. Similarly with ‘Bill Clinton was the US President immediately before George W.

Bush’ and ‘La Paz is the capital of Bolivia’. Note that, although someone making one of

these statements asserts their own belief, they are certainly not talking about themselves;

someone who asserts that La Paz is the capital of Bolivia asserts one of their beliefs, but the

statement, and their belief, is only about La Paz and Bolivia.

Now look at the second set of claims, which, as we have noted already, are expressed in the

same assertoric form. Each claim includes an indexical – ‘here’, ‘she’, ‘that’ and ‘today’,

respectively. An indexical is a word that picks out a particular thing (in philosophers’

terms, it is a ‘referring term’), but precisely which thing it picks out depends upon the

context of utterance, and sometimes on the intention of the speaker. Thus what it picks

out can change from utterance to utterance. This has the effect of making the truth-value

of the sentence context-relative too. ‘It’s raining here’ uttered in Glasgow might be true,

whereas uttered in Madrid at the very same moment it might be false. So determining

what location ‘here’ refers to in a given context is crucial to determining the truth-value

of the sentence in which it occurs. Similarly ‘She’s 35 years old’ might be true if uttered

about Jones, yet false when uttered about Smith; while it might be true that the boss is

visiting today when ‘today’ refers to Tuesday, it might be false if ‘today’ is Friday; and if

‘that book’ is a 100-page paperback that costs £50, then it is indeed too expensive for most

students, if, on the other hand, ‘that book’ refers to a 300-page edition at £5, then it is false

to claim that it is beyond the means of most students.

truth, knowledge and belief244

Sentences are often context-relative in a certain respect without explicitly containing an

indexical that signiﬁes it as such. Consider ‘It’s raining here’ again. That might be true if

uttered in Glasgow today, but false if uttered in Glasgow tomorrow (one can always hope).

The sentence does not contain the indexical word ‘now’, but it is context-sensitive with

respect to the time of utterance. It is exactly as if the sentence were ‘It’s raining here now’.

That is how it is with many typical uses of present-tense verbs: if you say ‘I’m hungry’, or

‘The car needs a wash’, you are saying that these things are so now (similarly with past and

future tenses – ‘She used to be married’, etc.). Location is also a contextual feature that is

often left tacit. For example, we usually say ‘It’s raining’, reserving ‘It’s raining here’ for the

case where speaker and hearer are in different places, as on the telephone. So ‘It’s raining’

involves two implicit indexicals: ‘here’ and ‘now’.

More generally, a sentence containing indexicality (explicit or implicit) expresses different

propositions in different contexts of utterance. A context is simply a collection of factors

relevant to determining what is said by a given utterance. This will include the identity of

the speaker (who is speaking), the time and place of utterance, and other factors such as

what a speaker happens to be pointing to. Thus if Groucho says ‘I’m hungry’ at 3.00 p.m.

and Chico says ‘I’m hungry’ at 5.00, then they express different propositions – Groucho

says that Groucho is hungry at 3.00, whereas Chico says that Chico is hungry at 5.00. If they

both speak truly, they report different facts.

Since what is expressed by a sentence involving indexicality depends on the context of

utterance, its truth-value depends on context of utterance. But such sentences are still fact-

stating: once we have determined the relevant features of the context, we have a complete

proposition with a ﬁxed truth-value. The truth-value of the proposition is not context-

relative: either Groucho was really hungry at 3.00 or he wasn’t, end of story (ignoring the

possible vagueness of ‘hungry’). Other indexical terms include personal pronouns such as

‘I’, ‘he’, ‘we’, ‘you’ and ‘they’; impersonal ones such as ‘this’ and ‘there’ (often accompanied

by a pointing gesture or suchlike); expressions employing possessive pronouns such as ‘my

house’, ‘your car’, ‘our dog’, ‘their holiday’; and temporal expressions such as ‘tomorrow’

and ‘yesterday’.

Turning to the third set of claims, if we consider the ﬁrst claim:

Algebra is hard.

It appears to assert a fact about the difﬁculty of algebra. But imagine Jane – who has had

no end of tutoring and has certainly tried her best – saying this to Mary; Mary replies, ‘No

it’s not! It’s easy!’ Must they really be disagreeing? It seems not. In such a case, it seems that

what Jane might really be saying is that algebra is hard for her; Mary is saying that she,

Mary, ﬁnds it easy (unless Mary is telling Jane that she’s so dim she can’t even do some-

thing that is in fact easy – but let’s assume she isn’t!). Since the sentence expresses a

different proposition depending on who utters it, the sentence is implicitly indexical and

hence context-relative. In this kind of case, we say that the claim is implicitly relative. A

claim is implicitly relative when it states a comparison or other relation to something it

truth, knowledge and belief 245

doesn’t explicitly mention (see Chapter 2, pp. 35–36, for a review of this concept). For

example, said of an adult man, ‘John is tall’ states a comparison, a relation, between John

and other men; it really says that John is taller than the average man.1

Furthermore, what Mary says about algebra is implicitly speaker-relative. Unlike ‘John is

tall’, the fact expressed is implicitly about the person making the assertion. Mary, we are

assuming, is really expressing the proposition that Algebra is hard for Mary. Similarly,

suppose that John has very fair skin, and says ‘The sun is too strong’ during a walk on a

Mediterranean beach. He alludes to the danger of sunburn. Julie, whose darker skin is less

sensitive to the sun, says ‘No it isn’t’. In such a case, John might only be saying that the sun

is too strong for him, and Julie saying that it isn’t too strong for her.

Implicit speaker-relativity is most common in the expression of attitudes, preferences and

the like, as illustrated by the remainder of the examples in the third set. If Julie says,

‘Chocolate ice cream tastes better than vanilla’, then what she is really saying is that she

prefers chocolate to vanilla. Similarly, if John asserts this very same sentence, then he is

saying that chocolate ice cream tastes better to him than vanilla does. So Julie and John are

saying different things, despite the fact that they use the same sentence to say it. These

two speakers’ assertions are statements of fact about their respective preferences, not

statements of fact about the superiority of chocolate over vanilla ice cream independent of

anyone’s preference.

To sum up the discussion of the third group: the sentence by means of which we express

such a proposition – ‘Chocolate ice cream tastes better than vanilla’ – is an incomplete

expression of the proposition we express by means of it. The statement actually expresses a

fact about the person making it, but the sentence does not explicitly mention this; that is

why the statement is implicitly speaker-relative.2

The importance of these differences emerges when we consider what happens when

people appear to disagree over claims that are implicitly speaker-relative in this way, and

compare this with genuine factual disagreement. Suppose now that Julie and John disagree

about the capital of Bolivia. Julie says:

La Paz is the capital of Bolivia.

But John denies it. He says: ‘La Paz is not the capital of Bolivia’ (perhaps he thinks it’s the

capital of Columbia). In this case, there is exactly one proposition – that La Paz is the

1 Of course there is no such thing as ‘the average man’, as if, in addition to Tom, Dick, Harry and the rest,

there were another chap, the average man. To say that John is taller than the average man is to say that if you

take the average (the mean) of the heights of all men, then John’s height exceeds that ﬁgure.

2 There is one slight complication, however: statements of this kind may mean that something is preferred or

liked by most people. For example, this is plausibly what someone means who says: ‘soured milk does not taste

good.’ Nevertheless, these statements are still implicitly relative, because they still depend for their truth on an

implicit reference to people’s preferences. In such a case, the statement is a generalisation about people’s actual

preferences rather than a statement of one person’s preference.

truth, knowledge and belief246

capital of Bolivia – such that Julie asserts it and John denies it. That is what genuine

factual disagreement is: genuine disagreement is when there is one proposition that is

asserted by one person but denied by another. If Julie and John value the truth, they will

want to know whose claim is true.

Contrast with the case when Julie says ‘I am wearing wool socks’, and John says ‘I am not

wearing wool socks’. The sentence that John asserts is the negation of the sentence that

Julie asserts, but obviously they are not disagreeing about anything. Due to the explicit

context-relativity introduced by the indexical ‘I’, the proposition asserted by Julie is not

the proposition denied by John.

But when context-relativity is implicit rather than explicit, there can appear to be genuine

factual disagreement when there isn’t. Suppose that Julie and John seemingly dis-

agree about the relative merits of chocolate and vanilla ice cream: Julie contends that

chocolate tastes better, while John is on the side of vanilla. As we have seen, in order to

make her meaning perfectly explicit, Julie would have to say ‘Chocolate ice cream tastes

better than vanilla to me’; John would have to say the same in order to be explicit. So what

Julie is really saying is that chocolate tastes better to her; John, that vanilla tastes better to

him.

The proposition that Julie expresses can equally well be expressed as:

(1) Chocolate ice cream tastes better than vanilla to Julie.

whereas John’s proposition is:

(2) Vanilla ice cream tastes better than chocolate to John.

These are two different propositions. There is certainly no logical conﬂict between them:

they could both be true. But in that case, Julie and John do not really disagree: there is not

one proposition here that either Julie or John asserts, and that the other denies. They are

not really disagreeing about the truth-value of the same proposition. That is, they do not

dispute the facts of the matter; their claims are simply expressions of different preferences.

To continue to dispute such an issue would be a waste of time. Indeed, notice that (1) and

(2) are no longer implicitly speaker-relative; they are explicitly speaker-relative. So there

should be no temptation to say that the truth of either (1) or (2) depends on who is

making the claim. If you say ‘Chocolate ice cream tastes better than vanilla’, then you are

implicitly talking about yourself, and the truth of what you say depends on facts about you

(your preferences). If you assert (1), however, the truth of your assertion depends only on

facts about Julie, not on facts about you.

Having discussed the concepts of indexicals and implicit speaker-relativity, we are now in a

position to confront the myth that truth is relative.

truth, knowledge and belief 247

TRUE FOR ME, TRUE FOR YOU

Often, people who have succumbed to the myth that ‘the truth is always relative’ respond

to a disagreement about the facts by saying something like: ‘Well, that may be true for you,

but it’s not true for me.’ In doing so, they use a common ploy to avoid proper engagement

with the argument. Unless the matter under discussion is one that is actually implicitly

speaker-relative, as it is in the ice-cream example, this is not a legitimate move to make

within an attempt to persuade rationally. It is a refusal to argue any further.3 A similar

refusal to engage in debate occurs when someone responds to others’ claims by saying,

‘that’s just your opinion’, as though expressing one’s mere opinion is not an attempt to

make a true claim about a matter but, rather, tantamount to expressing a preference for

chocolate rather than vanilla ice cream. But when we express our opinion on a matter –

the best way of reducing crime rates, say – we are expressing our beliefs about the truth of

a matter. It is really a kind of self-deception not to face up to this: that when we express

our opinion, we are making a claim to truth. So criticising someone’s contribution to a

conversation by saying ‘that’s just a matter of opinion’ is another attempt to hinder

rational persuasion or debate, and unjustiﬁably denies that there is any such thing as

disagreement.

The ‘true-for-me’ phraseology, however, is not just a device for evading arguments. It is a

characteristic way of expressing the relativity-myth (though the relativity-myth may itself

be motivated by the wish to avoid the sometimes unpleasant reality of disagreement).

Thus we shall try to dispel the myth by considering it in more detail. Consider again the

sentence:

Chocolate ice cream tastes better than vanilla.

The implicit speaker-relativity of a sentence like this might be described by saying that the

sentence is true for Julie, and not true for John. Upon hearing Julie assert this sentence,

John might say: ‘Well, that may be true for you, but it isn’t true for me.’ John might, in

this case, simply be making the point about implicit speaker-relativity. If so, then that is all

right; he is quite right to do so. However, phrases such as ‘true for me’ are sometimes used

in what appear to be factual contexts where implicit speaker-relativity is not in play. For

example, suppose that Julie believes in astrology, and says:

Scorpios tend to be luckier than Libras.

John does not believe in astrology, and therefore does not believe that one’s character

depends on what the part of the year one is born. So he thinks this proposition is false. But

John, wishing to avoid a painful disagreement, expresses himself by saying: ‘Well, that may

be true for you, but it isn’t true for me.’

3 When you think about it, it is very hard to see exactly what this claim amounts to. It seems to say that truth

is relative to persons; yet it is odd that the only way that this can be the case is for that statement itself to be true

in just the way that the statement itself denies – thus it seems that relativism about truth may be contradictory.

truth, knowledge and belief248

As we have just seen, where implicit speaker-relativity is involved, the use of such phrases

as ‘true for you’ is perfectly legitimate. But in the astrology case, the use of this phrase is

misleading. Is this sentence implicitly speaker-relative? Is the sentence about a preference,

belief or other attitude? It certainly does not seem to be. It is like the sentence about

La Paz: it purports to state a fact about the respective fortunes of Scorpios and Libras.

Someone asserting the sentence about La Paz expresses their belief concerning La Paz, but

they are not talking about themselves, they are talking only about La Paz and Bolivia. This

is shown by the fact that the truth of what they say depends only on how things are with

La Paz and Bolivia; its truth does not depend in any way on the beliefs of the speaker.

Likewise, someone asserting the astrology sentence expresses their own attitudes about

Scorpios and Libras, but is not saying anything about their own attitudes towards Scorpios

and Libras. So when John says, of the astrology sentence, that it might be true for Julie but

not for him, he cannot be saying that the sentence is implicitly speaker-relative, and could

therefore be true when Julie says it but false when he says it.

What, then, could John reasonably mean by ‘true for you’ in this context? As we noted,

when someone sincerely asserts a declarative sentence, they express a belief. By ‘true for

you’, then, John could simply mean that according to Julie, the sentence is true. That is to

say, he could mean simply that Julie believes the proposition expressed by the sentence;

that she believes that Scorpios tend to be luckier than Libras. John, of course, denies this

very same proposition. So this is a straightforward case of genuine disagreement over the

same proposition. In suggesting that the sentence is true for Julie and not for himself, all

that John is doing is pointing out the fact that he and Julie do disagree: Julie believes, and

John disbelieves, the very same proposition. Unfortunately, by using the phrase ‘true for

you’, he makes it sound as if it’s a case of implicit speaker-relativity, in which case there is

no actual disagreement. Since that is the sort of case where ‘true for me’ has a legitimate

point to it, he makes it sound as if there is no actual disagreement, thus smoothing over his

difference with Julie. This is perhaps polite of him, but it is really just an evasion.

With these points in mind concerning ‘true-for-me’, we can now dispel the myth that all

truth is relative. The myth is often expressed by saying that we cannot legitimately speak

simply of what is true, but only of what is true for me, or true for you, or more generally true-

for-X, where X is some person (or perhaps culture). If this is explained as the claim that

all statements are really implicitly speaker-relative, then this is clearly not so, as we have

seen: a statement like the one about La Paz just isn’t speaker-relative. However, the claim

that all truth is truth-for-X might also be understood in accordance with the way that

John employed the phrase in his dispute with Julie about astrology. According to this

interpretation of ‘true-for-X’, to say that a proposition is true for X is to say that X believes

it. Could all truth really be truth-for-X, in that sense?

Let us work out the implications of supposing that it is. Consider these two sentences:

(3) Scorpios tend to be luckier than Libras.

(4) It is true that Scorpios tend to be luckier than Libras.

truth, knowledge and belief 249

According to what we said about the word ‘true’ at the beginning of this chapter, (3) and

(4) are necessarily equivalent: it is impossible for one of them to be true and the other false.

That is why we can always register our agreement with a claim simply by saying, ‘that’s

true’. And that, we might say, is the point of having the word ‘true’: that is how the word is

used. However, according to the version of the myth we are considering, if Julie asserts (4),

then she would be speaking more accurately if she were to say: ‘It is true for me that

Scorpios tend to be luckier than Libras.’ Thus, as we ourselves would express it, what she

says by means of (4), according to the myth, is really:

(5) It is true for Julie that Scorpios tend to be luckier than Libras.

And this, as we said, is more accurately expressed by:

(6) Julie believes that Scorpios tend to be luckier than Libras.

So according to this version of the relativity-myth, Julie’s utterance of (4) is equivalent to

(5), which is equivalent to (6). So according to the myth, (4) is equivalent to (6). But (6) is

certainly not equivalent to (3). (3) makes no reference to Julie; it would be possible for (3)

to be true but (6) false, or the other way round (in fact, if (6) were true, then since

presumably (3) is false, they would actually differ in truth-value). Thus, according to this

version of the myth, we would have to say that (4) is not equivalent to (3). But that cannot be

right, for that is simply not how the word ‘true’ is used. This version of the relativity-myth

violates the actual, ordinary day-to-day meaning of the word ‘true’ according to which (3)

and (4) are equivalent. According to that meaning, Julie is right when she says (3) if, and

only if, she is right when she says (4). So (3) and (4), whoever utters them, cannot differ in

truth-value. If so, then since (5) and (6) mean the same thing, (5) cannot be what is meant

by (4), in which case ‘true’ cannot mean ‘true-for-X’.

There is no getting around it, then. There is no way to make satisfactory sense of the

relativity-myth. So truth is not relative. It is objective, and the truth of a proposition is

independent of our desiring or believing it to be true. Just as thinking or desiring cannot

make the moon be made of green cheese, thinking or desiring cannot make it true that the

moon is made of green cheese. To believe is to believe something to be true, but truth is

not the same thing as belief. This means that truth is independent of all of us; it does not

mean that one powerful person or being could hold the key to all that is true about the

world. Thus, in saying that truth is objective, we are certainly not taking any kind of

political stance, saying that certain cultures or institutions have or might have a monopoly

on truth. The aim of good reasoning and argument is to get at the truth, at the way the

world is, irrespective of how people think or feel it to be. Rationality is a great leveller. In

the pursuit of truth, we are all equally placed before the world, and no amount of political

power can provide an advantage.

truth, knowledge and belief250

TRUTH, VALUE AND MORALITY

So far we have been tackling the myth that all truth is relative. Many people are also

tempted to think that values like those central to moral issues are relative to personal or

cultural preferences. It is possible that people are tempted to think that truth is relative

because they think that value is relative. In fact, however, the non-relativity of truth does

not imply the non-relativity of value. The question of the relativity of value is a different

sort of question, and it is important to see how and why. By way of example, we’ll take the

claim:

Doctor-assisted suicide is immoral.

According to the relativist view, when opponents of doctor-assisted suicide say it is morally

unacceptable and their opponents contradict them and say that it is morally acceptable,

there is no real disagreement; rather the two sides do not share the same moral preferences.

Thus, for the relativist, value-statements are always speaker-relative, whether implicitly or

explicitly. Thus the incoherence of relativism about all truth does not entail that value-

statements are not relative in this way: the relativist can claim that all value-statements are

speaker-relative without claiming that all statements are speaker-relative. An apparent

disagreement over a value is in this respect like that between Julie and John concerning

chocolate versus vanilla ice cream. One reason why this relativistic view of moral issues is

so tempting is that we feel uncomfortable about being seen to dictate morals to other

people because we (rightly) value tolerance of different opinions.4

We cannot prove, and would not try to prove, that moral relativism is false. It is conceiv-

able that all claims about values are implicitly speaker-relative, or perhaps implicitly rela-

tive in some other way. We will, however, try to explain why there is good reason to resist

moral relativism. While moral issues are almost always complicated and can be difﬁcult to

agree upon, the problem with this simplistic relativist approach is that it leaves no room

for genuine disagreement about moral issues. It enjoins us to say, ‘You feel OK about

doctors helping their patients to die, I don’t, end of story’ without attempting rationally to

persuade one another of the truth of our beliefs. The poverty of such a view of morals is

illustrated by the following case. Suppose there emerged a terrible fascist regime that

murdered millions of people on grounds of race, religion or political beliefs. Simplistic

relativists who desire to remain consistent with their relativist commitment would be

unable to hope that the fascists are wrong, and that, therefore, others could rationally be

persuaded that the fascists are wrong; for the fascists’ views about the moral status of their

victims would be nothing more than preferences that just happen to be different from

most other people’s. In the same way that many people prefer ice cream to carrots, this

4 This repudiation of moral relativism is aimed only at the very naive type of relativism that holds that moral

questions are simply a matter of personal or cultural preference and therefore not the subject of genuine

disagreements. There are various more sophisticated versions of moral relativism. It is not our intention to

repudiate such theories.

truth, knowledge and belief 251

regime prefers murdering people who are different from them to living tolerantly along-

side them. This is a very extreme example, but the point is well made. To adopt naive

relativism about moral matters, to deny there can be a truth of the matter; and to say that

claims such as the claim that torture is wrong have a similar status to the claim that

chocolate ice cream tastes best, is to deny ourselves the opportunity to attempt rationally

to persuade others that their moral beliefs are false and to persuade them not to follow

courses of action that would be harmful to others. It places fundamental moral issues

outside of the ambit of critical thinking.

Yet the critical thinker does not have to give up hope. While people may continue to

believe that moral relativism is true, they must also be consistent in their judgements. For

example, it is irrational to hold that murderers are bad people, and at the same time, in

full knowledge of his crimes, hold that Jack the Ripper was not a bad person. Thus, the

critical thinker can at least demand logical consistency of the relativist; they can show

that there is a valid argument from a premise accepted by the relativist to the conclusion

that Jack the Ripper was bad. This means that it is possible to refute the relativist’s moral

views if it can be established that they are incoherent. In moral arguments a good way to

do this is to ﬁnd a general principle that the relativist accepts and go on to show how it

is inconsistent with the belief that you wish to challenge. For example, if a relativist is

pro-abortion and you discover that they are also against any form of killing, then you could

force them to revise their beliefs if you could establish by argument that abortion was a

type of killing.5

THEORIES

In similar fashion to the ‘that’s just an opinion’ response, we also dismiss assertions or

refuse to engage in arguments by labelling them as ‘just a theory’. This seems to belittle

theories as something subjective – to dismiss them merely as someone’s opinion. Properly

understood, however, the term ‘theory’ has a speciﬁc meaning that contrasts scientiﬁc

hypotheses with less methodologically sound and evidence-based views about the way that

the world is. To say that something is a theory is not in itself to cast doubt on its objectivity

in any way; we speak, for example, of the ‘theory of the calculus’ in mathematics or the

‘theory of gravity’ in physics, without meaning to cast doubt on the theories or the

reliability of their resulting applications, as for example in the building of bridges. Nor is

calling something a ‘theory’ to mark an invidious distinction from facts; a theory is a

system of propositions concerning some particular domain of facts, such that if true then

it is a correct account of those facts. True propositions are never themselves identical to the

facts they are about or represent.

5 See Louis Pojman’s essay ‘Ethical relativism versus ethical objectivism’ in his Introduction to Philosophy:

Classical and Contemporary Readings 3rd edition (New York: Oxford University Press, 2004) for an excellent

critical analysis of moral relativism and a convincing case for a version of moral objectivism. This very accessible

paper is aimed at beginning Philosophy students.

truth, knowledge and belief252

In general, a scientiﬁc theory posits an hypothesis that is testable, and those tests (or

experiments) are able to be carried out in a way that makes them perspective-free; that is,

they are able to be carried out by anyone able to observe the results and use any measuring

apparatus competently. This notion of a scientiﬁc theory is broad and need not refer

exclusively to theories posited and tested by professional scientists, although it does

require hypotheses to be tested by methods that are held to be scientiﬁcally respectable.

Thus a theory posited by school children concerning how mice or rats ﬁnd their way

out of a maze the fastest qualiﬁes as a scientiﬁc theory if it is tested according to accepted

methods. Evolutionary theory counts as a scientiﬁc theory on this account, and, again, to

say that is a ‘theory’ does not itself mean that there is something doubtful about it. Its

hypothesis about the evolution of the universe and the species in it can be, and has been,

exhaustively tested using data provided by scientiﬁcally respectable methods such as

carbon dating and DNA testing. By contrast, creationism, which also seeks to explain

the origins of the universe, is not a scientiﬁc theory by these lights because the

faith-based account of the creation of the universe it presents is not testable by such

means.

In Chapter 1 we distinguished between explanation and argument, pointing out that

whereas an argument seeks to provide reasons to accept a proposition, an explanation seeks

to show why a proposition is the case. If you are seeking an explanation of why the bread

didn’t rise, for example, you already accept that the bread didn’t rise – you don’t need to

be persuaded by means of an argument that it is so. Certain such explanations are scientiﬁc

explanations. They are supported by causal laws (laws covering the relation of causes to

their effects, which also enable us to make reliable predictions concerning the likely effects

of certain events). Thus the explanation ‘the bread didn’t rise because we forgot to add

yeast’ is licensed by causal laws that are a reﬂection of the fact that, all other things being

equal, whenever leavening products, such as yeast, are added to ﬂour and liquid and mixed

to form a dough, carbon dioxide will be produced in the dough and this will cause it to

swell in size.6

BELIEF, JUSTIFICATION AND TRUTH

It is not the case that, for any given proposition, we either believe it to be true (believe it)

or believe it be false (disbelieve it). We may simply have no attitude towards it, either

because it has never come to our attention, or because we choose not to consider the

question. Or we may have an attitude that is midway between belief and disbelief: we may

suspend judgement, because we ﬁnd, upon reﬂection, that we lack sufﬁcient evidence to

make the judgement. This happens when we lack an argument either for or against the

proposition that is rationally persuasive for us. The issue of the existence of a single deity

6 This just scratches the surface of various issues in the Philosophy of Science; see Alex Rosenberg, Philosophy

of Science: A Contemporary Introduction (Routledge 2005).

truth, knowledge and belief 253

who is said to have created the world provides a good example with which to illustrate the

point. Consider the claim:

The world was created by an omnipotent and omniscient being.

Some people, let’s call them ‘theists’, believe the proposition expressed here. Others, athe-

ists, disbelieve it. Others, agnostics, are not sure whether or not to believe it so they have

suspended judgement until such time as they acquire sufﬁcient evidence (or faith) to

support a belief either way. These three positions probably cover most adults in our

society. But consider the position of most pre-school children. They do not believe that a

deity made the world. They do not believe that a deity didn’t make the world. However, it

would not be accurate to say that they have suspended judgement on the issue. For they

have not considered the issue, indeed they are probably too young to understand the claim

that is the subject of debate. Of course, when assessing an argument’s soundness and

rational persuasiveness, the stance of having no opinion about the truth of the premises is

not an option for critical thinkers. Either we consider ourselves to have sufﬁcient evidence

to believe or disbelieve the proposition expressed by the premise(s) or we recognise that we

lack such evidence, and suspend judgement until such evidence is available. And even if

we believe the argument to be inductively sound, we may ﬁnd that, having accepted its

premises, the argument is not rationally persuasive for us because its conclusion is defeated

by some further evidence that we have.

It is crucial to bear in mind that in saying that someone does not hold a certain belief, we

are not saying or implying that they hold the opposite belief. If someone tells you that they

don’t believe that the British Prime Minister is a bad person, they are not thereby saying or

implying that they believe that the British Prime Minister is not a bad person, let alone that the

British Prime Minister is a good person. They may not know the British Prime Minister

very well and may want to learn more about the British Prime Minister before making a

judgement, or they may simply not care and have no intention of ever forming a belief

about the British Prime Minister’s moral standing. Or perhaps they have never even heard

of the British Prime Minister. As we saw in Chapter 7, an argument that assumes that

someone who does not believe a proposition believes its negation commits a version of the

epistemic fallacy.

Of the four stances we can take towards a proposition – believing it, not believing it,

suspending judgement, not engaging with it – two, believing and not believing, admit of

degrees. Smith and Jones may both believe that the Conservative Party will form the

Government after the next British general election, but they may not hold the belief with

the same degree of conﬁdence. Smith may be nearly certain, while Jones, an arch-sceptic

when it comes to predicting voting behaviour, still believes it, but to a lesser degree.

Similarly, Jack and Jill may both disbelieve the proposition that the Conservative Party

will form the next Government, but the strength of Jack’s disbelief may be such that

he’ll bet two weeks’ wages at odds of 20 to 1 on a Conservative defeat. Whereas Jill,

normally a keen betting woman, would not risk nearly as much money (if offered the same

odds).

truth, knowledge and belief254

Given that someone holds a certain belief, we can ask whether or not the belief is justiﬁed,

and whether or not it is true. Suppose Smith works for a national polling organisation and

has seen the results of several methodologically sound top-secret polls that predict the

Conservative Party will gain 80 per cent of the vote on election day. In the absence of any

evidence that goes against that prediction, Smith is in possession of an argument that is

highly rationally persuasive for him. He would thus be well-justiﬁed (other factors such as

the reliability of the data notwithstanding) in believing the conclusion of the argument

with a strong degree of certainty. As critical thinkers we may conclude that Smith’s belief

is reasonable or justiﬁed given what we know about the evidence available to them.

Whenever someone’s belief is backed by an argument that is rationally persuasive for

them, it follows that they are justiﬁed in believing the conclusion, precisely to the extent

that the argument is rationally persuasive for them.7

However, the fact that Smith is perfectly rational and justiﬁed in holding this belief does

not establish that the belief is true. That depends upon whether the Conservative Party

does in fact form the next Government. A belief ’s being true is a matter of its ﬁtting the

facts, not of there being good reasons to think that such-and-such is the case. We see this

clearly when we consider the possibility of being justiﬁed in holding a belief that is actually

false. Suppose I form the belief that the Government has just been deposed in a military

coup. I am led to form this belief because, while writing this chapter, I have been distracted

into reading newspapers online and I ﬁnd the same story appearing on several previously

reliable and reputable news sites. I track down one or two colleagues, they look at their

own favourite sites and, sure enough, ﬁnd the same story. Given the widespread coverage

of the coup and the fact that the sources are reliable and reputable, I would be justiﬁed in

believing that the Government had been deposed by a military coup. But in fact, despite

my good reasons for having formed this belief, it turns out to be false. A clever computer

hacker has managed to hack into several internet news services and post this false story. So

I have a justiﬁed but false belief. I may be in possession of an argument that is rationally

persuasive for me, but my belief in its conclusion need not be true.

JUSTIFICATION WITHOUT ARGUMENTS

In order to be justiﬁed in holding a certain belief, must one be in possession of a (rationally

persuasive) argument for that belief? No – or at least not in any ordinary sense. There are

forms of justiﬁcation that do not involve having reasons in the usual sense. The obvious

case is that of perception. If you perceive, under normal circumstances, that the cat is on

7 This is not to say that a belief is justiﬁed only if one has a rationally persuasive argument for it. According to

many theorists, some beliefs, especially those that arise in perception, are justiﬁed but not ‘inferentially’ – not,

that is, by means of arguments or reasoning. Others deny this, holding that even the justiﬁcation of perceptual

beliefs depends upon underlying premises or assumptions. Since this is a fundamental open question in the

theory of knowledge (epistemology), we have avoided taking a stand on it here. See the concluding section of

this chapter. For detailed discussion, see Robert Audi, Epistemology: A Contemporary Introduction to the Theory of

Knowledge, 2nd edition (Routledge, 2003).

truth, knowledge and belief 255

the mat, then you are normally justiﬁed in believing that the cat is on the mat. If you say

‘The cat is on the mat’, and someone asks ‘How do you know?’, it is a perfectly adequate

answer to say ‘Because I see it’. The question of exactly how perception is related to

justiﬁcation is a complicated philosophical problem, but for our purposes it is sufﬁciently

straightforward that a normal person in normal circumstances who perceives that such-

and-such is justiﬁed in believing it; put another way, perceiving something is good reason

for believing it. That is why, in our discussion of rational persuasiveness in Chapter 6, we

said that in order for an argument to be rationally persuasive for a person, they must be

justiﬁed in accepting the premises – having rationally persuasive arguments for those

premises in turn is one way for that requirement to be satisﬁed, but it is not the only way.

Other, less obvious non-argumentative forms of justiﬁcation include introspection, or

reports of one’s own thoughts, feelings and emotions (though these might be regarded as

‘perception’ in a somewhat extended sense of the word). Thus if you report that you are

hungry, happy or afraid of failing the exam, then, except in bizarre circumstances, your

belief that you are hungry, happy or afraid of failing the exam is surely justiﬁed, and does

not stand in need of an argument.

KNOWLEDGE

Truth and knowledge are intimately linked. Our desire to accumulate knowledge

stems from a desire to get at the truth. And certainly if one knows something, then the

proposition known must be true: one cannot rightly be said to know that the cat is on the

mat if the cat is not on the mat. The truth of a belief is certainly one necessary condition of

that belief’s being knowledge. So it may seem reasonable to suppose that if Jones believes

that the Government has been deposed in a military coup, and the Government has been

deposed in a military coup, then Jones knows that the Government has been deposed in a

military coup. This is to say that knowledge that such-and-such is the case is simply having a

true belief that such-and-such is the case.

However, this is not correct. Having a belief that is true is necessary, but not sufﬁcient for

knowledge. Suppose that Smith has been given LSD. He is hallucinating like mad, and his

reason has gone completely haywire. The conviction suddenly impresses itself upon his

unhinged mind that evil leprechauns have set ﬁre to his mother’s house in Sydney, 15,000

miles away. So he believes that his mother’s house is on ﬁre. In fact, Smith takes LSD every

day, and believes, every time, that his mother’s house is on ﬁre (though for a different

reason each time). But this time, it just so happens that his mother’s house is on ﬁre. Just

by chance, the belief, this time, was true. No one would say that Smith, in this situation,

knows that his mother’s house is on ﬁre. It was true belief, but not knowledge. He is like a

person who shoots at a target blindfolded, dozens of times, and ﬁnally hits it, despite not

having had any idea where the target was.

So knowledge cannot be identiﬁed simply with having a true belief. A further ingredient

must be added to true belief, if it is to be knowledge. In particular, a true belief counts as

truth, knowledge and belief256

knowledge only if we arrive at that true belief via the right route: we have knowledge only if

we have good reasons for a holding belief that turns out to be true. We have to be justiﬁed;

we need to have solid evidential support. We must, if you like, earn the right to be sure.

Lucky true beliefs do not count as knowledge.

This third requirement is incorporated into the traditional philosophical account of

knowledge, which is called the tripartite account:

For any subject (S) and any proposition (P), S

knows

that P if and only if:

(i) S believes that P.

(ii) P is true.

(iii) S is justiﬁed in believing that P.

According to this account, to know that P is to have a justiﬁed true belief that P. It

amounts to saying, then, that knowledge is identical with justiﬁed true belief. If I have a

justiﬁed true belief that Barack Obama is the US President, then I know that Barack

Obama is the US President.

JUSTIFICATION FAILURE

There are two ways in which belief can lack the justiﬁcation, the evidential support,

required for knowledge: it can either be genuine but insufﬁcient, or simply not genuine,

that is, mistaken.

Insufﬁciency

Consider Mrs Green, the greengrocer, who discovers that a customer has left their shop-

ping behind. She has served ﬁve customers so far that day – Mr Red, Mrs Pink, Mr Orange,

Mr Yellow and Mrs Blue. She has no reason to suppose that any one of them is any more

forgetful than any of the others. None of them is in the habit of forgetting their shopping,

for instance. Mrs Green concludes that one of the men left the shopping behind. She does

have some justiﬁcation for forming this belief: of the ﬁve customers three were male, so on

the balance of probability the forgetful shopper is more likely to be a man. That is to say,

she does have an argument for that conclusion which is somewhat rationally persuasive

for her. But, intuitively, we may feel that this probability is somewhat slim justiﬁcation for

her belief. Even if it turns out that the shopping belongs to Mr Orange, we don’t feel

inclined to say that she arrived at her true belief via the right route; that is, that her true

belief is really justiﬁed. So even if she’s right, we don’t feel that she knows that the forgetful

shopper is a man. This is not to say that probability as a justiﬁcation for true belief should

be ruled out per se. The problem here is that the probability is not strong enough. If there

truth, knowledge and belief 257

had been four male shoppers and one woman, we would be more inclined to allow that

Mrs Green’s belief is justiﬁed. If there had been 99 men and 1 woman, we would certainly

be so inclined.

There are occasions when there is far more at stake in having the proper justiﬁcation for

forming a true belief than simply making sure that someone gets their groceries. An

obvious case is where principles of justice are involved, where evidence is required to

demonstrate beyond reasonable doubt that a defendant is guilty of an alleged crime.

Suppose Jones is accused of the murder of Brown. In fact, Jones is guilty: he strangled

Brown to death. Smith is called as a prosecution witness to Jones’ crime. He is called as a

witness because he has given a police statement in which he claims to have seen Jones

emerging from Brown’s house carrying a knife. If this is all the evidence the jury has, is

it, by itself, sufﬁcient reason for jury members to form the true belief that Jones is guilty

of Brown’s murder? Clearly not, even though Jones is in fact guilty of the murder. So

although the jury members may have reached their true belief about Jones’ guilt on the

basis of Smith’s evidence, they do not have a justiﬁed belief about Jones’ guilt. If this

is the only evidence they have for reaching their verdict, then they should not convict

Jones of Brown’s murder. Again, note that this holds even though Jones happens to be

guilty.

How strong must our evidential support be, if a belief is to be justiﬁed? How strong must

it be if a true belief is to qualify as knowledge? Unfortunately, there is no precise answer

to this question. The terms ‘justiﬁed’ and ‘knowledge’, like ‘bald’, are somewhat vague:

just as there is no exact quantity or proportion of cranial hairlessness required for bald-

ness, there is no exact strength of evidence for a belief short of which it is not knowledge,

and beyond which it is knowledge. But this should not trouble us too much. In practice,

we are adept at recognising the cases where our degree of justiﬁcation is borderline. This

does not change the nature of our task as critical thinkers: we know that our task is to

fashion sound arguments that are rationally persuasive for ourselves or for their intended

audiences. By paying attention to the reasons why we are entitled to form true beliefs,

we are able to achieve the ﬁrmest possible grasp upon what we can legitimately claim to

know.

Mistakes about justiﬁcation

Sometimes misevaluation of evidence leads us to form irrational beliefs, even in cases that

are not so extreme as Smith and his hallucinations. In such cases we overestimate our

evidential support, or we think that the evidence supports a belief when it doesn’t. This

is an error that people who attempt to persuade by devious means can often exploit to

their advantage (indeed we noticed in Chapter 7 that some fallacies actually work well

as rhetorical ploys). For instance, they might describe one or two vivid examples of some

alleged phenomenon with the aim of getting us to form generalisations for which the

examples do not provide adequate support. An example that should be familiar to

observers of debates about immigration is that of a vivid description of the situation of a

fairly recent immigrant or asylum seeker that apparently supports the claim that they

truth, knowledge and belief258

enjoy an undeservedly luxurious lifestyle. Such examples are rolled out in an attempt to

persuade readers to believe that the majority of immigrants and asylum seekers who

receive state support are undeserving cheats. Often, the details of such examples and the

manner of their presentation are so rhetorically powerful that they cause us to misevaluate

the signiﬁcance of the evidence presented to us. In particular, we make an unjustiﬁed

inductive inference (one with very low force). When we are led to make such mistakes and

form irrational beliefs, we allow ourselves to be distracted by factors other than principles

of good reasoning.

There is another type of irrational belief. Sometimes we allow ourselves to accept a false

belief because we believe that accepting it will beneﬁt us in some way. In such cases we not

only lack evidence for the belief, but we also seem not to care that we have none. For

instance, someone might believe that the predictions of their astrologer will come true;

they might believe in faith-healing; ESP; life after death; that everything in the Bible is

literally true; that their terminally ill grandparent will make a recovery; that a certain

alternative healing method will cure cancer. We often feel that it would be unfeeling to

point out that such a person’s beliefs are irrational. Indeed, we often admire their faith and

sincerity. However, it would be a mistake to retreat into relativity and conclude that their

belief is ‘true for them’. The belief is false, that’s that. Indeed, such people can sometimes

paradoxically be described as believing that which they know to be false – self-deceived.

However, we should not be too cold-blooded. It’s not usually the case that such people are

intentionally deceiving themselves, but rather that they are trying to deal with their plight

by having faith that their hopes (however unlikely) will be borne out.8 So it’s rather unfair

and unfeeling to accuse such people of being irrational, even though strictly speaking they

are. While we should try to avoid irrationality, we must also accept that as human beings,

it is sometimes psychologically better for us if our beliefs and behaviour fall short of

rationality.

KNOWLEDGE AND RATIONAL PERSUASIVENESS

Rational persuasiveness requires that you be justiﬁed in accepting the premises of an

argument. If the argument is deductively valid, then if you are justiﬁed in accepting the

premises, you are equally justiﬁed in accepting the conclusion. If the premises of such an

argument are actually true, and you know that they are, then if you recognise that the

argument is valid, you know the conclusion to be true.9

8 There are, of course, cases where people are guilty of self-deception. A classic one is the person who knows

(for their clothing has become too tight) that they have gained weight, but refuses to believe that their scales are

functioning properly.

9 In epistemology, this is called the ‘closure principle’. It might seem undeniable, but in more advanced

philosophical treatments of these issues, it is called into question.

truth, knowledge and belief 259

However, there are two complications. First, a rationally persuasive argument can be

unsound: rational persuasiveness does not itself require that the premises of the argument

actually be true. It requires that one be justiﬁed in accepting the premises; but, we have

seen, it is perfectly possible to have good reasons, to be justiﬁed, in holding a false belief.

Thus one can be rationally persuaded by an argument but not know the argument’s

premises to be true. In such a case, one can be rationally persuaded by an argument

without thereby acquiring knowledge. Knowledge that an argument is sound, on the

other hand, makes a stronger demand on our epistemological relationship with its

premises. To know that an argument is sound, we have to know that its premises are true.

To know that an argument is sound, we need justiﬁed true beliefs in the premises.

Whereas for rational persuasiveness, we need only the justiﬁcation; the belief need not

be true.

Second, in the case of an inductively forceful argument that is not defeated, the degree of

justiﬁcation transmitted from known premises to the argument’s conclusion may be

insufﬁcient to establish the conclusion as knowledge. For the degree of inductive force

may be too weak. One might, for example, know with certainty that 51 of 100 stones in a

bag are black; one would thus have an inductively sound argument that is rationally

persuasive for the conclusion that the next stone drawn at random from the bag will be

black. But the argument is only slightly rationally persuasive. Even if that conclusion turns

out to be true, the belief in it would be insufﬁciently justiﬁed by the argument, and so

would not count as knowledge. More generally, the degree of justiﬁcation one has for the

conclusion of an argument that is inductively forceful but not deductively sound will

be smaller than the degree one has for the premises (unless one has some other source of

justiﬁcation for the conclusion).

Finally, here is a case that displays what knowledge is, as opposed to what it isn’t. The

following scenario provides an example of the fulﬁlment of the requirements placed on

knowledge claims:

Rachel Redtop, a journalist, is at a restaurant one evening and sees a prominent

celebrity at an adjacent table with a person she knows not to be their spouse.

‘Perhaps there’s a story in this’, she thinks. Later, as she walks to her car, she notices

a couple locked in a passionate embrace in a parked car that just happens to be

parked under a street lamp. On discreet but close inspection she sees that the couple

is the celebrity and their companion. She forms the belief (which happens to be

true) that the celebrity is having an illicit affair with this person. In fact, she believes

that the evidence for her belief is sufﬁciently strong that she persuades her editor,

and the newspaper’s legal team, that her story should be the next morning’s front-

page lead.

Here we have the three components that are apparently required for legitimate knowledge

claims: a true belief that the politician is having an affair and a rational justiﬁcation for that

belief based upon what Rachel witnessed in the restaurant and subsequently in the parked

car, that is, the criteria provided by the tripartite account of knowledge are all met and it is

truth, knowledge and belief260

reasonable to say that Rachel knows that the celebrity is having an intimate relationship (or

at least a one-off passionate embrace) with the person in question.10

PHILOSOPHICAL DIRECTIONS

In this ﬁnal section, we mention just a few questions that arise naturally out of some of

the main topics of this chapter, answers to which require more detailed or strenuous

philosophical analysis than would be appropriate here. This may help you to see why

philosophical inquiries are not always ‘irrelevant’ to real life: they arise inevitably when we

reason critically about things, or try to determine exactly what is involved in doing so. We

will quickly sketch these issues and recommend some sources for further reading. They are

all issues in epistemology and the theory or science of knowledge.11

Foundationalism vs coherentism

We said that, unlike other sorts of beliefs, we do not normally think of beliefs based on

perception as standing in need of reasons, that is, arguments. We think of normal per-

ceptual beliefs as justiﬁed just as they stand, just by virtue of being grounded in perception.

So long as we think so, then it is natural to think of other beliefs as ultimately being based

on perception. Scientiﬁc theories, for example, seem to be ultimately based upon observa-

tion, that is, perception. Thus for each non-perceptual belief P, it seems plausible that it is

justiﬁed – and hence potentially knowledge – only if we can trace it back along a chain of

reasons to some perceptual belief or set of beliefs. Since perceptual beliefs are self-justifying;

they can transmit justiﬁcation along the train of reasons back up to the belief P that was in

question.

This way of conceiving the structure of knowledge ﬁts common sense very well, and is

known as foundationalism. There is, however, a contrary point of view that – strangely

enough – also appeals to commonsense. As everybody knows, perception is not 100 per

cent reliable. We are subject to visual illusions (the man outside the train seems to be

moving – no, it’s the train beginning to move) and other less exotic perceptual mistakes

(the football referee honestly but mistakenly sees the player as offside). More dramatically,

we dream and even hallucinate; aren’t we then having false perceptions or, at least,

experiences that are indistinguishable from true perceptions? Of course much or most of

the time our perceptions are correct – we are quite certain we’re not dreaming or other-

wise mistaken. But even so, aren’t we implicitly assuming that the circumstances are

10 In a famous essay, Edmund Gettier described cases that appear to be justiﬁed true belief but not know-

ledge, thus casting doubt on the intuitive theory that knowledge is justiﬁed true belief. If you’d like to learn

more, see Robert Audi, Epistemology: A Contemporary Introduction, 2nd edition (Routledge, 2002). Gettier’s

original paper, along with notable attempts to solve the problem, is reprinted in Michael Huerner, Epistemology:

Contemporary Readings (Routledge, 2002).

11 For further reading on these and other issues in epistemology, see Audi, Epistemology: A Contemporary

Introduction, and Huerner, Epistemology.

truth, knowledge and belief 261

favourable? Aren’t we reasoning something like this: this is the experience I would have if

I were really seeing the cat on the mat under favourable circumstances. Circumstances are

favourable. Therefore I really am seeing the cat on the mat. If so, then the question arises:

what are the premises of that little argument based upon? The anti-foundational position

known as coherentism claims that if we always insist on a foundation in self-justifying

perceptual beliefs, then we can never get it, and no belief is ever justiﬁed. Since that is

absurd, the foundationalist demand must be misconceived. Instead, we should think of

our whole network of beliefs as mutually supporting: each belief – even if it is a perceptual

belief – is justiﬁed just insofar as it ﬁts with or coheres with the network we already have.

Perceptual beliefs typically do pass this test, but not always: it looks like the magician saws

the woman in half, but that does not cohere with other things we already know, so we

don’t believe it. On the other hand, coherentism has its problems too. Most conspicuously,

surely a whole set of beliefs could be mostly false (the person is deluded about almost

everything!); if another belief coheres with that set, does that justify it? It seems not.

Both theories have problems, but they are the only obvious options.

Internal vs external justiﬁcation

Exactly how is it that perceptual beliefs are justiﬁed? One answer is that perception is

reliable. That is, in normal circumstances, when a perceptual belief arises in a normal,

properly functioning human being, the belief is almost always correct. Perception is in

this way truth-conducive. Thus we might suppose: if a person has a perceptual belief, then

so long as the person is functioning normally and the perceptual circumstances are normal,

the belief is justiﬁed; if not, then the belief is not justiﬁed.

On the other hand, you might wonder: surely it is not enough for the circumstances to be

favourable in that way; doesn’t the person have to know that the circumstances are favour-

able? Otherwise, by what right would he or she accept the belief ? This might seem like a

reasonable demand, until you recognise how much it requires, for how are we supposed to

know that the circumstances are favourable, except by perception? But if we need more

perceptions in order to justify the ﬁrst perception, don’t we need yet more to justify these?

And so on; we are off, it seems, on what philosophers call a vicious regress. It is vicious,

because unless we can put a stop to it, it seems we are unable to justify any perceptual

beliefs.

Again, both sides have their advantages and disadvantages. The view that beliefs may be

justiﬁed simply by having been acquired in the right way – whether or not we know them

to have been so acquired – is called, for obvious reasons, externalism; the view that one

must always be aware of the means of justiﬁcation is internalism. The issue between them

is by no means merely academic. For example, in 2002, British military forces participated

the US-led invasion of Iraq at least partly on the grounds that Iraq was concealing so-called

weapons of mass destruction. There turned out not to be any. But the (then) British Prime

Minister Tony Blair defended the decision on the grounds that at the time of the invasion,

the evidence available to him suggested that Iraq was concealing such weapons. Many

truth, knowledge and belief262

people who granted Blair’s sincerity on the issue were nonetheless unsatisﬁed. Plausibly,

such critics were thinking that, however Blair’s decision may have been justiﬁed on internal

grounds, it was not justiﬁed from an external point of view, because the means of justiﬁca-

tion was not in fact reliable.

Probability and justiﬁcation

Where our reason for believing something is an argument with inductive force, is the

question of justiﬁcation simply the same thing as the degree to which the argument is

rationally persuasive for us? In most cases, it is correct to assume so. But not, in seems, in

all. Suppose that a few minutes ago you ﬁlled and switched on the electric kettle. So you

know there’s hot water in the kettle. Now compare this case. Your sister tells you she’s got

a lottery ticket. You happen to know that the chance that her ticket is a winner is one in

ten million. As it happens, the draw has already taken place; neither of you know it, but

her ticket is not a winner. In such a case, you naturally believe that your sister’s ticket is a

non-winner; this belief is true, and its probability of being true was very high. But do you

know that her ticket is a non-winner? It seems wrong to say so. Yet the probability of this

belief ’s being correct is much higher than that of your belief about the kettle! The failure

rate of kettles is much higher than one in ten million. To repeat: both beliefs are true. The

kettle-belief constitutes knowledge but the lottery-belief does not, despite the fact that the

kettle-belief had a greater chance of being wrong.

One could respond to this seeming paradox in different ways. At ﬁrst, you might think

maybe you do know that the lottery ticket is a loser. But that seems wrong: every purchaser

of a lottery ticket is in exactly the same position, has exactly the same evidence as to

whether or not they’ve won: everyone knows their chance is minuscule, namely one in ten

million. So everyone would be equally justiﬁed in claiming to have lost. But one such

person would be wrong to claim this, namely the winner. If we say that the losers knew

they were losers, then knowledge seems to be a matter of mere luck, which seems wrong; it

also makes it seem completely irrational to play the lottery – why would you buy lottery

tickets if you know that you’re not going to win?

Another response is to suppose that standards for what counts as justiﬁcation – criteria of

justiﬁcation – shift depending on the subject-matter. So in some cases we demand a higher

probability of being right than in others. Or perhaps probability can never sufﬁce for

justiﬁcation: perhaps if the only reason for accepting a certain proposition is its probability

of being true, then we cannot be justiﬁed in believing it, even if in point of fact it is true.

But this seems to ﬂy in the face of the notion of probability itself, which we explained as

degree of rational expectation; probability just is a measure of the degree to which it is

reasonable to believe something. Yet another tack is to suppose that only what is certain –

100 per cent probable – can properly be said to be known. The problem with that route

is that it leads swiftly to philosophical scepticism, the view that nothing, or very little, can

actually be known. It remains one the deﬁning endeavours of philosophy to formulate a

consistent theory of knowledge that does not result in scepticism.

truth, knowledge and belief 263

CHAPTER SUMMARY

It is crucial for critical thinkers to recognise that truth is objective and not relative.

Otherwise the critical thinker’s objective of analysing and assessing arguments with the

aim getting at the truth of a matter is deeply undermined. Some sentences that appear

to be straightforward assertions are in fact implicitly relative expressions of subjective

preferences and tastes: they are implicitly speaker-relative. In such cases there cannot be

genuine disagreements about the facts of the matter, whereas when a non speaker-relative

proposition is asserted, a genuine disagreement can occur because a truth is at stake. To

deny this, to accept the myth that all truth is relative, is to accept something of which it

seems impossible to make sense. In the case of moral beliefs, or beliefs about value,

relativism may not be readily refutable, but (1) the consequences of denying that there is

truth in this realm appear to be extremely pernicious and (2) relativism does not com-

pletely close the door to rational persuasion, because we may still demand consistency of

the relativist. If our stance is not that of not considering it, or refusing to consider it,

which one of the three remaining stances we choose to take towards a given proposition

depends upon the evidence available to us. We require sufﬁcient evidence for the truth or

falsity of a proposition in order to justify believing or rejecting it. If such evidence is

unavailable, we should suspend our judgement. It is perfectly possible to be justiﬁed in

holding a false belief. The evidence available to us might make it rational for us to accept a

proposition despite the fact that it turns out to be false. Some forms of justiﬁcation do not

involve arguments or reasoning. Perception is the obvious case. Merely having a true belief

in a proposition is not sufﬁcient to count as knowing the proposition, though it is neces-

sary for knowledge of it. Traditionally, philosophers have concluded that knowledge

requires a true belief arrived at via the right route; that is, via good reasoning based upon

sufﬁcient evidential support. This leads to the formulation of an account of knowledge

known as the tripartite account according to which to know that P is to have a justiﬁed true

belief that P. Knowledge is a stronger requirement than having a rationally persuasive

argument. One may have a rationally persuasive argument for a proposition without

thereby knowing it, if the degree of rational persuasiveness of the argument is not

sufﬁciently high.

EXERCISES

1 Without looking back at the relevant section of the book, write a paragraph

explaining the difference between indexical sentences and implicitly speaker-relative

sentences and then give an example of each.

2 For each of the following sentences, say whether it is indexical, implicitly speaker-

relative or neither. If it is implicitly speaker-relative, explain also whether it could be

implicitly relative to the preferences of the person asserting it. Explain your answers.

Note that, in some cases, there is room for reasonable disagreement as to the correct

answer. So don’t worry if you are not sure how to answer; the important thing is to

try to explain the answer you do give.

truth, knowledge and belief264

a The maximum speed limit on any UK road is 70 miles per hour.

b Chicago is nearby.

c Andy Murray did not win the 2008 US Open Tennis Championship.

d It’s raining there.

e Euthanasia is morally acceptable.

f The climate in southern Italy is too warm.

g Haggis is delicious.

h George W. Bush was a great President.

i I am in pain.

j Drink-driving should be punished by a prison sentence.

k The Government should cut petrol taxes.

l Ale tastes better than lager.

m I like ale better than lager.

n Mariah Carey has sold more records than Coldplay.

o Mariah Carey’s music is better than Coldplay’s.

p If you eat more fruit and vegetables you will be healthier.

q It’s going to snow tomorrow.

r Tchaikovsky wrote the 1812 Overture.

s We all live in a yellow submarine.

t That hurts!

u France and Great Britain were Second World War allies.

v 10 is the square root of 100.

w All pop/rock music is pathetic cacophony and a waste of any intelligent

person’s time.

x All triangles have three angles totalling 180 degrees.

y Blood is thicker than water.

z This one is better than that one.

3 Without looking back at the relevant section of the book, write out the tripartite

account of knowledge. Then, using your own example, explain why simply having a

true belief that P is insufﬁcient for knowledge that P.

4 Suppose you are justiﬁed in believing a proposition that is in fact false. Could there

be an argument for that proposition which is rationally persuasive for you? Would

the situation change if the proposition were actually true rather than false? Explain

your answer, using examples – your own examples – if you ﬁnd it useful.

5 It is sometimes held that testimony – what people tell you – is like perception, in

that one is normally justiﬁed in accepting the proposition without having an argu-

ment for it. The alternative view would be that in accepting something on the basis

of testimony, one is implicitly doing some reasoning, relying on an argument. What

would the argument be?

6 Give an example of a scientiﬁc theory and explain why it would count as an example.

Contrast that example with an example of something that might be labelled a

‘theory’ but is not a scientiﬁc theory.

truth, knowledge and belief 265

glossary

Words written in bold indicate references to relevant further glossary entries.

Ambiguity A sentence is ambiguous in a given context if there is more than one possible

way to interpret it in that context. A word is ambiguous in a given context if there is more

than one possible way to interpret in that context. See also lexical ambiguity, syntactic

ambiguity. Compare vagueness.

Antecedent A conditional statement asserts a relation between two propositions, the

antecedent and the consequent. When the antecedent of a true conditional statement

is true, the consequent must also be true. Thus the antecedent of ‘If John wins then Mary

will cry’ is ‘John wins’; if one accepts both this conditional and its antecedent as true, then

one must also accept that Mary will cry.

Argument An argument is a system of propositions comprising one or more premises

advanced by the arguer in support of a conclusion. Arguments may be evaluated as valid,

inductively forceful or neither, but not as true or false.

Argument commentary An argument commentary is a short essay that discusses an

argument-reconstruction, covering the following points: (i) how and why the argument

was reconstructed as it was; (ii) the validity or degree of inductive force of the argument;

(iii) the truth-values of the premises; (iv) the degree of rational persuasiveness of the

argument for relevant audiences, where this is not already addressed by (iii).

Argument-reconstruction A presentation of an argument in standard form in which

premises may be added, made explicit or clariﬁed in order to make the argument either

valid or inductively forceful.

Argument-tree A graphical representation of the structure of an argument. See

pp. 73–76.

Causal generalisation A causal generalisation is a generalisation to the effect that things

of one kind tend to cause things of another kind. Such a generalisation is true if the

presence of a thing of the ﬁrst kind raises the probability of things of the second kind, even

when other possible causes are absent.

Conclusion An argument’s conclusion is the proposition that its premises are intended

to support. The distinctive aim of giving an argument is to persuade an audience rationally

that the conclusion is true.

Conclusion indicators These are words such as ‘therefore’, ‘so’ and ‘thus’ that are often

used to indicate the conclusion of an argument. Such words sometimes serve other pur-

poses, however, such as indicating a causal relationship.

Conditional A conditional proposition is single proposition that joins two propositions,

the antecedent and consequent. Its usual function is to assert that if the antecedent is true,

then so is the consequent. It is most characteristically expressed by means of ‘if–then’.

Conditionals, unlike arguments, may be evaluated as true or false.

Conditional probability The conditional probability of a proposition P, given evidence

(set of premises) A, is the probability, if A holds (that is, if all the premises in A are true),

that P is true. Conditional probabilities are to be assessed ignoring any evidence not

included in A that might be relevant to the truth-value of P.

Connecting premises These are conditionals or generalisations, usually implicitly

assumed by an arguer, that are needed in order to infer the argument’s conclusion. For

example, if the argument is ‘Mary is a doctor, therefore Mary has a university degree’, a

suitable connecting premise is ‘All doctors have university degrees’.

Connotation, primary/secondary The primary connotation of a term is the condition

that is necessary and sufﬁcient for something’s being a member of the extension of the

term: it is the rule that determines whether or not a given thing is or is not correctly

designated by the term. The secondary connotation of a term is the range of further

attributes that a thing is commonly assumed to possess if it is thought to be correctly

designated by the term. The primary connotation of ‘mink coat’, for example, is ‘coat made

from the furs of minks’; its secondary connotation might include ‘expensive’, ‘posh’, ‘old-

fashioned’, ‘warm’ and ‘beautiful’ or ‘immoral’, depending on opinion. Unlike a term’s

primary connotation, its secondary connotation can vary from person to person.

Consequent See antecedent and conditional.

Context The context of an argument is the set of circumstances in which an argument is

actually advanced by an arguer. Context is signiﬁcant because in order to reconstruct an

argument (see argument-reconstruction) we often have to ﬁll in premises that are only

implicitly assumed by the arguer. To determine what an arguer is likely to have assumed,

we usually need to know the circumstances in which the argument is advanced. We also

need to know the context in order to know the meaning of indexical (context-relative)

expressions used.

Counterexample (i) A counterexample to a generalisation is a particular statement – a

statement that is not a generalisation – that is the negation of an instance of the generalisa-

tion. For example, ‘Darcey Bussell is a great ballerina who is tall’ is a counterexample to

‘No great ballerinas are tall’. (ii) A counterexample to an argument is an argument of

the same form or pattern as the ﬁrst argument that is clearly invalid or inductively non-

forceful. It is used as an illustration to make it clear that the ﬁrst argument is invalid or

inductively non-forceful.

glossary 267

Covering generalisation Often, where a premise of an argument is a conditional prop-

osition of the form ‘If Mary is a doctor, then Mary has a university degree’, it is implicitly

inferred from a generalisation of which it is an instance – in this case, ‘All doctors have

university degrees’. This relation is made more conspicuous if we express the generalisa-

tion in the form ‘For any given person, if that person is a doctor, then that person has a

university degree’.

Credibility The degree to which someone’s having said something constitutes a reason to

think it true. While critical reasoning requires us to focus on an argument and not on the

person putting it forward, a person’s character and actions are certainly relevant to their

credibility.

Deductive validity Validity can be deﬁned according to either of the following, equiva-

lent formulations: (1) An argument is valid if and only if it would be impossible for its

premises to be true but its conclusion false. (2) An argument is valid if and only if,

necessarily, if its premises are true, then its conclusion is true.

Defeated argument An inductively forceful argument, whose premises a person

reasonably believes, is defeated for that person if he or she has good reasons to think the

conclusion false.

Deﬁnition The necessary and sufﬁcient conditions under which something counts as an

instance of some type of thing or phenomena.

Descriptive claim Descriptive claims are typically propositions stating facts, whereas

prescriptive claims are propositions stating values, rules, norms or virtues; typically they

contain such words as ‘should’, ‘ought’, ‘right’ and so on. For the purposes of this book,

there is no real distinction between them; both may be true and false, and thus serve as

premises and conclusions of arguments.

Expected value The expected value of a given action depends on the values and

probabilities of the possible outcomes. In particular, if o1, o2, . . . and so on are the possible

outcomes of an action, V(o) is the value of a given outcome, and Pr(o) is the probability of

a given outcome, then the expected value of the action is:

[P(o1) × V(o1)] + [P(o2) × V(o2)] + . . . [P(on) × V(on)]

The value of each outcome must be assigned a number, but the purpose of the numbers is

only to indicate the comparative values of the possible outcomes. For example, if one

outcome is judged to be twice as good as a second, we could assign them any two numbers

so long as the ﬁrst is assigned a number that is twice that assigned to the second. Expected

value is the central concept of cost/beneﬁt analysis. The idea is that, given a range of

possible actions, one should perform the action with the highest expected value.

Explanation We give an argument for something when we seek to persuade an audience

that that proposition is true. By contrast, when we give an explanation of something, we

know, or assume, that the audience already accepts that the proposition to be explained is

glossary268

true. Our aim is not to give reasons for believing that proposition, but to specify, for

example, the causes of the event that it mentions. Both arguments and explanations can be

described as answering ‘why’ questions, but there is a crucial difference: whereas the

question in the case of explanation is ‘why is it so?’, or ‘why did it happen?’, the question

in the case of argument is ‘why should I believe it?’. Potentially confusing is that in order to

establish that an explanation is the correct one – e.g. that it speciﬁes the actual cause of an

event – we often have to give reasons why it should be believed, i.e. an argument. That is,

we sometimes have to argue for an explanation.

Extended argument An extended argument for a proposition is one containing more

than one inference: a conclusion is used as a premise for a further argument, the conclu-

sion of which may be used as a premise for a further argument, and so on. Conclusions

used as premises for further inferences in an extended argument are called intermediate

conclusions.

Extension The extension of a general term such as ‘cat’ or ‘red car’ is the set or group of

things designated by the term.

Factual assessment The stage in the assessment of an argument in which we deter-

mine whether or not the argument’s premises are true. If the argument is either valid or

inductively forceful, then the argument is sound if and only if all its premises are true.

Fallacies The term ‘fallacy’ encompasses certain commonly encountered failures of

argumentation; it is partly because they are often effective as rhetorical ploys that they are

commonly encountered. Formal fallacies are simply logical mistakes; that is, arguments

that fail to be valid or inductively forceful in certain characteristic ways. Substantive

fallacies are arguments that implicitly assume some quite general premise of a kind which,

when more closely and explicitly considered, can readily be seen to be false. Some other

common defects in argumentation ﬁt neither classiﬁcation, but since they involve fooling

the audience in the context of argument they can be appropriately classiﬁed with fallacies.

Faulty argument techniques Common defects in argumentation that ﬁt neither classiﬁ-

cation of fallacies but do, like fallacies, involve fooling the audience in the context of

argument.

Generalisation A generalisation is a proposition concerning a class of things, either

explicitly or implicitly involving a quantiﬁer such as ‘all’, ‘every’, ‘no’, ‘some’, ‘most’,

‘twelve’, ‘at least twelve’ and so on. For example, whereas ‘That dog is black’ is not a

generalisation, replacing ‘that dog’ with ‘every dog’, ‘no dog’, ‘at least one dog’ and so on,

yields a generalisation. Sometimes the verb must be changed to the plural form, and

likewise the predicate if it involves a noun rather than an adjective.

Good reasons For someone to have good reasons for believing a proposition is for that

person to possess an argument for that proposition that is rationally persuasive for them.

Hard generalisation A hard generalisation is one that is correctly conveyed by using a

quantiﬁer such as ‘all’, ‘every’, ‘each’ and ‘no’. Unlike soft generalisations, such generalisa-

tions are true only if there are no counterexamples.

glossary 269

Implicature (conversational implicature) A proposition is said to be implicated or con-

versationally implicated by a statement (asserted utterance of a declarative sentence) when

the proposition (i) is not explicitly stated by the utterance and (ii) is such that a listener

who knew the relevant facts about the context would reasonably take it to have been

intended by the speaker. Example: a tailor asks whether you want your jacket made in this

particular fabric; you say, ‘That’s ugly’. The tailor reasonably takes you to be intending to

convey that you don’t want it made in that fabric.

Implicit A premise is implicit in an argument if it has been assumed but not actually

stated by the arguer. Conclusions may also be implicit, though this is less common.

Whether or not, as a matter of psychological fact, a given premise has been assumed by an

arguer is often beside the point. In general, implicit propositions are those not stated by the

arguer that would be included in an argument-reconstruction produced in accordance

with the principle of charity.

Implicit relativity A statement is implicitly relative when the type of fact it expresses

involves a relation to something that is not explicitly mentioned in the statement. For

example, ‘John is tall’ is implicitly relative because what it really means is ‘John is taller

than the average man’ (if John is a man). The relation to the average man is not explicit in

the original statement.

Implicit speaker-relativity An implicitly speaker-relative statement is one that is impli-

citly relative, where the implicit term of the relation is the person making the statement.

Thus the statement is speaker-relative, but only implicitly so. For example, ‘Chocolate ice

cream tastes better than strawberry ice cream’ is implicitly speaker-relative because what it

really means is ‘Chocolate ice cream tastes better to me than strawberry ice cream does’.

(Some might say that the implicit term here should not be ‘me’ but something like ‘most

people’.)

Inductive force The inductive force of an argument is the conditional probability of its

conclusion relative to its premises.

Inductive inference To draw an inductive inference is to conclude, on the basis that a

certain proportion of a sample of a population possesses a certain feature, that the same

proportion of the whole population possesses that feature. The inference is inductively

forceful to the degree that the sample is representative of the population.

Inductive soundness See soundness.

Inference An inference is a step in reasoning from one or more premises to a conclusion.

All arguments contain at least one inference. Inferences are evaluated not as true/false, but

as valid/invalid and inductively forceful/inductively non-forceful.

Inference bar In an argument-reconstruction, an inference bar is a line written between

a premise and conclusion, indicating that the proposition expressed below the line has

been inferred from one or more of the propositions above it. It can be read as ‘therefore’.

Every reconstructed argument contains at least one inference bar.

glossary270

Instance An instance of a generalisation is a proposition about an individual that is

directly implied by the generalisation. Normally this will be a conditional. For example, ‘If

Socrates is a philosopher, then he is wise’ is an instance of ‘All philosophers are wise’. The

inference from a hard generalisation to a corresponding instance is always deductively

valid. That from a soft generalisation to an instance is inductively forceful.

Intermediate conclusion In an extended argument, an intermediate conclusion is a con-

clusion inferred from some set of premises that is used, in the same argument, as a premise

for a further inference.

Invalid Synonymous with ‘not deductively valid’. An argument may be invalid yet

inductively forceful, or neither valid nor inductively forceful.

Justiﬁcation One’s degree of rational justiﬁcation for believing a proposition is the

degree to which one is entitled to think it true. In many cases this will depend on whether

or not one has good reasons – arguments that are rationally persuasive – for thinking so.

In other cases – especially beliefs acquired by perception – one may be justiﬁed with-

out being able to give further reasons. Rational justiﬁcation can be distinguished from

pragmatic justiﬁcation, according to which one is justiﬁed in believing something if

believing it has desirable consequences. Rational justiﬁcation and pragmatic justiﬁcation

do not always coincide.

Knowledge See tripartite account of knowledge.

Lexical ambiguity An ambiguous sentence is lexically ambiguous if it contains an

ambiguous word.

Logic Logic is the systematic study of arguments, especially deductive validity and

inductive force.

Logical assessment Logical assessment is the stage of argument assessment at which it is

determined whether the argument is valid or invalid, and at which the degree of inductive

force of invalid arguments is determined. Except where inductive inferences are con-

cerned, it is sharply to be distinguished from factual assessment.

Necessary and sufﬁcient conditions The necessary conditions of counting as an instance

of some kind of thing or phenomenon X are the conditions that a thing must satisfy to

count as an X. The sufﬁcient conditions of counting as an instance of some kind of thing

or phenomenon X are the conditions such that satisfying them is enough for the thing in

question to count as an X.

Practical reasoning Practical reasoning is the use of arguments whose conclusions

recommend an action. See expected value.

Premise A premise in an argument is advanced as a reason for inferring the argument’s

conclusion.

Premise indicators These are expressions such as ‘since, ‘because’ and ‘for the reason

that’, which are often used to indicate a premise in an argument. As in the case of

glossary 271

conclusion indicators, however, such words sometimes serve other purposes, such as indi-

cating a causal relationship.

Prescriptive claim See descriptive claim.

Principle of charity According to this principle, if our aim is to discover the truth about a

given issue, then we should reconstruct arguments so as to yield the maximum degree of

rational persuasiveness for the relevant audience (which normally will include ourselves).

Probability The probability of a proposition is the degree to which it is likely to be true,

where this degree is expressed as fraction or decimal between 0 and 1. There are different

ways of explaining this, such as proportion and frequency, but in this book the degree to

which a proposition is likely to be true is taken to be the degree to which it would be

perfectly rational to expect it to be true. Since this obviously depends on the evidence one

has, the key concept is that of conditional probability: the degree to which it is rational to

expect a proposition to be true given such-and-such evidence.

Proposition A proposition is the factual content expressed by a declarative sentence on

a particular occasion of using (writing or uttering) the sentence. In particular, it is what is

expressed that admits of being true or false. Different sentences can express the same

proposition. For example, ‘Antony kissed Cleopatra’ expresses the same proposition as

‘Cleopatra was kissed by Antony’. Different propositions may be expressed by means of

the same sentence. For example, if Antony and Cleopatra each utter the sentence ‘I’m

hungry’, they express different propositions, since they talk about different people. A

sentence’s propositional content is independent of its rhetorical or emotive content.

Pseudo-reasoning Attempts to persuade which appear to give reasons for accepting/

rejecting a claim but in fact do not give us any reason for doing so are instances of pseudo-

reasoning. Fallacies and faulty argument techniques are types of pseudo-reasoning.

Quantiﬁers Quantiﬁers are expressions such as ‘all’, ‘some’, ‘every’, ‘many’, ‘twelve’, not

very many’ and ‘no’, used in the explicit statement of generalisations. Often, where both

hard and soft generalisations are concerned, they are left implicit.

Rational persuasiveness This is the concept we use to characterise a person’s having

‘good reason’ for accepting a conclusion. An argument is rationally persuasive for a person

if, and only if: (i) the person accepts its premises, and is justiﬁed in doing so; (ii) the

argument is either deductively valid or inductively forceful; and (iii) if it is inductively

forceful, the argument is not defeated for that person.

Refutation by counterexample This is a method of criticising an argument. One

fabricates an argument that embodies the same form or strategy as the argument one

means to criticise, but which is clearly invalid, not inductively forceful or fallacious. This

shows that the strategy or form of the argument one means to criticise is defective in the

same way.

Relevance The falsity of a premise can be more or less relevant, where the aim is to

discover reasons for or against the conclusion in question. Sometimes a false premise can

glossary272

simply be removed from an argument without destroying its validity or degree of inductive

force; the resulting argument may thus be sound. Other times the false premise can be

replaced by another, similar premise that is true, again without compromising validity or

inductive force. For example, the scope of a generalisation may be reduced.

Representative See samples.

Rhetoric A verbal or written attempt to persuade someone to believe, desire or do

something that does not attempt to give good reasons for the belief, desire or action, but

attempts to motivate that belief, desire or action solely through the power of the words

used is an instance of rhetoric.

Rhetorical force Not part of the proposition that a sentence expresses, but the emotive

or otherwise suggestive window-dressing that surrounds that proposition and is used to

persuade us to believe or do something by appeal to our non-critical faculties.

Rhetorical ploys Commonly encountered instances of rhetorical use of language, these

include: appeal to novelty, appeal to popularity, appeal to compassion, pity or guilt, appeal

to cuteness, appeal to sexiness, appeals to wealth, status, power, hipness, coolness, etc.

appeal to fear (also known as scare tactics), the direct attack and hard sell, buzzwords, scare

quotes, trading on an equivocation and smokescreen (changing the subject).

Rhetorical question An interrogative sentence that is not really intended as a question,

but as a statement, usually of a proposition with which the speaker or writer assumes the

audience will agree.

Samples An inductive inference is inductively forceful if, and only if, the sample cited in

the premise of the inference is representative of the population cited in the conclusion of

the inference. Suppose that n is the proportion of the sample known to bear a certain trait.

We can reasonably conclude that the proportion of the population bearing that trait is n

only if we have good reason to think that nothing has caused that proportion in the sample

that does not equally affect the population as a whole.

Scope To speak of the scope of a generalisation – for example, one of the form ‘All X are

Y’ – is a way of discussing the size of the class X. For example, the scope of ‘All dogs are

friendly’ is wider than that of ‘All beagles are friendly’. See relevance.

Soft generalisation A soft generalisation such as ‘Most dogs are friendly’ is contrasted

with a hard generalisation such as ‘All dogs are friendly’. Unlike hard generalisations, soft

generalisations cannot be refuted by a single counterexample. Soft generalisations are

frequently expressed without an explicit quantiﬁer, as in ‘Siamese cats meow a lot’.

Soundness An argument is sound if, but only if, its premises are all true, and it is either

deductively valid or inductively forceful.

Speaker-relativity A kind of statement is speaker-relative if it expresses a different

proposition depending on who makes the statement. For example, if John says ‘I am left-

handed’ he says that he is left-handed, whereas if Mary says ‘I am left-handed’ she says that

she is left-handed. The two propositions, then, could have different truth-values.

glossary 273

Stance There are four possible stances that can be taken towards a proposition with

which one is presented: believing it, not believing it, suspending judgement, not engaging

with it. Believing and not believing a proposition admit of degrees dependent upon the

evidence available to provide justiﬁcation for belief in that proposition.

Standard form This is a style of displaying an argument’s premises, conclusion and

inferences, in which each proposition is enumerated, and each inference indicated by an

inference bar. For example:

P1) If Mrs McFee were murdered, there would be signs of a struggle.

P2) There are no signs of a struggle.

C1) Mrs McFee was not murdered.

P3) If Mrs McFee was not murdered, then Inspector Radcliffe ought to leave the

premises.

C2) Inspector Radcliffe ought to leave the premises.

Syntactic ambiguity An ambiguous sentence is syntactically ambiguous when the

arrangement of its words is such that the sentence could be understood in more than one

way (as expressing more than one proposition.) See also lexical ambiguity.

Tripartite account of knowledge According to this account of knowledge, someone

counts as knowing a proposition if and only if (i) they believe it, (ii) it is true and (iii) they

are justiﬁed in believing it.

True To say, of a proposition that it is true is to say that things are as the proposition says

it is. For example, to say that it is true that snow is white is to say that snow is as that

proposition says it is, namely white. Another way to put the point: to say that it is true

that snow is white is equivalent to saying that snow is white. Unless a statement is speaker-

relative, the proposition that it expresses cannot be true for one person but false for

another.

Truth-value Sometimes it is convenient to speak of the truth-value of a proposition (see,

for example, speaker-relativity): the truth-value of a true proposition such as ‘snow is

white’ is truth, and that of a false proposition such as ‘snow is green’ is falsity.

Vagueness An expression is vague if (i) its extension is indeﬁnitely bounded, e.g. ‘bald’,

‘tall’, or (ii) in a given context it is unclear what is meant by it. In the ﬁrst case, the meaning

of the term may be clear, but the extension is ‘fuzzy’ because there is no clear point at

which things arranged on a single dimension (e.g. degree of baldness) cease to have the

quality denoted by the term. In the second case, particular uses of a term such as ‘political’

are vague: it may not be clear exactly what is meant by calling something political in a given

context. Because of this, a word such as ‘political’ may be vague in both senses – because its

meaning is vague, so is its extension.

Validity See deductive validity.

glossary274

answers and

hints to selected

exercises

CHAPTER 1

1(a) Argument. (b) N/A it’s an explanation (hint: the text tells us why the room is

messy. It does not try to persuade us that the room is untidy). (c) N/A it’s a question.

(d) N/A it’s a rhetorical question (hint: this could legitimately be converted into this

proposition, ‘The dollar is over-valued’, but an argument needs at least one premise

in support of a conclusion, and this proposition is unsupported). (e) N/A it’s an

unsupported proposition. (f) Argument. (g) Argument. (h) N/A it’s a command. (i )

Argument. (j) N/A it’s an unsupported proposition. (k) Argument. (l ) Argument

(hint: if you insert a conclusion indicator such as ‘therefore’, you see more clearly

that this is an argument). (m) N/A it’s a conditional. (n) N/A it’s an unsupported

proposition. (o) Argument. (p) N/A it’s an explanation (hint: there is no attempt to

persuade us that the speaker is late). (q) Argument. (r) N/A it’s an unsupported

proposition (hint: don’t be misled by the use of ‘since’ here, it’s used to talk about a

period of time). (s) N/A it’s an explanation (hint: there’s no attempt to persuade us

that the biscuit tin is empty). (t) Argument.

CHAPTER 2

2(a) ‘Court’ could mean a judicial institution, a place for playing a sport, such as

tennis, or an enclosed outdoor area. (b) ‘End of life’ could mean the ﬁnal part of one’s

life or the goal/function of life. (c) ‘Organ donor’ could mean someone who donated

a body part or someone who donated a musical instrument (hint: the term is

ambiguous here because of the context – the Archbishop of Canterbury praises the

donor). (d ) ‘Mummy’ could mean either someone’s mother (probably the victim’s) or

an ancient Egyptian exhibit (hint: the context makes the term ambiguous – the attack

takes place in a museum). The phrase ‘by mummy’ could also be ambiguous: the

sentence could mean either that someone’s mother or a museum exhibit was respon-

sible for the attack, or that the attack took place in the vicinity of either someone’s

mother or a museum exhibit. (e) ‘By statue’ could mean that the statue found the car

or that the car was found beside the statue. (f) ‘British left wafﬂes’ could mean that

British left-wing politicians talk meaninglessly about Ireland or it could mean that the

British (military, maybe) left some square pancake-like pastries in Ireland. (g) ‘Arms’

could mean weapons or limbs. ‘Head’ could also be ambiguous here, meaning either a

head of state or a body part, so there are four possible interpretations of the sentence,

though not all of them are equally plausible. (h) ‘Depression’ could mean a drop in

the atmospheric pressure or a psychological condition. (i) ‘The right’ could mean that

Obama is physically leaning further over to the right-hand side or that he is shifting

his political position rightwards. (j) ‘More lies ahead’ could mean that the Finance

Minister is facing further challenges or that the public can expect to be told more

untruths.

3(a) Before the ofﬁcers’ arrival the two suspects ﬂed the area in a red Ford Escort

that was driven by a woman in black. (b) Yesterday I was invited to go to the movies.

friends were feeling depressed. (d ) Often people who use cocaine die early or

People who often use cocaine tend to die early. (e) Smith had ﬁve pairs of boots as

well as a pair of slippers. He lent the slippers to Jones or Smith had ﬁve pairs of boots

and a pair of slippers and he lent them all to Jones. (f) Wanted: a bay mare with

white socks, suitable for a novice. (g) When Jones left the company, it was in a better

state or When Jones left the company, he was in a better state. (h) Glasgow’s ﬁrst

commercial sperm bank opened last Friday with twenty men’s semen samples frozen

in a stainless steel tank. (i) A week ago, they were exposed to someone who was

infected with the virus or They were exposed to someone who had been exposed to

the virus a week ago. (j) The police would like to speak to two women and a van

driver who all ﬂed the scene of the accident or The police would like to speak to two

women and also to a van driver who ﬂed the scene of the accident.

5(a) No one / Hard. (b) Few / Soft (c) Most / Soft (d ) A majority of / Soft (e) All / Hard

(f) Generally / Soft (g) Almost all / Soft (h) Hardly any / Soft (i) Every / Hard (j)

Almost none / Soft

6 Only (d ) is uncontroversially true as a hard generalisation and you need to use ‘No

owls’. (a), (b), (c), (e), (f), (g), (i) and (j) should all be soft. (h) may turn out to be

true as a hard generalisation, but it is unlikely that readers (and their lecturers)

have sufﬁcient information about UK universities’ English departments at their

ﬁngertips to determine this. Also, there may be some disagreement about what

constitutes a ‘department’, hence a hard generalisation is unlikely to be uncon-

troversially true.

7(a) Scare quotes. (b) Appeal to novelty. (c) Buzzwords (‘knowledge management’,

‘competitive advantage’, ‘learning culture’, ‘shared vision’, ‘common purpose’). (d )

Appeal to popularity. (e) Smokescreen (hint: avoids the question of our moral duty).

(f) Equivocation (over the vagueness of ‘most successful’). (g) Appeal to fear.

answers and hints to selected exercises276

(h) Buzzword (‘censorship’). (i) Appeal to novelty or appeal to vanity; ‘hair manage-

ment technology’ is a buzzword (phrase). (j) Many questions.

CHAPTER 3

4Hint: according to the deﬁnition of soundness, an unsound argument may have a true

conclusion.

5Hint: review the remarks on pp. 60–61 on the concept of truth.

6(a) Valid. (b) Valid (hint: see what follows from P2 and P3, then see what follows

from that proposition together with P1). (c) Valid. (d ) Invalid. Even if no member of

the Green Party voted for the tax cut, it could be that people outside the Green Party

voted against it as well (or failed to vote for it). So Mr Jacobs could be one of those

outside the Green Party who didn’t vote for it. (e) Valid. (f) If every member of the

Conservative Party voted for the tax cut, it could be that others outside that party

voted for it as well. (g) P2 says that some of those who voted for the tax cut voted to

increase defence spending, but it doesn’t say that all who voted for the tax cut voted

to increase defence spending. So it could be that some voted for the tax cut without

voting for increased defence spending; if so, then that group could contain all the

Liberal Party members who voted for the tax cut. (h) Invalid: to make the argument

valid, we would have to add the premise ‘Infanticide is not morally permissible’. That

premise might be obviously true, but until it is actually added to the argument, the

argument remains invalid. (i) Valid. (j) Invalid(!): what follows from the premises is

that the antecedent of the conditional P1 is false – namely, that it is not the case that

each person has the right to determine what happens to his or her own body. This

means: not every person has that right. This leaves it open that some people might

have that right, even if not everyone does. The conclusion, however, says that no

people have that right. So the premises could be true and the conclusion false. As a

further exercise, you might try to construct an argument similar to (j) but which is

valid. (k) Invalid: P1 allows that a regime might be both corrupt and inefﬁcient.

(l ) Invalid: P1 doesn’t tell us that only one of those two things could have happened.

Compare: if the car has no petrol (gasoline), then it will not start. If the car does have

petrol, it doesn’t follow that it will start – it might have a dead battery, a faulty

starter, etc. (m) Valid. (n) Invalid: P1 tells you that if a political system is just, then it

is a democracy. It doesn’t tell you anything about unjust political systems; it could

be that, although all just systems are democracies, not all democracies are just.

(o) Invalid: the word ‘only’ can be tricky. Actually P1 here says exactly the same thing

as P1 in the previous argument. Compare: ‘Only boys are members of the club’ and

‘The only members of the club are boys’ – these say exactly the same thing, namely

that every member of the club is a boy. (p) Valid. (q) Invalid: Mr Cleever may have

been drunk at the time of the accident, even though his drunkenness did not cause

the accident. (r) Invalid: in order to infer the conclusion from the conditional P1, we

need to know that Constantius’ Christianity was genuine, but P2 only tells us that we

do not know that it was not genuine; it doesn’t tell us that it was. So perhaps

answers and hints to selected exercises 277

Constantius’ faith was a fraud, but no evidence of that fraudulence has survived.

(s) Valid. (t) Invalid. If no Roman emperors were wise, then it could be that Marcus

Aurelius was not wise, and P1–P3 are all true. (u) Valid. (To see this, see what

happens if we try to suppose the conclusion false but the premises true. Thus

suppose C is false, i.e. that Augustus was wise. Then according to P3 Marcus Aurelius

was not wise. Then according to P1 no Roman emperor is wise. But then Augustus, a

Roman emperor according to P2, is wise! So it is impossible for the premises to be

true but the conclusion false.) (v) Valid. (w) Invalid: P1 says that Mary will be

disappointed if both John and Susan are late, so perhaps she won’t be disappointed if

only John is late. (x) Invalid: perhaps P1–P3 are all true, but Mary is disappointed for

some other reason; perhaps John’s being late was enough to disappoint her (P1

doesn’t say Mary will be disappointed only if both John and Mary are late). (y)

Invalid: this is disputable, but it seems that P1 tells us that Mary will be disappointed

if John and Susan are married to each other. Perhaps John and Susan are both

married but not to each other, in which case the premises could all be true but the

conclusion false. (z) Valid.

7(a) False. (b) True. (c) False. (d ) True. (e) False. (f) True. (g) False. (h) False. (i) False.

(j) False. (k) True. (l ) False. (m) False. (n) False. (o) True. (p) False. (q) True.

9Note: each of these admit of more than one correct answer; for example, ‘If Hadrian

was not great then Trajan was great’ is equivalent to the answer given to (a), and

would be equally correct. (a) If Trajan was not great then Hadrian was great. (b) If

they are not mistreated, then dogs are loyal to their masters. (c) If there were any

benevolent emperors, then Marcus Aurelius was a benevolent emperor. (d ) If you

do not study, then you will not pass. (e) If your dog does not get the ball, then my

dog will get the ball. (f) If you are not wearing a tie, then you will not be admitted.

(g) If you are not wearing a tie, then you will not be admitted. (h) If my dog barks,

then your dog barks (or: if your dog does not bark, then my dog does not bark). (i) If

you drink every night, then you will not pass. (j) If you do not study, then you will

not pass. (k) If you do not study, then you will not pass. (l ) If the champion does not

ﬁght aggressively then he will not win. (m) If the ball does not go in the water, then

either your dog will get the ball or mine will. (n) If Maximin was admired in Rome,

then Galerius was not admired in Rome.

CHAPTER 4

P1) Most sex crimes are committed by victims of child abuse.

1(a) (A)

P2) The defendant committed a sex crime.

C) Probably, the defendant was a victim of child abuse.

Inductively forceful.(B)

answers and hints to selected exercises278

P1) Most old people have poor eyesight.

(d ) (A)

P2) No one with poor eyesight should be allowed to drive.

C) Probably, most old people should not be allowed to drive.

Inductively forceful.(B)

Both are inductively forceful. (B) They could both be sound. If Mr X is a2 (A)

non-homosexual AIDS patient living in Orange County, then still the

premises of both arguments could be true. (C) The four premises together do

not give us a reason to conclude that Mr X is a homosexual, and do not give

us a reason to conclude that he is not.

(a) Incompatible. (b) Compatible. (c) Compatible. (d ) Compatible (accord-3

ing to our convention, ‘some’ means ‘at least one’). (e) Compatible. (f)

Incompatible. (g) Compatible. (h) Incompatible. (i) Compatible. (j) Com-

patible. (k) Compatible. (l ) Compatible. (m) Compatible.

Reconstruct it as a single argument; its tree would have three premises4

pointing separately to the conclusion ‘Probably, Lance Armstrong is not

going to win another Tour de France’.

P1) If this meat was grown in Scotland, then it is extremely unlikely that it

5(d ) (A)

is infected with BSE.

P2) If this meat is infected, then it is very unlikely that eating it will make

you ill.

C) If this meat was grown is Scotland, then eating this meat will not

make you ill.

Invalid. (C) But the argument can be made valid as follows:(B)

P1) If this meat was grown in Scotland, then it is extremely unlikely that it

is infected with BSE.

P2) If this meat is infected, then it is very unlikely that eating it will make

you ill.

C) If this meat was grown is Scotland, then, probably, eating this

meat will not make you ill.

This assumes that the expressions ‘extremely unlikely’ and ‘very unlikely’ in(D)

the premises are strong enough to justify the word ‘probably’ in the

consequent of the conclusion.

P1) Brazil is more likely to win the World Cup than Argentina.

(e) (A)

C) Brazil will win the World Cup.

answers and hints to selected exercises 279

Invalid, and not inductively forceful. (D) The arguer is probably thinking(B)

that Brazil is the team most likely to win the World Cup, but that could

be true even if the probability of Brazil winning is less than one-half.

P1) Probably, English football fans will make trouble at the World Cup.

(g) (A)

P2) If English football fans make trouble at the World Cup, then England

may be expelled from the European Cup.

C) England will be expelled from the European Cup.

Invalid, and not inductively forceful. (C) However, it could be made valid as(B)

follows:

P1) English football fans will make trouble at the World Cup.

P2) If English football fans make trouble at the World Cup, then England

may be expelled from the European Cup.

C) England may be expelled from the European Cup.

Alternatively, it could be made inductively forceful:

P1) Probably, English football fans will make trouble at the World Cup.

P2) If English football fans make trouble at the World Cup, then England

will be expelled from the European Cup.

C) Probably, England will be expelled from the European Cup.

P1) If the murderer passed through here, then, probably, there would be

(h) (A)

hairs from the victim on the rug.

P2) But there are no hairs from the victim on the rug.

C) Probably, the murderer did not pass through here.

Not valid, but it is inductively forceful.(B)

(l ) Hint: note that ‘many’ of a given population can be thus-and-so, when

most are not. For example, many people have gym memberships, but most

do not go to the gym.

(a) and (b) seem to be inductively forceful; (a) is very forceful because the6

sample looks to be representative; (b) seems to be less so, since it is possible

that communist systems might succeed in other historical circumstances.

Reconstructions should be obvious.

This is a bit more tricky to reconstruct. One way is as follows:(c) (A)

P1) The average IQ from among 17 conductors of major orchestras is

17 points higher than that of UK doctors, and 18 points higher than

that of UK lawyers.

C) Probably, the average IQ of musicians is higher than that of

either doctors or lawyers.

answers and hints to selected exercises280

This argument is not inductively forceful because the sample is not repre-(B)

sentative. The relevant population mentioned in the conclusion is musicians,

but the sample cited in the premise is only that of conductors of major

orchestras. These are likely to be among the most intelligent musicians, so it

is no wonder that they should be found to have high IQs.

P1) Most of the teenagers who have come to me (a counsellor for

(d ) (A)

teenagers) and confessed to taking illicit drugs have serious family

problems.

C) Probably, most teenagers who take illicit drugs have serious

family problems.

Not inductively forceful because the sample is not representative. It might(B)

be that most teenagers who take illicit drugs do not have serious family

problems, and do not do seek the services of a counsellor. The counsellor sees

only those teenagers who are sufﬁciently troubled to seek a counsellor.

P1) No English club has won the treble twice.

(e) (A)

P2) Manchester United is an English club.

C) Probably, Manchester United is not going to win the treble again.

The argument is not inductively forceful. For all that the premises tell us,(B)

perhaps only one English club (United) has won the treble (FA Cup, League/

Premiership, Champions League/European Cup). (In fact, that is true; only

United has done it – but you don’t need to know this in order to see the

weakness of the argument.) Thus, even if no English clubs have won it twice,

it could be that, given that a club has won the treble once, it is likely to win it

again. That is, P1 could be true even though the conditional probability of an

English club’s winning the treble given that it has won it before is quite high.

Note also: it is tempting to think we should add ‘Manchester United won the

treble once’ as a premise, but that statement does not support the conclu-

sion, so it is not part of the argument.

P1) People who take vitamins regularly live longer than average.

(g) (A)

P2) Jenna takes vitamins regularly.

C) Probably, Jenna will live longer than average.

This is inductively forceful. If you think it isn’t, it is probably because you(B)

are reasoning as follows: ‘We cannot conclude from P1 that taking vitamins

regularly causes people to live longer than average, because it might be that

already healthy people are more likely to take vitamins (perhaps well-off

people tend to take vitamins more, and are healthier because they are

answers and hints to selected exercises 281

well-off, not because they take the vitamins); therefore we can’t conclude

that because Jenna takes vitamins regularly she’s likely to live longer.’ It is

true that P1 doesn’t tell us anything about a causal relationship. But C

doesn’t tell us about a causal relationship either! Compare: ‘Most people

with sore throats get a runny nose. Jenna has a sore throat. Therefore,

probably, she’ll get a runny nose.’ The sore throat doesn’t cause the runny

nose, but still the argument is inductively forceful.

CHAPTER 5

1 Except in the case of (k), we provide only the missing premises. (a) ‘You should not

marry an idiot’, where this is understood as a hard generalisation, or perhaps ‘If

someone is an idiot, then you should not marry him’. (b) Same. (c) ‘Everyone who

likes the Jeeves books likes the Blandings Castle books.’ (d ) ‘If that fat man sits in

that chair, then it will break.’ Or possibly add two premises (though this is not

speciﬁed as an option in the instructions: ‘If a very heavy person sits on that chair,

then it will break,’ and ‘That fat man is a very heavy person’. (e) Possibly a hard

generalisation: ‘Prices rise only when the savings rate decreases’, or ‘When the savings

rate does not decrease, prices do not rise’; or a soft one, i.e. ‘Usually, when the savings

rate does not decrease, prices do not rise’. (f) ‘If Hamilton’s mechanic is not inept,

then Hamilton’s car will not break down.’ It may help in this case to translate all

the uses of ‘unless’ into sentences using ‘not’ and either ‘if’ or ‘only if’. The ﬁrst

sentence would be ‘Massa will win only if Hamilton’s car breaks down’, or ‘If

Hamilton’s car does not break down, then Massa won’t win’. (g) ‘Rossini was

greater than Puccini.’ (h) ‘No socialist country is a democracy.’ (i) ‘If we withdraw

the offer, then we carry on with a second-rate manager.’ (j) ‘If there isn’t any wine,

then we’ll drink beer.’ (k) The conclusion – ‘Cigarette advertisements encourage

people to smoke more’ – is not quite explicit. One likely implicit premise is simply

the conditional: ‘If ads for chocolates encourage people to eat chocolates, then

cigarette advertisements encourage people to smoke.’ One might think the implicit

premise is something like the covering generalisation: ‘All ads for a given brand of

consumable product encourage people to consume that product.’ This generalisa-

tion would be too broad in scope, however; it doesn’t seem true that ads for

toothpaste or toilet paper encourage people to use more toothpaste or toilet paper

(as opposed to encourage them so select a particular brand). Yet the suggested

conditional is surely motivated by a generalisation (why should there be a con-

nection between chocolates and cigarettes?). A good exercise would be to ﬁnd a

plausible generalisation (or appropriate scope) that would serve the purpose of the

argument.

2 There are many ways in which these sentences might be reformulated; we offer one

suggestion for each. (a) The democratic candidate adopts whatever position is most

popular. (b) The invasion of Iraq was a huge (large, massive, etc.) miscalculation. (c) If

they impose trade tariffs then trading agreements will not be fair. (d ) Since beginning

answers and hints to selected exercises282

to write novels aimed at a young female adult audience, she has earned a great deal of

money. (e) However long they attempt to persuade us of their position, we will not be

persuaded. (f) Although it is widely believed that shares in Ramsay represent good

value, they do not. (g) We will continue our attempts to ban the advertisement on

children’s television of innutritious convenience foods until such advertisements

have been completely eliminated. (h) Mistakes by doctors contributed to the deaths

of 40,000 patients last year. (One might use ‘caused’ instead of ‘contributed to’, but

one would have to know more of the relevant facts in order to determine which is

appropriate.)

3(a) If you do not release prisoners then there will be no cease-ﬁre. (b) If we do not

increase our appeal to women then we will not win the election. (c) All universities

allow the most offensive forms of speech (conceivably, this means only that

some universities allow such speech). (d ) Every leaf-blower is louder than every

rake. (e) If embryo research is allowed then human cloning will be allowed.

(f) Everyone who laughs last laughs longest. Alternatively: for every group of people,

the one who laughs after everyone else in the group has laughed laughs longer than

anyone else in the group. (g) No one who receives no pain (or, no pain of the sort

appropriate to the given activity) will receive any gain (or rewards appropriate for the

given activity).

4 As is often the case, each of these might be answered in either of several ways; here

are some suggestions, but try to ﬁnd an alternative. (a) No one under the age of 18

can legally purchase alcohol in the UK. (b) All scorpions are poisonous. (c) Most non-

French wines are not overpriced or Few non-French wines are overpriced. (d ) Most

oil paintings from before 1500 are either Dutch or Flemish or Except for Dutch and

Flemish paintings, few paintings from before 1500 were painted in oil. (e) Most

successful lawyers are good at analysing arguments. (f) The blood pressure of any

haemorrhaging patient will decrease. (g) Most drivers aged 17 are too young to drive

long distances.

P1) Everyone who supports across-the-board pay rises for female

7(a)

academics supports a reduction in the evidential standard for rape

convictions.

P2) Mrs Jones supports across-the-board pay rises for female

academics.

C) Mrs. Jones will support a reduction in the evidential standard for

rape convictions.

P1) Most healthy, young horses can be trained without too much

9(a)

difﬁculty.

P2) Your new horse is healthy and young.

C) Probably, your new horse can be trained without too much

difﬁculty.

answers and hints to selected exercises 283

P1) Most men marry.

(b)

P2) Every married woman has, at the time of her wedding, a mother.

C) Most men have, have had, or will have a mother-in-law.

Since human beings are primates, the scope of the generalisation must be(c)

reduced. The argument might be represented in different ways, but, how-

ever it is done, some implicit premises will need to be made explicit.

P1) All chimpanzees are primates.

P2) No chimpanzee is human.

P3) Bobo is a chimpanzee.

C1) Bobo is a non-human primate.

P4) No primates except humans can learn to talk.

C2) Bobo cannot learn to talk.

Not all countries can be attacked by sea – Paraguay, Laos and Switzerland,(d )

for example, are land-locked (assuming that ‘attacked by sea’ means ‘attacked

using ships or boats’, and does not include attacks by aeroplanes from aircraft

carriers and the like). But most countries have a seacoast.

P1) Most countries can be attacked by sea.

P2) Any country that can be attacked by sea requires a naval defence.

C) Most countries require a naval defence.

P might well be disputed. Does, say, Equatorial Guinea require a naval

defence?

The conclusion is that same-sex marriage should not be legal. Note that the following12

reconstruction would be inadequate:

P1) No deviant sexual relationship should be legally protected.

P2) The legalisation of same-sex marriage would legally protect

homosexual relationships.

P3) Homosexual relationships are deviant sexual relationships.

C) Same-sex marriage should not be legalised.

First, this reconstruction leaves out of account the ‘slippery slope’ appealed to in the

last sentence (turn to Chapter 7 pp. 231–232 for further discussion of slippery slope

arguments). The point seems to be that the only reason that only heterosexual

relationships (between mature persons not genetically closer than cousins) are entitled

answers and hints to selected exercises284

to legal protection is that others are deviant. Therefore, if homosexual relationships

are entitled to legal protection, then since they are deviant, all deviant sexual relation-

ships are entitled to it. Second, this reconstruction uses the word ‘deviant’. But there

are at least three possible meanings here, one of which is rhetorically charged: the

word can mean simply ‘deviating from the norm’, which might mean ‘not biologically

typical’, or ‘not socially typical’. But it also carries an opprobrious connotation of

sickness or unhealthy abnormality, as when we speak of ‘social deviants’. The factual

basis of the argument can be clariﬁed by eliminating the term.

15 There are just two relevant outcomes here: you draw an ace, or you do not draw

an ace. A pack of playing cards contains 52 cards, of which four are aces. So the

probability of drawing an ace is 4/52 =1/13, and the probability of not drawing one

is 12/13. So:

EV =(1/13 ×10) +(12/13 ×−1)

=(0.77 ×10) +(0.92 ×−1)

=0.77 +(−0.92)

=−0.15.

The expected value is negative, so you shouldn’t accept the wager.

17 The ﬁrst two sentences are true, but only the second is relevant as a premise. Hints:

the ﬁrst conclusion is ambiguous. Interpreted one way, there is a sound argument

for it using the second sentence as a premise, but it does not support the second

conclusion. Interpreted the other way, it supports the second conclusion but is not

supported by the second sentence.

19 (b) The conclusion might be ‘The stress of modern life is caused by the amount

of shopping we do, combined with our not going to church’, or something like

‘Our lives are more stressful than our parents’ lives were because we shop more

and attend church less than they did’. Taking the latter as the conclusion, a simple

reconstruction might be:

P1) Our lives are more stressful than our parents’ lives were either

because we shop more and attend church less than they did, or

because we work more than they did.

P2) We do not work more than they did.

C) Our lives are more stressful than our parents’ lives were either

because we shop more than they did, and they went to church

whereas we do not.

Note, however, that the argument hints at an argument for P1 itself. Since

shopping is said to be a highly stressful activity, the arguer might also be assuming

that attending church reduces stress.

answers and hints to selected exercises 285

CHAPTER 6

1(a) No. (b) No. (c) Yes. (d ) Yes. (e) Yes. (f) No. (g) Yes. (h) No. (i) The argument

is defeated for James because he has much stronger evidence that the conclusion is

false (in fact, he knows that the conclusion is false).

2(a) Yes. (b) No. (c)–(f) The argument is rationally persuasive for Catherine if we

assume she was justiﬁed in accepting what David told her. It seems that she was.

Jane’s case is less clear, but it seems the argument is not rationally persuasive for her

because her reason for accepting P2 is not good. The argument is defeated for Mary,

hence not rationally persuasive for her. Though she does not accept the conclusion, it

seems the argument is rationally persuasive for Anna: her reason for rejecting the

conclusion is poor.

3 (i) Hint: Remember that false beliefs can be reasonable, i.e. well-supported and justi-

ﬁed. The word ‘wrong’ is possibly ambiguous in this context; does it mean ‘false’ or

‘unjustiﬁed’?

P1) Every educated Roman knew Homer.

4(h)

P2) Everyone who knows Homer knows the story of Achilles.

C) Every Roman knew the story of Achilles.

Suppose X is any Roman. According to P1, X knew Homer. Then, according

to P2, he knew the story of Achilles. So whatever Roman X is, X knew the

story of Achilles. So, every Roman knew the story of Achilles.

P1) If P then Q.

7(a)

P2) If Q then R.

C) If P then R.

P1) If a is not an S, then a is a D.

(d )

P2) All Ds are T, and a is not T.

P3) If a is an S, then either a is R or a is A.

P4) Every W is either not-A or Y.

P5) Everything that is S and Y is T.

C) If a is W, then a is R and S.

We can try checking for validity just using the logical form. We suppose a is

W, and see whether the premises tell us that a must be R and S. We know

from P2 that a is not T. Therefore from P2 a cannot be a D (if it were, then it

would be T, which it is not). Then P1 tells us that a is an S. So we know that a

is an S. It remains to show that a is R. P4 tells us that a is either not-A or Y.

Let us see what follows on each alternative: ﬁrst that a is Y, then that a is

not-A. So suppose a is Y. Since we know that a is an S, P5 tells us that a is a T.

answers and hints to selected exercises286

But we know from P2 that a is not a T. So a can’t be Y. So suppose a is not-A.

Then P3 tells us that if a is S, a is R. According to P1, if a is not S, then a is D.

So a is either D or R. But we know that a is not a D. So a is R. So if a is W,

then a is both S and R, and the argument-form is valid.

CHAPTER 7

1(a) Deriving ought from is (hint: the conclusion is prescriptive, but the premise is

descriptive). (b) Post hoc ergo propter hoc. (c) Fallacy of majority belief. (d ) Afﬁrming

the consequent. (e) Denying the antecedent. (f) Conﬂation of morality with legality.

(g) Mistaking correlation for cause. (h) Ad hominem. (i) Tu quoque (hint: it is implied

that the chef is rich and does not follow his own prescriptions with respect to feeding

a family on a budget). (j) Perfectionist fallacy.

2General hint: remember that the crucial move when reconstructing substantial

fallacies is that of adding the premise (which is usually hidden and operates in all

instances of the fallacy) that exposes the fallacy.

Ad hominiem circumstantial:(a)

P1) Lecturers are always extolling the virtues of critical thinking.

P2) Lecturers only have jobs if they have students to teach.

P3) Whenever someone would beneift from something we should reject

their arguments in favour of that thing.

C) We should reject lecturers’ arguments in favour of critical

thinking.

Conﬂation of morality with legality:(b)

P1) It’s not illegal for me to exaggerate my skills on my CV.

P2) Anything which is not illegal is not immoral.

C) It’s morally acceptable for me to exaggerate my skills on my CV.

Tu quoque:(c)

P1) My doctor says that wearing high heels is bad for your knees and

should be avoided.

P2) My doctor wears high heels.

P3) Whenever someone’s actions are inconsistent with their advice, we

should not follow their advice.

C) I should not follow my doctor’s advice to avoid wearing high

heels.

answers and hints to selected exercises 287

Inversion of cause and effect:(d )

P1) Smoking causes lung cancer.

P2) Whenever one thing X causes another Y, an absence of X will cause

an absence of Y.

C) People who do not smoke will not suffer lung cancer.

Could be either confusion of correlation with cause or post hoc ergo propter(e)

hoc, depending on whether we interpret P1 as saying that the trees blossom

and the weather begins to get warmer at the same time (confusing corre-

lation with cause), or as saying that ﬁrst the trees blossom, and then the

weather gets warmer. The ﬁrst interpretation is probably more plausible, but

the reasoning remains fallacious.

P1) Whenever the cherry trees blossom, the weather begins to get

warmer.

P2) Whenever two events are correlated, one is the cause of the

other.

C) Cherry blossom makes the weather warmer.

P1) Whenever the cherry trees blossom, the weather begins to get

warmer.

P2) Whenever one event precedes another, the ﬁrst is the cause of the

second.

C) Cherry blossom makes the weather warmer.

3(a) Slippery slope. (b) False dilemma. (c) Begging the question. (d ) Red herring.

(e) Straw man. Hint: hidden behind the rhetoric is a misrepresentation of the

minister’s proposal to cut taxes for people who earn average incomes as a proposal to

give money to people earning considerably more than the average wage.

CHAPTER 8

2(b), (d ), (i ), (m), (q), (s), (t) and (z) are indexical. (t) could also be implicitly speaker-

relative if it means ‘that hurts me’, as could (z) if it means something like ‘I think this

one is better than that one’, in which case it could also be implicitly relative to the

preferences of the speaker (but need not be).

(g), (h), (l ), (o) and (w) are implicitly speaker-relative and also implicitly relative to

the preferences of the speaker with respect to food, presidents, beer and music,

respectively.

answers and hints to selected exercises288

(f) depends on context. It could be both implicitly speaker-relative and relative

to the preferences (in respect of climate) of the speaker if she is explaining, for

example, why she doesn’t want to go to southern Italy for a holiday. On the other

hand, the speaker might be talking about, say, the suitability of the climate for

growing a certain crop – Riesling grapes, for instance – in which case the sentence

would be neither implicitly speaker-relative nor relative to the preferences of the

speaker. Note that it would be implicitly speaker-relative in the sense dealt with in

Chapter 1.

(e), (j) and (k) make prescriptive claims ((e) and (j) are speciﬁcally moral claims, (k)

arguably so). These are tricky. If we take the philosophical view that moral values are

relative to the preferences of an individual or to a group of individuals or a culture

(the position called moral relativism, discussed in this chapter), then we should say

that these sentences are both implicitly speaker-relative and implicitly relative to the

preferences of the speaker(s) asserting them. If, on the other hand, we take the

philosophical view that moral values are independent of individual or collective

preferences (the position called moral objectivism), then we should say that the sen-

tences are neither implicitly speaker-relative nor relative to the preferences of the

speaker(s).

4 A sample answer: Yes, if I were justiﬁed in believing a proposition that is in fact false,

there could still be an argument for that proposition that is rationally persuasive for

me. This is because rational persuasiveness only requires (a) that an argument be valid

or inductively forceful, (b) that I have good reason to accept the premises and, if the

argument is inductively forceful, (c) that the conclusion is not defeated for me. So

providing these criteria are met, the fact that the conclusion is false does not under-

mine the argument’s rational persuasiveness for me. The situation would not change

if the proposition were actually true. Apart from (c), which is not relevant to this

case, the criteria for rational persuasiveness do not make reference to the actual truth

values of an argument’s conclusion.

Example

P1) Jeremy is a nine-year-old boy.

P2) Most nine-year-old boys like to play football.

C) Probably, Jeremy likes to play football.

I have good reason to believe that Jeremy likes to play football because I

frequently see him playing football, he has football posters in his bedroom,

reads football comics, and so on. In fact, the proposition is false. He doesn’t

really like to play; he just goes along with it to please his father, a very keen

football fan. The argument is inductively forceful and I have good reasons

to accept P1 and P2 – I know Jeremy and I have more than a passing

acquaintance with the likes and dislikes of nine-year-old boys – so criteria (a)

and (b) are met. I have no evidence that should lead me to reject C); that is,

answers and hints to selected exercises 289

I don’t know that Jeremy’s apparent football fervour is really a front to please

his dad, so the argument is not defeated for me. Thus it is rationally per-

suasive for me. If it turned out to be true that Jeremy likes to play football,

the argument would still be rationally persuasive for me.

answers and hints to selected exercises290

INDEX

absolute and relative difference 236–237

ad hominem fallacy 210–212, 238; ad

hominem circumstantial fallacy 211

afﬁrming the consequent: fallacy of 44,

202–203, 205, 238

ambiguity 28–30, 33, 47, 50, 266;

eliminating from an argument 138–141,

159; and generalisations 144; lexical

28–29, 31, 271; syntactic 29–30, 274

appeal to: compassion, pity or guilt 42–43,

50, 273; cuteness 43, 45, 50, 273; fear

44–45, 50, 273; novelty 41, 50, 273;

popularity 41–42, 50, 273; sexiness

43–44, 50, 273; wealth, status, power

44, 51, 273

appeal to authority: fallacy of 214–216,

238

appeal to ignorance: fallacy of 224–225,

238

argument: chain 73, 102, 138; contrasted

with explanation 20–22; contrasted

with rhetoric 6–7; deﬁnition of 9;

extended 15, 22–23, 63, 82, 104–105,

112–113, 121, 124, 269; practical

147–153; signiﬁcance of 4–6; see also

practical reasoning

argument assessment 56, 271; factual

113, 271; logical 113, 177, 271;

programme for 112–113

argument commentary 180, 185–187,

266; commentary on 195; example of

190, 193–195

argument reconstruction 13, 20, 24, 27,

56, 57, 89, 99, 119, 185, 238, 266, 267,

270; defusing rhetoric in 122–123;

elimination of extraneous material in

119–121; logical streamlining in

123–125; making premises explicit in

125–132; principle of charity in 127,

137, 143

argument tree 73–76, 266

assertoric form 244

base rate fallacy 104, 206–207, 238

begging the question 233–234

belief 176, 225, 226, 228, 238, 243, 244,

248, 249, 251, 254

buzzwords 45–46, 51, 273

coherentism 262

common practice: fallacy of 209–210,

238

conclusion 9, 12, 13, 14–17, 24, 56, 60,

98, 104, 121, 126, 171–172, 186–187,

203, 243, 259, 266

conditional 68–71, 81, 82, 120–121,

124, 125, 138, 158–159, 267, 271;

antecedent of 71–72, 82, 101, 120, 205,

238, 266; as conclusion 73, 177–180,

196; consequent of 71, 82, 101, 203,

238, 266; relation to generalisations

133–135, 159, 268

conditional probability see probability

conditionals as 73, 177–180, 196;

explanations as 153–155, 160;

generalisations as 177–180, 196;

implicit 17, 127, 159, 270; indicators

15–17, 24, 267; intermediate 22–23,

74, 119, 121, 124, 271; prescriptive

205, 206, 232, 238; probability in 105;

supposing to be false 180

conﬂation of morality with legality: fallacy

of 217–218, 238

connotation, primary/secondary 33–34,

45, 122, 123, 267

context 10, 14, 19, 24, 28–29, 30, 57, 58,

185, 186, 195, 245, 267

context relativity 244–247

correlation 157–158, 160; mistaking for

cause: fallacy of 220, 221–222, 224,

238

cost/beneﬁt 149–153, 160, 268; see also

expected value

counterexample 38, 39, 267; refutation

by 81, 82, 180–182, 196, 272

credibility 46, 212–213, 214, 268

deductively sound 77–78, 82, 112, 113,

131, 146, 170, 190, 238, 260; deﬁnition

of 77

deductive validity see validity

defeated argument 171–174, 176, 184,

186–187, 196, 243, 254, 260, 268;

deﬁnition of 171

denying the antecedent: fallacy of 205,

238

deriving ought from is: fallacy of

205–206, 232, 238

descriptive claims 67–68

direct attack 45, 51, 273

epistemic fallacy 225–228, 238,

254

epistemology 255 n. 7, 261

equivocation: fallacy of 229–230; trading

on an 47–8, 51, 273

evidence 105–07

expected value 151–153, 160, 182, 187,

268; see also cost/beneﬁt

explanation 225, 268–269; as conclusion

153–155, 160; contrasted with

argument 20–22, 24, 160

expressive epithets 122–123

extension 28, 31, 32, 33, 141, 269

extraneous material 19–20, 24, 119–121,

135–138

fallacies 40–41, 175, 186, 202–204,

237–238, 269, 272; formal 186, 202,

204–207, 237–238; substantive 186,

203, 207–228, 238

false dilemma 227 n. 7, 234–235,

239

faulty argument techniques 228–235

formal logic 78–81

foundationalism 261–262

generalisation 37–38, 50, 108–112, 114,

125, 130–132, 159, 160, 181, 208

258–259, 266, 269, 271; causal

156–158, 160, 266; as conclusion

177–180, 196; covering 133–135, 155,

159, 268; hard/soft 38–40, 50, 99, 144,

159, 269, 273; scope of 144–147, 159,

273; see also counterexample

Gettier cases 261 n. 10

hard sell 45, 51, 273

Implicature 10–11, 270; conversational

10, 96–97, 122; trading on 48–49

Indexical 244–247, 267

inductive inference 107–112, 113, 114,

134, 136, 137, 183, 259, 270; deﬁnition

of 109

inductively forceful 56, 90–91, 93–8,

100, 103, 104–105, 108, 112,

113–114, 127, 174, 175, 177, 186, 187,

index292

196, 225, 238, 260, 263, 270; deﬁnition

of 94

inductively sound 100, 112, 113, 114,

136, 143, 146, 170, 173, 186, 187,

196, 206, 254, 260, 270; deﬁnition of

100

inference 23, 63, 270

inference bar 13, 16, 270

inversion of cause and effect: fallacy of

220, 222–224, 238

irony 35, 50, 122

justiﬁcation 4, 21, 22, 46, 92 n. 3, 176,

253–259, 261, 264, 271; failure of

257–259; insufﬁciency of 257–258;

internal vs external 262–263; and

probability 263; see also knowledge

knowledge 186, 195, 225, 226, 228, 238,

255 n. 7, 256–257, 258, 260–261, 263,

264, 274; and belief 176, 243,

253–255, 264, 271; and justiﬁcation

257; and rational persuasiveness 196,

259–261, 264; tripartite account of

257, 260–261, 264, 274; and truth

256–257

labeling the position 184–185, 197

Leibniz’s Law 226

linguistic phenomena 15, 27–40, 50, 122

logic 60, 61, 66, 80–81, 82, 141 n. 3, 143,

271

logical streamlining 123–125, 138, 159

lottery problem 263

majority belief: fallacy of 42, 207–209,

238

margin of error 237

morality 40; and truth 251–252

perfectionist fallacy 216–217, 238

post hoc ergo propter hoc: fallacy of

220–221, 238

practical argument see practical reasoning

practical reasoning 147–153, 159–160,

271

premise 9, 12, 13, 14, 15, 17–19, 22, 23,

24, 56, 63, 64, 66, 72, 73–74, 76, 82,

91, 94, 97, 100, 111, 112, 113, 114,

119, 121, 138, 170, 171, 172, 173, 175,

176, 177, 178, 179, 180, 183, 186, 187,

196, 202, 203, 243, 254, 259–261, 262,

266, 269, 271, 272; conditional 73,

134–135, 158–159, 204, 205;

connecting 76, 132–133, 135, 137,

159, 267; implicit 57, 125–132, 159,

186, 202, 208, 233, 270; indicators

18–19, 24, 271–272; prescriptive 206

prescriptive claims 67–68

principle of charity 56–60, 82, 127, 137,

143, 185, 272

probability 91–8, 113–114, 150–153,

156, 160, 257, 267, 272; in conclusion

of an argument 105–107; degrees of

95–96; as frequency 92, 113; and

justiﬁcation 263; in premises of an

argument 100–104; as proportion 92,

113

proposition 9–12, 14–15, 17, 18, 19, 24,

28, 29, 34, 36, 56–57, 61–64, 82, 119,

125–126, 136, 140, 159–160, 243,

245–246, 266, 272, 273, 274; deﬁnition

of 9; stances toward a 254, 264, 274

propositional attitude 228

pseudo-reasoning; see also fallacy; rhetorical

ploy 40, 200–241

quantiﬁer 36–40, 50, 90, 92, 96, 99, 100,

125, 144, 159, 269, 272, 273

rational persuasiveness 169–176, 196,

254, 256, 264, 266, 272; deﬁnition of

172; and knowledge 259–261

red herring 49, 230–231, 238

relativity: context 244–245, 247; implicit

35–36, 122, 270; implicit speaker

244–246, 270; and truth 242, 243–247

relevance 135–138, 159, 272–273

index 293

representative see sample

rhetoric 6–7, 11, 23, 31, 36, 39, 119, 120,

131–132, 137, 141, 143, 174, 186, 193,

273; deﬁnition of 6, 40; defusing of

122–123, 159

rhetorical force 10, 24, 34, 273

rhetorical ploy 11, 28, 40–50, 175, 186,

204, 209, 216, 229, 230, 258, 273

rhetorical question 34–35, 50, 122, 123,

273

sample 107–112, 114, 270, 273

scare quotes 46–47, 51, 273

scepticism 263

slippery slope 204, 231–232, 238

smokescreen 49, 51, 100, 230, 273

soundness see deductively sound;

inductively sound

spin 50

standard form 12–13, 16, 17, 24, 56, 57,

81, 102, 112, 119, 177, 185, 186, 266,

274

straw man 232–233, 238

truth 5, 8, 9, 39, 56, 59, 60–62, 81,

94–96, 172, 203, 250, 264, 274;

deﬁnition of 8; and knowledge

256–257; and relativity 242, 243–250,

264

truth-value 61, 66, 76–78, 97, 113, 138,

186, 243, 244, 245, 247

tu quoque fallacy 213–214, 238

vagueness 31–33, 36, 37, 42, 47–48, 50,

122, 274; in arguments 138, 141–144,

159, 184, 186

validity 23, 56, 62–67, 72, 76–77,

78–9, 82, 91 n. 1, 95, 97, 112–114,

133, 170, 172–173, 175, 177,

178–179, 180, 186, 187, 196, 202,

204–206, 238, 259, 266, 268, 269,

270, 271, 273, 274; deﬁnition of

63–64; test for 66, 234

weak analogy: fallacy of 218–220, 238

‘who is to say?’ criticism 183–184, 186,

197

index294

Critical Thinking: A Concise Guide, 3rd Edition 33505 Thinking

Navigation menu

Versions of this User Manual:

Views

Navigation