A Primer on Knowledge -- Chapter One

A P R I M E R o n K N O W L E D G E

A d r i a n H e a t h c o t e

Dyer’s Hand Press

Dyer’s Hand Press

Sydney, Australia

© Adrian Heathcote mmxv

isbn 978-0-9758281-4-4

This book is typeset in Linotype Granjon

All rights reserved. No part of this publication may be reproduced,stored in a retrieval system, or transmitted , in any form, or by any

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The moral right of the author has been asserted

Contents

Preface xi

Chapter 1. Analysis of Knowledge 11. Global Scepticism 32. Is JTB sufficient for knowledge? 43. Certainty or Less? 84. A Useful Device 9

Chapter 2. Preliminaries on Truth 141. Nihilism 152. Relativism about Truth 173. Relativism: what has gone wrong? 194. Facts and Values 225. The Tolerance Defence 246. “Relative Truth” and Relativity 257. History and Truth 278. Supervenience of Truth on Being 299. Some Questions and Answers 31

Chapter 3. Descartes’ Rationalism 331. The Method 332. The Arguments for Doubt 363. The Missing French-Remainder Theorem 454. The Symmetry of Doubt 475. Possible Errors and Evidence of Errors 486. The True or the Certain 507. The Two Faces of Doubt 528. Markie on Descartes 53

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vi CONTENTS

9. An Afterword on Scepticism 56

Chapter 4. Hume and Knowledge of the Future 591. Hume’s Argument 602. The A Priori Horn 633. The A Posteriori Horn 654. Hume’s Naturalistic Solution 675. The Positivist Misinterpretation 706. Problems with Hume’s Dilemma 757. Problems for Hume’s Naturalistic Solution 848. Hume as an Inductive Probabilist 879. The Necessity of Induction 9010. Humean Islands 9211. Appendix: The Failure of Naturalism 93

Chapter 5. Empiricism and the External World 1001. Berkeley’s Argument 1002. Hume’s Argument 1093. Primary and Secondary Qualities 1144. The “Phenomenal World” 1175. Regress of Representations 1206. “Causal” Idealism 1257. Ending in Solipsism 126

Chapter 6. Obstacles to Knowledge 1281. Breakdown of the Terrain 1282. The Whorf-Sapir Thesis 1303. Colour Terms 1394. Some Whorfian Concessions 1485. Kuhnian Relativity 156

Chapter 7. Facts, Truth, and Knowledge 1591. Facts 1592. Frege on Truth 1663. The “Sling-Shot” Argument 1684. Deflationism 1755. Correspondence 182

CONTENTS vii

6. Mathematics, Morality and Beauty 187

Chapter 8. Fallible Knowledge 1941. Knowing that One Knows 1942. Certainty 2003. Internalism versus Externalism 2064. What is Justification? 208

Afterword 218

Bibliography 222

A Primer on Knowledge

Preface

The Concept of Knowledge

Adrian HeathcoteDepartment of Traditional & Modern Philosophy

The University of Sydney

P r e f a c e

How do we manage to know the things we know? What is it about some of our beliefs that allows them, and not others, to qualify as knowledge? Or do we, when we examine the matter closely, find that we really know nothing at all? These are fundamental questions, so fundamental that some answer to each of them is required before

we can proceed with any particular enquiry. The ¤udent of history, anthropology, or English literature, no less than the physicist or the biologist, needs to know whether it is possible for us to know anything, and, if so, how we might best try to acquire that knowledge. A legal system needs to know the conditions under which a person could reasonably be said to be known to be guilty of some crime. An engineer needs to know the conditions under which a bridge will collapse. The concept of knowledge is such an important part of our intellectual tradition that it is hard to see how we could say what we often want to say without it. How would we fare, for example, if we could not say that we now know that cholera is caused by a strain of bacteria; that the sun is one ¤ar among many; that Pope translated the Illiad? But for all the importance that the concept of knowledge undoubtedly has, we cannot take that alone to settle the matter of whether we actually know anything. For all that we know the doubters may be right and there be no such thing as knowledge. Our intellectual tradition may rest on an illusion of which we would do well to be rid. Many might feel that we are already in that position, and thus that we are already in possession of the arguments that will free us from thralldom to an invidious distinction between opinion and knowledge. On this view, yes, we might believe that the sun is one star among many, but we don’t really know it; we don’t really know that Pope translated the Illiad, that is merely one possible story among many that we tell ourselves. On this view there is only belief, with knowledge in any strong sense being an impossible ideal. It involves conditions that we can never satisfy, or, perhaps more

ow do we manage to know the things we know?What is it about some of our beliefs that allowsthem, and not others, to qualify as knowledge? Ordo we, when we examine the matter closely, findthat we really know nothing at all? These are fun-damental questions, so fundamental that some an-

swer to each of them is required before we can proceed with any par-ticular enquiry. The student of history, anthropology, or English liter-ature, no less than the physicist or the biologist, needs to know whetherit is possible for us to know anything, and, if so, how we might best tryto acquire that knowledge. A legal system needs to know the condi-tions under which a person could reasonably be said to be known tobe guilty of some crime. An engineer needs to know the conditionsunder which a bridge will collapse. The concept of knowledge is suchan important part of our intellectual tradition that it is hard to see howwe could say what we often want to say without it. How would wefare, for example, if we could not say that we now know that cholerais caused by a strain of bacteria; that the sun is one star among many;that Pope translated the Iliad?

But for all the importance that the concept of knowledge undoubt-edly has, we cannot take that alone to settle the matter of whether weactually know anything. For all that we know the doubters may beright and there be no such thing as knowledge; our intellectual tradi-tion may rest on an illusion which we would do well to rid ourselves.Many might feel that we are already in that position, and thus that weare already in possession of the arguments that will free us from thral-dom to an invidious distinction between opinion and knowledge. On

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this view, yes, we might believe that the sun is one star among many,but we don’t really know it; we don’t really know that Pope translatedthe Iliad, that is merely one possible story among many that we tellourselves. On this view there is only belief, with knowledge in anystrong sense being an impossible ideal. It involves conditions that wecan never satisfy, or, perhaps more weakly, can never know that wesatisfy.

My own view, and I think that it would be the view of the majorityof philosophers, is that this would be a mistaken conclusion. In thesechapters I aim to give an answer to the question what is knowledge? ananswer that meets some of the most common objections, and tries toclarify the concept of knowledge and free it of some common confu-sions and misunderstandings. But I will attempt to address not onlythose questions that are of interest to academic philosophers, but alsothose that are of interest to students and academic non-philosophers. Iam convinced that the two types of concern are not identical and thatthe needs of the latter group have now become so pressing that it is thelit taper of a genuine crisis in our attempt to think rationally about theworld.

And, without wishing to be portentous, we would do well to re-member one of the important lessons of history: that on such seem-ingly abstract matters as rationality, very ordinary human happinessoften depends.

Thus, this book has a different focus to standard books in episte-mology. Most books — whatever their authors say in prefaces likethis this one — are not really addressed to an educated general reader.Rather they are addressed to their learned colleagues in philosophy de-partments around the world. Their concerns are abstruse and techni-cal, and most students have no idea why they are discussing the issuesthey are discussing — for whereas the professor sees an interesting is-sue at point X, the student thinks that there are pressing problems longbefore one ever gets to X. I think (hope?) this is not that kind of book.Where I become involved in abstruse matters I trust that the readerwill be able to see why, and what the issues are. And if not, then youmay at least be assured that they will not last for long. Basic questions

PREFACE xiii

will be our main concern, and we will be continually pulled back tothem — as if by a philosophical force of gravity. Fly low, will be ourwatchword — which I hope you will find, is not incompatible with: flydeep.

CHAPTER 1

Analysis of Knowledge

We ordinarily take ourselves — that is, before we allow our-selves to be convinced otherwise by exotic philosophical ar-guments — to know many things. At the very least we

take ourselves to know our own names and where we live. But wealso, usually, take ourselves to know very much more than this. Andif we want to know what we mean when we say we know something,a reasonable procedure would seem to be to list the various things wetake ourselves to know and try to extract the commonalities from theelements of the list. Let us try this approach and see how far we canget. Here is a list of just some things that I hope the reader will agreethat we both know. (Again, I stress that this agreement is prior to beingaffected by philosophical arguments that might lead us to doubt someor all of the items on the list. I am appealing to our pre-philosophicalsense of things.)

∙ Some people are more than three feet tall.∙ Australia is in the Southern Hemisphere.∙ Water is H2O.∙ Two apples plus two apples makes four apples.∙ If a cat is black then it is black.∙ The Battle of Hastings was in 1066.∙ 32 = 9.∙ Any bacterium is smaller than any Volkswagen.

All of these are propositions that I am reasonably sure that we wouldagree that we know — and if they sound rather trivial that is just toensure that we will agree that we know them. We might hesitate oversome items, and we might innocently cavil over some others (might

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2 1. ANALYSIS OF KNOWLEDGE

there not be a bacterium somewhere in the Universe that is larger thanany small German car?) but I think the list can stand.

Yet the striking thing about the members of the list is what a het-erogeneous bunch they are. There was method in this: we have madethe list heterogeneous to ensure that we do not inadvertently simplifyour resulting account of knowledge. So what account of knowledge dowe end up with if we try to abstract the commonalities from this ratherdisparate group of elements? Plato gave an answer to this question inthe 4th Century bc that is still accepted today. Knowledge, he said, wasjustified, true, belief — or, expressed as an equation K(A) = JTB(A),where A stands for any arbitrary proposition. If one checks back overthe list one finds that it accords well with the Platonic account: all ofthe items on the list look to be examples of justified, true, beliefs. (Ah!you say, but how do we know that they are true? Well, that is what thejustifications are for! To know A is to know that A is true.)

Philosophers now call accounts of knowledge like Plato’s conceptualanalyses of knowledge. In general, a conceptual analysis takes a commonconcept and attempts to understand the conditions under which it isused. It breaks the concept into its constituent components and showshow it is the obtaining of these constituent component conditions thatdetermines whether we would say that a particular item — in the cur-rent case a statement, a belief, or a proposition — does or does not fallunder the concept. So in the above case we would say that we believethat we know each of the above propositions, and we also believe thateach is a case of a justified, true, belief. We conclude that when we saywe know something we just mean that we have a justified true belief.

But the mere fact that we have an analysis of the concept of knowl-edge does not by itself mean that we really know anything. A concep-tual analysis tells us how we apply concepts, it does not, and cannot, tellus that there is something that genuinely answers to the concept. Weare, for example, in possession of a perfectly good analysis of the con-cept of a unicorn — it is a horned horse — but that, by itself, does notmean that there are any unicorns. Just so, there may be no knowledgeat all even though we are perfectly able to use the concept to speak ofthose things we think we know. For all that the above discussion tellsus there may be an argument to the conclusion that even though our

1. GLOBAL SCEPTICISM 3

concept of knowledge is exactly as Plato suggested, that neverthelessthere is no knowledge at all. Just as, in fact, there are no unicorns.

1. Global Scepticism

In fact there is such an argument — one that is almost as old asPlato’s analysis itself. It is called the Regress of Reasons Argument.

The argument runs as follows. Suppose that there were to be some-thing that we know — call it A. Then according to the analysis Awould have to be a justified true belief. But if it is a justified true beliefthen there would have to be some proposition that provides A with itsjustification: call it B. But now B must be known as well, for if it is notknown then we would not be in possession of the justification (B mightjustify A but it would not be a justification that we have.) But if B isknown then there has to be some proposition C that acts as its justifica-tion — but then C will have to be known as well. And so on, for someD, some E, some F, and on ad infinitum. Therefore, in order to knowanything we would have to know an infinite number of things. Butsince we can’t know an infinite number of things — our brains, afterall, are only finite — then we can’t know anything at all. (The reasonthat we may draw this conclusion is that since our supposition that weknow at least one thing leads to the falsehood that we know an infinitenumber of things, that original supposition must have been false. Thelogic here is that only the false implies the false — an impeccable pieceof logic by the way.) Thus we can’t know anything at all. This is theRegress of Reasons Argument. The conclusion of the argument, thatnothing can be known is called global scepticism — i.e. it is scepticismabout everything.

What should we make of this argument, so striking in its simplic-ity?

Well, first we may note that it does not involve the truth compo-nent of the definition. The argument would work even against the lessdemanding concept of justified belief. So it is obviously a very power-ful (in the sense of far reaching) argument. Secondly, the structure ofjustifications does look plausibly like an infinite regress. (We cannotimagine the justifications going round in a circle without A ultimatelybeing the reason for believing itself. But since a circular justification is


no justification at all and since an infinite regress involves a quantitythat goes beyond our capacity, the problem does seem genuine.)

But even though the argument looks persuasive at first blush, it isalso very peculiar. For note that it actually purports to be a proof ofthe claim that nothing can be known. But if we have really proven thatnothing can be known then we now seem to be in a position to say thatwe know that nothing can be known. Yet if we know that nothing canbe known then something is known after all, namely that! So if wewere to think that the regress of reasons argument proved that nothingcan be known then we would have to accept that its conclusion is nowknown and we would have a contradiction. Something has gone verywrong! But what? The regress argument certainly looked convincing,but now we see that it leads to an absurd conclusion. In fact, the moreconvincing the argument the more we cannot accept its conclusion.

We seem to have arrived at a position that is bizarre and near para-doxical. Still, philosophers love challenging problems — they are theirmeat and drink. We can solve this one by noting that the regress ofreasons argument must be a misleading argument for its conclusionbecause the more convinced we are by the argument the more it is im-possible for the conclusion to be true. So how is the argument mislead-ing? We will answer this question when we have gone much furtheralong in our study, when we have more tools at our disposal. For themoment we leave it as a mystery for the reader to ponder.

2. Is JTB sufficient for knowledge?

Our previous discussion of Plato’s account of knowledge is incon-clusive on one important point. It does not tell us whether to knowsomething might require more than simply having a justified true be-lief. In the philosophical jargon, the existence of a justified true beliefmay be necessary for knowledge, but may not be sufficient. Our nextquestion, therefore, is whether JTB is sufficient for knowledge.

In 1963 a philosopher named Edmund Gettier published a now fa-mous paper which purported to show that it could not be. He gavewhat are called counterexamples to the thesis that justified true be-lief is sufficient for knowledge — in fact two of them. Here is thefirst counterexample. Smith and Jones have applied for the same job.

2. IS JTB SUFFICIENT FOR KNOWLEDGE? 5

Smith has (non-conclusive) evidence for the conjunctive proposition:

(d) Jones will get the job, and Jones has ten coins in his pocket.

Smith’s evidence for (d) is that he has been told by someone who shouldknow that Jones is going to get the job and (by some method best notenquired into) he has counted the coins in Jones’ pocket only a fewminutes ago. This is not conclusive evidence for (d) but it is still evi-dence, sufficient to justify belief. Proposition (d) logically entails (e):

(e) The person who will get the job has ten coins in his pocket.

Smith sees that (d) entails (e) and accepts (e) on the basis of (d). Theevidence for (d) is thus transmitted to (e); Smith therefore has goodreason to believe that (e) is true.

It will turn out, however, that he, Smith, will actually get the job,and also that he himself — all unknown to himself — has ten coinsin his pocket. (e) is then true though the proposition (d) from which itwas inferred is false. So (e) is true, Smith has good reason to believe (e)and does in fact believe it. But Smith couldn’t really be said to know(e) because what makes (e) true is the fact that he will get the job andthe number of coins in his pocket, and he is ignorant of both of thesethings. Smith’s belief in (e) is based on the false, but well-supported,belief that Jones will get the job.

So, Gettier concludes, since someone could have a justified true be-lief but not have knowledge, having knowledge must require the sat-isfaction of some extra condition over and above having a justified truebelief.

Should we agree with this assessment? I think we shouldn’t. Theproposition that Smith believes — that the person who will get thejob has ten coins in his pocket — is ambiguous, and it is on this am-biguity that the example depends. If we ask ourselves whom Smithmeans when he is believing this proposition, the answer is obvious: hemeans Jones. For sentences, philosophers of language would call thisthe speaker meaning. If, however, we ask ourselves who the referringexpression (“the person who will get the job. . . ”) objectively picks out— who it is in fact true of — then the answer is that it picks out Smith,


not Jones. We could call this the objective referent meaning. Now usu-ally the speaker meaning and the objective referent meaning coincide— but here they have come apart. Now if we consider the speakermeaning interpretation of (e) we see that it turns out to be a justifiedbut false belief. On the other hand, if we consider the objective refer-ent meaning then we have a true belief but one that is unjustified. Sowhen we disambiguate (e) we either get a justified false belief or weget an unjustified true belief — but in neither case do we get a jus-tified true belief. The example does not show therefore that justifiedtrue belief is insufficient for knowledge; it’s just a case where we donot have knowledge because we don’t have a justified true belief in thefirst place.

Still, as I said, Gettier gave two counterexamples, and we have onlyconsidered the first of them. Perhaps the next one fares better. Here itis.

Smith — for once again it is he — has strong evidence for proposi-tion (f):

(f) Jones owns a Ford.

Smith’s evidence — which we will not rehearse — is strong thoughnon-conclusive. Quite separate from this, Smith has a friend, namedBrown, of whose whereabouts Smith is completely ignorant. Smithrandomly chooses three place names: Boston, Barcelona, and Brest-Litovsk. He then formulates the following three propositions:

(g) Either Jones owns a Ford, or Brown is in Boston;

(h) Either Jones owns a Ford, or Brown is in Barcelona;

(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Each of these propositions is logically entailed by (f) — a fact thatSmith is well aware of. The meaning of the ‘either. . . or’ expressionhere is what logicians call inclusive disjunction; the compound is true ifeither or both the disjuncts is true. Since Smith was justified in accept-ing (f) he is also justified in accepting (g), (h), and (i) — despite the fact

2. IS JTB SUFFICIENT FOR KNOWLEDGE? 7

that in each case he has no reason to believe that the second disjunct istrue.

As it turns out, however, (f) is false — Jones does not own a Ford— but Brown is in Barcelona. Therefore, (h) is a justified true belief,but says Gettier, Smith does not know that (h) is true. So again, saysGettier, justified true belief is not sufficient for knowledge.

Note that in both of these counterexamples Gettier gives no reasonfor his judgement that Smith does not have knowledge — he merelysays that it is obvious. One response that we could make to these caseswould be simply to say that Gettier is mistaken: Smith does know. (Iam setting aside my response to the first of them, just for the sake ofthis point.) The cases are strange and our intuitions are unpreparedfor them, but Smith does know. Or at least, Gettier has to say morethan that it is obvious that he doesn’t.

Could we not, however, say more than this? Suppose that we wereto share Gettier’s intuition that Smith does not know (h) — as in fact Ido. Couldn’t we use the examples themselves to tell us what is missingfrom our account of knowledge? Surely we could. For if we exam-ine what seems to have gone wrong in the case it is that Smith has noevidence (to support his belief in (h)) of the circumstance that makes(h) true. We could amend our definition of knowledge to include thiscondition.

The K-conditions. X knows A iffdef X believes A ; X is justified inbelieving A ; A is true; and the evidence that X has which constitutesthe justification is evidence of the very state of affairs that makes Atrue.1

For this to work, however, we must unpack the idea of evidencebeing evidence of a state of affairs. Let us take it to mean this:

1In effect this is a truthmaker solution to the Gettier problem — but that maynot mean a lot until we describe truthmaking in chapter 7. For the full developmentof this idea see Heathcote (2006), (2012), (2014) and (2015). The abbreviation ‘iffdef’means ‘if and only if, by definition’. It is a way of stating the necessary and sufficientconditions for satisfying the definition.


E is evidence of a state of affairs s iffdef E is a part of s and sonecessarily if s obtains then E , as a part of s , obtains.

Not only will this solve both the counterexamples that Gettier has given,it will also solve the other Gettier counterexamples that I am aware of.Thus, take this case: we see what we think is a sheep in a field and weform the belief that there is a sheep in the field (A ). But what we sawwas not a sheep but a cardboard prop. However behind a rock, wherewe can’t see it, there is in fact a sheep. So our belief is true, and madetrue by the sheep that we can’t see, though it is the prop sheep thatprovides the justification for the belief. In this case it is plain that theprop sheep, which is our evidence, is not evidence of the circumstancethat makes A true.

Mostly, however, it is unnecessary to add this extra condition explic-itly, because the kinds of situations that constitute the Gettier coun-terexamples are a bit like elements in the periodic table higher thanUranium: they are not often found in nature but have to be formed inthe nuclear reactor of bizarre philosophical imaginings. Henceforth,unless stated otherwise, we will ignore them and the extra condition— or rather, we will just silently pack the extra condition into the no-tion of justification.

3. Certainty or Less?

While we are wondering how the concept of knowledge is used, wemight also wonder about the notion of justification. When we say thatsomeone knows some proposition — say that mice are mammals —does that mean that they know it with absolute certainty, in the sensethat it is not possible for them to be in error; or do we mean that theyhave strong reason to believe it, even though the reason might be in-conclusive? On the side of the first view, we do sometimes press peoplewho claim to know something and, if we find even the slightest occa-sion for doubt, pronounce that they do not really know after all. On theside of the other view, we do often think that we know things wherethe basis for the belief is inconclusive. As we’ve just seen, such non-conclusive beliefs lie at the heart of the Gettier counterexamples. We

4. A USEFUL DEVICE 9

even have quite a few of them in our list on p. 1. The view of knowl-edge that allows non-conclusive justifications is called fallibilism.

This is a matter that cannot, I think, easily be solved by conceptualanalysis. The concept of knowledge is used in both ways and we can-not settle it just by seeing whether we do or do not require the stricterstandard when confronted with examples. Instead we will have to tryto investigate the way each view might work, and see what seems right.In fact, we will see in ch. 3 that requiring certainty would have direconsequences for the applicability of the concept of knowledge.

There is one aspect of this difference that is worth noting now,however. If we think that knowledge requires certainty we do notneed to put in, as a separate condition, that the belief is also true. Thatis because when we say that someone is certain about a matter we arealready implying that it is true (if it is not possible for the belief to befalse then it must be true). In short, it would not be possible to have a(conclusively) justified false belief.

But if we allow non-conclusive justifications then someone couldhave a justified false belief — in fact Smith had at least two in the lastsection: they were (d) and (f). Because of this, if we allow that someonecan have knowledge when the reasons are non-conclusive, we mustadd in the fact that the belief must be true as a separate condition.Not to prejudge matters we have done just this, above. (It is worthpointing out, however, so that there is no danger of misunderstanding,that someone who embraces the certainty view has not escaped thenotion of truth — it is just silently included in the view.)

In the next chapter we will discuss the notion of truth — with thehope that we can dispel some of the strange misunderstandings andconfusions that now attend the concept.

4. A Useful Device

We are going to introduce a very useful way to graphically rep-resent the justification component of belief: it is an analog of a ther-mometer for measuring temperature. It measures how much justifica-tion a person has for a particular belief. Thus suppose the propositionis that there is going to be rain tomorrow. I may have no evidence ei-ther way — no reason to believe that it will, and none to believe that it


won’t. We may call that indifference. (Note: indifference doesn’t meanthat I don’t care whether it rains, it just means I don’t know eitherway whether it will. We may also call it being agnostic.) But suppose Ihave good reason to believe that it will rain tomorrow. (I’ve seen theweather forecast, and I know from past experience that those peopleare usually pretty accurate, at least for the next day.) Then my justifi-cation is higher than indifference. How high is it? Well it doesn’t seemto be maximal. For example I also know that those weather forecast-ers sometimes make mistakes; maybe they’ve made a mistake on thisoccasion as well. So it is somewhere between indifference and maxi-mality.

Now the idea is that every proposition that we consider can bemeasured in this way. To use the analogy with a thermometer, everyproposition, for every person, has a “temperature”.

Many propositions will, it is true, be at the half-way point: indif-ference. That is because there are many things that I have no reasonto believe or disbelieve. It will be the same with you. But other propo-sitions will be at different points on the scale. I can even compare therelative positions of these propositions. Thus: I have more reason tobelieve that it will rain tomorrow than that I will win the lottery thisyear. And I can compare the two of us: you may know much moreabout the weather than I do — your degree of belief that it will raintomorrow may be much higher than mine.

We need a name for this device. I would suggest ‘credometer’, be-cause in technical terms what the device is measuring are credences:degrees of the confidence of a belief. But I fear that the name is notsufficiently descriptive and will not stick in the reader’s mind. So Iwill call it a belief-o-meter.

Now it is useful to make the scale between 0 and 1. This is whatmathematician’s call ‘normalising.’ And as they also say, it is some-thing we can do ‘without loss of generality.’ So the number that at-taches to indifference is ½ , while maximal justification is 1 and min-imal justification is zero. But now that we have the numbers we cansay more precisely what our device is measuring.

Firstly, it is measuring the average, or the resultant, of my totalevidence for a belief. Suppose I have a very strong reason to believe


a proposition, but also an equally strong reason to disbelieve it, thenthese cancel out to indifference. (Note that in practise it is very unlikelythat you would get such a precise cancellation — the more normalthing is to try to resolve that kind of conflict one way or another, bylooking for more evidence)

Secondly, the belief-o-meter is for the belief of one person at a time— just as a thermometer is for one place at a time. So there is onefor me, and one for you. Of course we can compare our different mea-sures. Thus you can say that you now have a high justification for yourbelief that the Battle of Agincourt was in 1415 (you’ve just done thepainstaking research) whereas I may have no idea. I can even borrowyour evidence by having you tell me about your research, thus makingmy degree of belief go up. But the important thing is that our differentbelief-o-meters are measuring different things: our different degreesof belief.

Thirdly, all the things I have good reason to believe are in the tophalf of the belief-o-meter, and all the things that I have reason to disbe-lieve are in the bottom half. So we can describe the difference betweenthe two accounts discussed in the previous section now very simply: onthe certainty account of knowledge (where knowledge requires cer-tainty) I will only know some proposition p if I have a maximallyjustified true belief — only those beliefs that have the justification of 1could be said to be known.

The alternative view, the fallibilist view, is a little more complicated.The simplest version would say that my justification for the belief pmust be greater than one half — and then, if it is true, I have knowl-edge. But that seems too weak. So I will say that the justification mustbe “high” without being specific here as to exactly how high. Sufficeit to say that it can be — and is — a perfectly objective matter whenjustification is “enough” despite the increase of justification being acontinuous matter with no sudden jumps. (I return to this briefly atthe end of the book on p. 216.) And it often makes perfect sense toask of someone who claims to know p whether they really know it —i.e. whether they have really met the standards that are appropriate toa particular question or issue. The uncertainty — if that is really thecorrect term here — is a natural part of our usage of the concept of


knowledge. But, though we require the justification to be high if it isto count as knowledge, we do not ever require it to be maximal, withmeasure 1 — i.e. we do not ever require it to be certain — for this is alimit only.

What this means in ordinary terms is that if I have good reasonto believe p and p is true then I know p . That is the basic ideaof fallibilism. To this we add the “fourth condition”, namely thatthe evidence for the belief be evidence of the very state of affairs thatmakes the belief true. And there we have our analysis of the conceptof knowledge — the one we will be working with in this book.

It will turn out that almost all of the views that we describe in thisbook can be put very simply in terms of the belief-o-meter. This isbecause most of the classical discussions of knowledge have involveddisagreements about what beliefs are justified, and how. So as we goon we will describe the different positions in terms of what they implyabout the measures of beliefs on the belief-o-meter.

When I first conceived of this little device I thought it was novel, ifnot patentable. But I was wrong — it is not even novel. It was antici-pated by Morgan William Crofton in 1885, in an article called ‘Proba-bility’ for the 9th edition of the Encyclopædia Britannica — which manypeople regard as the greatest encyclopædia ever written; greater eventhan the more famous 11th edition. Crofton — a wonderful mathe-matician of the time, who specialised in the area of geometric prob-ability — called this measure of degrees of belief, a ‘thermometricalscale’. (It might have been nice to have called it an “alethiometer”,but alas that name is now taken also, in Philip Pullman’s wonderfulnovels.)

We will be particularly on the lookout for views that vacillate be-tween the certainty and the fallibilist view. But as we go on we willalso refine our view of how the device works. We will then come backto it in chapter 8 and tie up some loose ends.2

2There is one issue which cannot be represented along this dimension, and thatis the question of whether the justifications should be understood as objective or sub-jective. This is the, awkwardly named, externalism–internalism issue. We will cometo this issue also in chapter 8 §3.


Figure 1. A belief-o-meter marked with the impor-tant points for the measure of belief. One might bet-ter call indifference ‘agnosticism’.

A Primer on Knowledge -- Chapter One

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