concept of knowledge

7/29/2019 Concept of Knowledge

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The Concept of Knowledge Adrian Heathcote

Department of Traditional & Modern PhilosophyThe University of Sydney

Preface

How do we manage to know the things we know? What is it about someof our beliefs that allows them, and not others, to qualify as knowledge?Or do we, when we examine the matter closely, nd that we really knownothing at all? These are fundamental questions, so fundamental thatsome answer to each of them is required before we can proceed with anyparticular enquiry. The student of history, anthropology, or English lit-erature, 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 try toacquire that knowledge. A legal system needs to know the conditions

under which a person could reasonably be said to be known to be guiltyof some crime. An engineer needs to know the conditions under which abridge will collapse. The concept of knowledge is such an important partof our intellectual tradition that it is hard to see how we could say whatwe often want to say without it. How would we fare, for example, if wecould not say that we now know that cholera is caused by a strain of bac-teria; that the sun is one star among many; that Pope translated the Illiad?

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 be rightand there be no such thing as knowledge. Our intellectual tradition mayrest on an illusion of which we would do well to be rid. Many might feelthat we are already in that position, and thus that we are already in pos-session of the arguments that will free us from thralldom to an invidiousdistinction between opinion and knowledge. On this view, yes, we mightbelieve that the sun is one star among many, but we dont really know it;we dont really know that Pope translated the Illiadthat is merely onepossible story among many that we tell ourselves. On this view there is


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only belief, with knowledge in any strong sense being an impossible ideal.It involves conditions that we can never satisfy, or can never know thatwe satisfy.

My own viewand I think that it would be the view of the majori-ty of philosophersis that this would be a mistaken conclusion. In thesenotes I aim to give an answer to the question what is knowledge?ananswer that meets some of the most common objections, and tries to clar-ify the concept of knowledge and free it of some common confusions andmisunderstandings. But I will attempt to address not only those questionsthat are of interest to academic philosophers, but also those that are of interest to students and academic non-philosophers. I am convinced thatthe two types of concern are not identical and that the latter need has nowbecome so pressing that it is the lit taper of a genuine crisis in our ration-al thinking about the world.

Andwithout wishing to be too portentouswe would do well toremember one of the important lessons of history: that on such seeming-ly abstract matters as rationality, very ordinary human happiness oftendepends.

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Chapter 1. Analysis of the Concept

we ordinarily take ourselvesthat is, before we allow our-selves to be convinced otherwise by exotic philosophicalargumentsto know many things. At the very least we

take ourselves to know our own names and where we live. But we also,usually, take ourselves to know very much more than this. And if wewant to know what we mean when we say we know something, a rea-sonable procedure would seem to be to list the various things we takeourselves to know and try to extract the commonalities from the elementsof the list. Let us try this approach and see how far we can get. Here is alist of just some things that I hope the reader will agree that we bothknow. (Again, I stress that this agreement is prior to being affected byphilosophical arguments that might lead us to doubt some or all of theitems in the list. I am appealing to our pre-philosophical sense of things.)

Some people are more than three feet tall. Australia is in the Southern Hemisphere. Water is H 2O. Two apples plus two apples makes four apples. If a cat is black then it is black. The battle of Hastings was in 1066. 3 2=9. Any bacterium is smaller than any Volkswagen.

All of these are propositions that I am reasonably sure that we wouldagree that we knowand if they sound rather trivial that is just to ensurethat we will agree that we know them. We might hesitate over someitems, and we might innocently cavil over some others (might there notbe a bacterium somewhere in the Universe that is larger than any smallGerman car?) but I think the list can stand.

Yet the striking thing about the members of the list is what a hetero-geneous bunch they are. There was method in this: we have made the listheterogeneous to ensure that we do not inadvertently simplify our result-

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ing account of knowledge. So what account of knowledge do we end upwith if we try to abstract the commonalities from this rather disparategroup of elements? Plato gave an answer to this question in the 4 th

Century bc that is still accepted today. Knowledge, he said, was justied,true, beliefor, expressed as an equation K(A) = JTB(A), where Astands for any arbitrary proposition. If one checks back over the list onends that it accords well with the Platonic account: all of the items on thelist look to be examples of justied true beliefs. (Ah! you say, but how dowe know that they are true? We will answer that question in due courseand at unseemly length.)

Philosophers now call accounts of knowledge like Platos conceptual analyses of knowledge.In general, a conceptual analysis takes a commonconcept and attempts to understand the conditions under which it is used.It breaks the concept into its constituent components and shows how it isthe obtaining of these constituent component conditions that determineswhether we would say that a particular itemin the current case a state-ment, a belief, or a propositiondoes or does not fall under the concept.So in the above case we would say that we believe that we know each of the above propositions, and we also believe that each is a case of a justied,

true, belief. We conclude that when we say we know something we justmean that we have a justied 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 conceptualanalysis tells us how we apply concepts, it does not, and cannot, tell usthat there is something that genuinely answers to the concept. We are, forexample, in possession of a perfectly good analysis of the concept of a uni-cornit is a horned horsebut that, by itself, does not mean that thereare any unicorns. Just so, there may be no knowledge at all even thoughwe are perfectly able to use the concept to speak of those things we thinkwe know. For all that the above discussion tells us there may be an argu-ment to the conclusion that even though our concept of knowledge isexactly as Plato suggested, that nevertheless there is no knowledge at all.

Just as, in fact, there are no unicorns.

1.1 Global Scepticism

In fact there is such an argumentone that is almost as old as Platosanalysis 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 A would

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have to be a justied true belief. But if it is a justied true belief thenthere would have to be some proposition that provides A with itsjusticationcall it B. But now B must be known as well, for if it is notknown then we would not be in possession of the justication (B mightjustify A but it would not be a justication that we have.) But if B isknown then there has to be some proposition C that acts as itsjusticationbut then C will have to be known as well. And so on, forsome D, some E, some F, and on ad innitum . Therefore, in order toknow anything we would have to know an innite number of things. Butsince we cant know an innite number of thingsour brains, after allare only nitethen we cant know anything at all. (The reason that wemay draw this conclusion is that since our supposition that we know atleast one thing leads to the falsehood that we know an innite number of things, that original supposition must have been false. The logic here isthat only the false implies the falsean impeccable piece of logic by theway.) Thus we cant know anything at all. This is the Regress of Reasons

Argument . The conclusion of the argument, that nothing can be known iscalled global scepticismi.e. it is scepticism about everything.

What should we make of this argument, so striking in its simplicity?Well, rst we may note that it does not involve the truth component

of the denition. The argument would work even against the less

demanding concept of justied belief. So it is obviously a very powerful(in the sense of far reaching) argument. Secondly, the structure of justications does look plausibly like an innite regress. (We cannotimagine the justications going round in a circle without A ultimatelybeing the reason for believing itself. But since a circular justication is nojustication at all and since an innite regress involves a quantity thatgoes beyond our capacity, the problem does seemgenuine.

But even though the argument looks persuasive at rst blush, it isalso very peculiar. For note that it actually purports to be a proof of theclaim that nothing can be known . But if we have really proven that noth-ing can be known then we now seem to be in a position to say that we

know that nothing can be known. Yet if we know that nothing can beknown then something is known after all, namely that! So if we were tothink that the regress of reasons argument proved that nothing can beknown then we would have to accept that its conclusion is now knownand we would have a contradiction. Something has gone very wrong! Butwhat? The regress argument certainly looked convincing, but now wesee that it leads to an absurd conclusion. In fact the more convincing theargument is the more we cannot accept its conclusion. (Still, this in itself

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tells us something very interesting: it could only be true that nothing isknown if we never have reason to believe it!)

We seem to have arrived at a position that is bizarre and near para-doxical. Still, philosophers love challenging problemsthey are theirmeat and drink. We can solve this one by noting that the regress of rea-sons argument must be a misleading argument for its conclusion becausethe more convinced we are by the argument the more it is impossible forthe conclusion to be true. So how is the argument misleading? We willanswer this question when we have gone much further along in ourstudy, when we have more tools at our disposal. For the moment we leaveit as a mystery for the reader to ponder.

1.2 Is JTB sufcient for knowledge?

Our previous discussion of Platos account of knowledge is inconclusiveon one important point. It does not tell us whether to know somethingmight require more than simply having a justied true belief. In thephilosophical jargon, the existence of a justied true belief may be neces-sary for knowledge, but may not be sufcient. Our next question, there-fore, is whether JTB is sufcient for knowledge.

In 1963 a philosopher named Edmund Gettier published a nowfamous paper which purported to show that it could not be. He gave

what are called counterexamples to the thesis that justied true belief issufcient for knowledgein fact two of them. Here is the rst coun-terexample. Smith and Jones have applied for the same job. Smith has(non-conclusive) evidence for the conjunctive proposition:

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

Smiths 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 few min-utes ago. This is not conclusive evidence for (d) but it is still evidence,sufcient 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). The evi-dence for (d) is thus transmitted to (e); Smith therefore has good reason tobelieve that (e) is true.

It will turn out, however, that he, Smith, will actually get the job,and also that he himselfall unknown to himselfhas ten coins in hispocket. (e) is then true though the proposition (d) from which it was

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inferred is false. So (e) is true, Smith has good reason to believe (e) anddoes in fact believe it. But Smith couldnt really be said to know (e)because what makes (e) true is the fact that he will get the job and thenumber of coins in his pocket, and he is ignorant of both of these things.Smiths belief in (e) is based on the false, but well-supported, belief thatJones will get the job.

So, Gettier concludes, since someone could have a justied true belief but not have knowledge, having knowledge must require the satisfactionof some extra condition over and above having a justied true belief.

Should we agree with this assessment? I think we shouldnt. Theproposition that Smith believesthat the person who will get the job hasten coins in his pocketis ambiguous, and it is on this ambiguity that theexample depends. If we ask ourselves whom Smith means when he isbelieving this proposition, the answer is obvious: he means Jones. Forsentences, philosophers of language would call this the speaker meaning.If, however, we ask ourselves who the referring expression (the personwho will get the job) objectively picks outwho it is in fact true ofthen the answer is that it picks out Smith, not Jones. We could call thisthe objective referent meaning. Now usually the speaker meaning and theobjective referent meaning coincidebut here they have come apart.Now if we consider the speaker meaning interpretation of (e) we see that

it turns out to be a justied but false belief. On the other hand, if we con-sider the objective referent meaning then we have a true belief but onethat is unjustied. So when we disambiguate (e) we either get a justiedfalse belief or we get an unjustied true beliefbut in neither case do weget a justied true belief. The example does not show therefore thatjustied true belief is insufcient for knowledge; its just a case where wedo not have knowledge because we dont have a justied true belief in therst place.

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

Smithfor once again it is hehas strong evidence for proposition

(f):

(f) Jones owns a Ford.

Smiths evidencewhich we will not rehearseis strong though non-conclusive. Quite separate from this, Smith has a friend, named Brown,of whose whereabouts Smith is completely ignorant. Smith randomlychooses three place names: Boston, Barcelona, and Brest-Litovsk. Hethen formulates the following three propositions:

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(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 that Smith iswell aware of. The meaning of the eitheror expression here is whatlogicians call inclusive disjunction; the compound is true if either or boththe disjuncts is true. Since Smith was justied in accepting (f) he is alsojustied in accepting (g), (h), and (i)despite the fact that in each case hehas no reason to believe that the second disjunct is true.

As it turns out, however, (f) is falseJones does not own a Fordbut Brown is in Barcelona. Therefore (h) is a justied true belief, but saysGettier, Smith does not know that (h) is true. So again, says Gettier,justied true belief is not sufcient for knowledge.

Note that in both of these counterexamples Gettier gives no reasonfor his judgement that Smith does not have knowledgehe merely saysthat it is obvious. One response that we could make to these cases wouldbe simply to say that Gettier is mistaken: Smith does know. (I am settingaside my response to the rst of them, just for the sake of this point.) Thecases are strange and our intuitions are unprepared for them, but Smith

doesknow. Or at least, Gettier has to say more than that it is obvious thathe doesnt.

Could we not, however, say more than this? Suppose that we were toshare Gettiers intuition that Smith does not know (h); couldnt we usethe examples themselves to tell us what is missing from our account of knowledge? Surely we could. For if we examine what seems to have gonewrong in the case it is that Smith has no evidence (to support his belief in(h)) of the circumstance that makes (h) true. We could amend ourdenition of knowledge to include this condition.

X knows A iff def X is justied in believing A; A is true; and the evidence

that X has which constitutes the justication is evidence of the very cir-cumstance that makes A true.

Not only will this solve the counterexamples that Gettier has given, it willalso solve the other counterexamples that I am aware of.

Mostly, however, it is unnecessary to add it explicitlybecause thekinds of situations that constitute the Gettier counterexamples are a bitlike elements higher in the periodic table than Uranium: they are notfound in nature but have to be formed in the nuclear reactor of bizarre

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philosophical imaginings. Henceforth, unless stated otherwise, we willignore them and the extra condition.

1.3 Certainty or Less?

While we are wondering how the concept of knowledge is used we mightalso wonder about the notion of justication. When we say that someoneknows some propositionsay that mice are mammalsdoes that meanthat they know it with absolute certainty, in the sense that it is not possi-ble for them to be in error; or do we mean that they have strong reason tobelieve it, even though the reason might be inconclusive. On the side of the rst view, we do sometimes press people who claim to know some-thing and, if we nd even the slightest occasion for doubt, pronounce thatthey do not really know after all. On the side of the other view, we dooften think that we know things where the basis for the belief is incon-clusive. As weve just seen, such non-conclusive beliefs lie at the heart of the Gettier counterexamples.

This is a matter that cannot, I think, be solved by conceptual analy-sis. The concept of knowledge is used in both ways and we cannot settleit by seeing whether we do or do not require the stricter standard whenconfronted with examples. Instead we will have to try to investigate theway each view might work.

There is one aspect of this difference that is worth pointing out now,however. If we think that knowledge requires certainty we do not needto put in as a separate condition that the belief is also true. That is becausewhen we say that someone is certain about a matter we are already imply-ing that it is true (if it is not possible for the belief to be false then it mustbe true). In short, it would not be possible to have a (conclusively) justied

false belief.But if we allow non-conclusive justications then someone could

have a justied false beliefin fact Smith had at least two in the last sec-tion: they were (d) and (f). Because of this, if we allow that someone canhave knowledge when the reasons are non-conclusive, we must add in

the fact that the belief must be true as a separate condition. Not to pre-judge matters we have done just this, above. (It is worth pointing out,however, so that there is no danger of misunderstanding, that someonewho embraces the certainty view has not escaped the notion of truthit is

silently included in the view.)

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In the next chapter we will discuss the notion of truthwith thehope that we can dispel some of the strange misunderstandings and con-fusions that now attend the concept.

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Chapter 2. Some Notes on Truth

2.0 Nihilism

Knowledge implies truthso says the Platonic conception of knowledge,and so far we have found no reason to disagree with it. Butsomeonemight objectwhat is this notion of truth ? Surely in these modern timeswe regard the notion of truth with the deepest suspicionas something

strangely metaphysical? Many people now share this view. We can encap-sulate this position by stating the declaration that usually accompanies it,forceful and emphatic: There is no Truth! We will call such a position:

Nihilism (not to be confused with the 19 th Century political view of thesame name). If we want to be more specic we might call it Nihilismabout Truththough usually that is an unnecessary mouthful.

It is difcult to nd any philosopher throughout history who hasadvanced this vieweven in recent timesand yet such a view isundoubtedly quite common among non-philosophers and (in the propersense) philosophical amateurs. There are hints of such a view inNietzsche, but no more than hintsand ultimately it runs counter to thetenor of most of his other pronouncements. Even Jacques Derrida, whenhe has been pressed on whether he holds, or has ever held, such a view,has denied it (and not, it has to be said, without some show of irritation).

But our concern here is not with who might have started such a view,it is with whether the position is tenable. That is the hare we are chasing.

So is it tenable? The best way to approach this question is indirectlythrough a long-standing philosophical problem: the Paradox of the Liar .This paradox is thought to have originated in the 5 th Century b.c. in thephilosopher Empedocles, though it is likely to be much older than that.Very simply, it is this: consider the sentence This sentence is false: is ittrue or false? If it is true then, because it says that it is false, then that mustbe so: so it is false. But if it is false then that is what it says about itself, andso what it says is true. But then we have: if it is true then it is false and if it is false then it is true. So it seems to be neither true nor false; or perhapsis both. This is known as the Paradox of the Liar, the Liar Paradox, orsometimes, more properly, as the Antinomy of the Liar. Despite manyattempts over the last two and a half thousand years it is still unsolved.

Now let us look at a closely related paradox: the so-called Cretan

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Paradox. In this version, a Cretan says, All Cretans are Liars . The questionis: is that statement a lie or not? If it is a lie then some Cretans must betruth-tellers. Could this Cretan be a truth-teller? If he is, then, since hehas said that all Cretans are liars, that must be truebut then it cant betrue since he has told the truth. So if the statement is true then it is false.But note that if the statement is false then we cannot conclude that it istrue, since all that would tell us is that some Cretan somewhere is not aliar. So if it is false then all we know is that it is false. Putting these togeth-er, we know that All Cretans are liars, when uttered by a Cretan, mustbe false.

For a long time the Liar Paradox and the Cretan Paradox werethought to be the same paradox. But they are not. In fact the CretanParadox is not really a paradox at all. It is just an example of a statementthat cant be true.

Now let us look at Nihilism. Could the statement there is no truth betrue? Well, no, not without contradicting itself; for if it is true, then itwould be an example of the very thing that it says doesnt exist. So it cantbe true. What happens if we take it as not true? Does it then turn out tobe truelike the Liar Paradox? No. If it is not true then it follows thatsome statement, somewhere, is true, and that is all. It wont be this state-ment that is true, but some other. So, if it is true then it is not true, and if

it is not true then it is not true: so it is not true. It is false. In other words,Nihilism has the same structure as the Cretan Paradox, not the LiarParadox. It is an example of a statement that cannot be true.

The underlying problem for the person who wants to avow Nihilismis that we have no idea what it would mean to hold a view and not to holdit as true . If someone says I believe X then we cannot understand themexcept as saying that they believe X to be true. (Think of the oddity of someone who says Horses are mammals, but, at the same time, it is nottrue that horses are mammals.) So when someone espouses Nihilism wenaturally understand them to be saying something that they believe istrue. But that is what they cannot be doing. So what can their saying it

possibly mean? Well, we know that, whatever it is, it is nothing thatstrue.

Because of these problems Nihilism is not a view that has ever beentaken terribly seriously: it has an air of sounding radical and daring but itdoes not stand up to any kind of close scrutinyunder which it tends tobecome ever more vacuous. But usually, in fact, those who believe thatthey believe it are really trying to say something else. What might thatother thing be?

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2.1 Relativism about TruthIf someone who espouses the doctrine that there is no truth is pressed,they will likely elaborate as follows: I mean that there is no absolutetruth; that all truth is relative, something being merely true-for-me, ortrue-for-you, but not true in any absolute sense. Very well, let us consid-er this doctrine, which we will call Relativism. (I nd that I already wantto make a protest against prexing the adjective absolute to truth: it isutterly misleading to do so, and creates the false impression that a gen-uine contrast is being described. But more of this complaint later; for nowwe will go along with this faon de parler.)

Let us assume that the statement R: All truth is relative, correctlydescribes how things are, so that all truth is relative. Now since what ittakes for a statement to be absolutely true is nothing more than that itcorrectly describes how things are, R must be absolutely true. But since itis absolutely true it is an example of the very thing which it says doesntexist. So it is falseand absolutely so. It is not the case that all truth is rel-ative.

We get the same result from a slightly different angle if we ask,could R be relatively true? Well, if R is relatively true then it will be true-for-A and not true-for-B. But if it is not true for B, then for B truth isabsolute. But it makes no sense to speak of something being absolute for

B but not for Aso it is just absolute full-stop. So again Relativism isfalse. (I think this argument is less clear than the previous one eventhough they reach the same conclusion. The unclarity comes from tryingto apply a confused position to itself.)

So Relativism is falseand absolutely so.This style of argument is a little abstract and the point may be lost on

some readers, but we can reach the same conclusion in a more graphicway with the following scenario. Imagine two people involved in a dis-cussion: call them A and B again. B is making a number of assertionsabout the weather, the identity of the Prime Minister, that 2+2=4, thatAustralia is in the Southern Hemisphere, etc. To each of these assertionsA responds by saying that these things are true-for-B. All well and good.Finally, however, B makes one more assertion: he says that some state-ments are absolutely true. Now if A says that that is also just true-for-Bthen A is directly contradicting Bin other words A is saying that Bsstatement is absolutely false. Of course the reason A thinks Bs statementis absolutely false is that he thinks no statements are absolutely truebutthen he must think this statement is absolutely true. And from there the

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argument continues as before. (If R is absolutely true then it is absolutelyfalse, and so it is false.)

There is a common logical structure to all of these argumentsagainst both Nihilism and Relativism. It is called the Law of Clavius , orsometimes also Reductio ad Absurdam. Symbolically it looks like this:

( p p) p.

What this says is that if a statement p is such that it implies its own denial(negation) then that statement must be false. ( here stands forifthen and stands for not or negation.) Strictly we call this rule theLaw of Clavius when is, what is called material implication, and

Reductio ad Absurdam when it is understood as logical implication. Butwe can afford to be a little loose with our terminology here.

2.2 Relativism: what has gone wrong?

We have just shown that Relativism is falseand, in fact, necessarilyfalse. But to understand what has gone wrong, why so many peoplebelieve a view that is so easily shown to be mistaken, it is necessary to seewhat has made the view attractive in the rst place. We must diagnosethe underlying error.

If someone believes something then they naturally believe it to be

true. We can all agree to that. But it is too easy to slide from A believes X to be true to X is true-for-A. These dont say the same thing at all. For therst is compatible with X being falseA believes X to be true but A iswrong about thiswhereas the second claim isnt.

In fact this seems to be how the view arose in the rst place. In thebeginning A believes X to be true is harmlessly paraphrased as X is true for

A, where this second claim is taken to say no more than the rst.Eventually X is true for A morphed into X is true-for-A, where this is nowtaken as a new species of trutha species that supersedes the old absolutetruth with a new relative kind.

By itself this probably would not have succeeded in confusing any-

one, however, had it not been for a second fatal ambiguity. This can bestbe brought out in the following snippet of dialogue.

Ab: Some statements are true. This property of being true is a matter of thestatement correctly describing how things are.

Rel: But if it is just a matter of the statement correctly describing how thingsareif this relationship is external to usthen how would we know that itholds? In other words: how would we know when a statement is true in this

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absolute sense?This is a very common response, and one that has probably done morethan any other to convince people that there is something wrong with theidea of absolute truth. But it involves a mistake; a slide from a statementbeing true, to our knowing that it is true. These are not the same thing.There is no incoherence involved in saying that a statement is true if itcorrectly describes how things are and at the same time admitting thatmany statements that are true may never be known to be true. Moreover,the Relativist has no grounds for muddling up the conditions that makea statement true and the conditions that must obtain for us to know that astatement is true. We will explicate this difference in the next section.

In summary Relativism arises from a confusion between truth andbelief and truth and knowledgeand it eventually causes a confusionbetween the conated items, belief and knowledge. But these are all sep-arate things, separate and unlike.

2.3 Truth and Knowledge

What is it for a statement to be true? We have spoken, above, of a state-ment correctly describing how things are, and for most purposes that isexact enough. But we can do better, if the need arises. We can dene aformula that captures the notion quite directly.

For all sentences p, p is true if and only if p.

(This is sometimes called Tarskis Analysis of Truth, but this is a vexedissue given that several different things are called by this name.) We cansee what this formula means if we put an actual sentence in the p variableposition. Grass is green is true if and only if grass is green. Obviouslywe could put any other statement-making sentence in the p position andit will yield up a condition of what it means for that sentence to be true.

On this account, truth is said to be a property of sentences, and toemploy it we need a way of referring to sentences. That is ne because wehave a ready way of doing that: it is called quotation. But truth is some-

times employed in a way that doesnt require quotation; it is employedaswhat philosophers are inclined to calla propositional operator. Asan operator it can be dened by the following formula:

For all sentences p, it is true that p if and only if p.

Thus we would say it is true that grass is green if and only if grass is green.This operator, which we will abbreviate to T , has interesting propertiesit can be added or deleted without effect. Thus, representing iff by , we

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haveTTTTTT p TTTTT p TTTT p TTT p TT p T p p.

This has important implications for our account of knowledge. For whenwe say that A knows p means that p is a justied true beliefthis is alsowhat it means for A to know that p is true. Thus, when in the last section,the Relativist asked the question Yes, but how do we know that p istrue the simple answer is The same way you know p. This is because

KA( p) KA (T p).

This follows from the above formula and the denition of knowledge.

Here, experience tells me, people are inclined to get rather nerv-ousas though they had been led into a dark labyrinth. How can it be,they will say, that to know that grass is green I must have, not only agood reason to believe it, but it must be true, and yet knowing that it istrue is nothing more than knowing that grass is green. Surely somethinghas gone wrong!

In fact nothing has gone wrong. To know A, A must be true. But toknow that A is true, it must be true that A is truewhich reduces to A istrue. In formulae, it would look like this.

KA( p) (T p) and (T p) p.

KA(T p) (TT p) and (TT p) (T p) and (T p) p.

The rst line says that if A knows p then p is true; and if it is true that pthen p. The second line says that if A knows that p then it is true that it istrue that p; and if it is true that it is true that p then it is true that p; and if it is true that p then p. There is no inconsistency in any of this. The upshotis that

KA( p) KA(T p).

Undoubtedly by now all of this seems quite complex. In its essence it is infact quite simple; but the fact that it can sound complex has acted as a kindof Shell Gamea single lapse in ones attention and suddenly it seemsright to say You see! It is impossible that there be an absolute truth. Alltruth is relative! We could never know that anything is absolutely true.

But that is just to lose sight of the p.

2.4 Facts and Values

Let us now ask a different kind of question: what is the source of the

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attraction people have to Relativism? Why does it seem to say somethingthat people feel needs saying? It seems wrong and uncharitable to sup-pose that there are no positive aspects that lead people to feel attracted tothe view. I agree that it is and will now try to assay what that positivething is.

The true-for-you expression does not get deployed in every circum-stancebut in some rather than others. Suppose B says: Honesty is thebest policy. A might then say: Well, that is true for you, but it is not truefor me. Or suppose B says: The purpose of life is self-sacrice. Then,again, A might say: That may be true for you, but it is not true for me.

But suppose B says: Kylie Minogue is the Prime Minister of Australia. It would be bizarre of A to respond to this by saying: Thatmay be true for you, but it is not true for me. In fact, under this circum-stance we would be hard pressed to say who is the more insane of the two,A or B! Or suppose A asks B the price of a chair in the showroom win-dow. B replies: Fifty dollars. If A then says: that may be true for you, butit is not true for me, B would likely start dialling for security.

This tells us something important: when straightforward matters of fact are involved Relativism seems bizarre and inappropriate. The onlytime it seemsto be the right thing to say is when the matter in question isa matter of value or is otherwise unresolvable by rational means. So hon-

esty is the best policyand the purpose of life is self-sacriceare not things thatwe could easily say are true or falseindeed we may feel that we do noteven know how to begin nding outwhat they are. And that seems to bewhat the Relativist is trying to say, albeit awkwardly: You may believethat it is true that honesty is the best policy, but I do not believe itandmoreover I dont see any way of settling who is right. Let us not argueabout it, then! And that is why Relativism would be inappropriate in theother cases. There is an obvious fact of the matter as to who is the PrimeMinister of Australia and the price of a chair and in neither case is it thatdifcult to discover what they are.

So we can say that the relativist locution is used when, either there is

thought to be no fact that could ground some particular claim (as in amatter of value), or when there is such a fact but that it is rationally inac-cessible. It would probably be as a result of this latter circumstance thatsomeone might say, if someone else were to declare that God exists, thatthat might be true for you but is not true for me.

But it is a mark of how confused Relativism is that it is equally like-ly that someone who says that it is true for you that God exists, but nottrue for me, might also mean that God exists for you in virtue of your

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thinking that He does, but does not exist for me in virtue of my thinkingHe doesnt. All of which makes no sense at all, and is merely a descentinto gibberish.

Still, even if we now have a sense of what someone might reasonablymean in saying that something is true-for-you, not-true-for-me, that doesnot imply that it is the right thing to say, even in the most favourable con-ditions. For suppose we agreejust for the sake of argumentthat thereare no facts that can ground our value judgements. That does not meanthat we should say your judgement is true for you. Onceor should I sayif we become aware that there are no facts that can ground (in the jar-gon: provide truth-conditions for) our judgements then we should simplysay that all such judgements are false. And that means absolutely false.There is no point trying to soften this with Relativist comfort-phrases. If the motivation for Relativism is that there are insufcient facts in theworld to ground our assertions and judgements then it is no motivationat all: for all those judgements are simply false, in virtue of their beingnothing that could make them true.

In a sense Relativist locutions provide a kind of cushion against com-ing to terms with this point. If there are no facts which can ground valuejudgementsincluding moral value judgementsthen what theRelativist should say to the person who says that murder is wrong is that

that statement is strictly false. But that is a tough thing to say. In fact it isperhaps such a tough thing to say that it is no wonder that the Relativistis looking for a way any waynot to say it.

2.5 The Tolerance Defence

Some people feel that Relativism is a desirable positionthat is, that itought to be true, or at least that we ought to believe it to be true. Thisis because, they say, it is a tolerant positionit lets people believe whatthey want to believe. How credible is this defence?

Well, there is an immediate problem: there is no known connectionbetween it being nice for a view to be true and it actually being true. So

desirability is not going to make the view believable. In fact no positionis one whit more likely to be true no matter if it were as desirable as itcould be. Suppose a view was maximally desirableevery inhabitant of the Earth would perish tomorrow unless it is true. That would not makethe view believable or any the more likely to be true. Sad, but there it is.

There is a second problem. As we have already seen, Relativism isnot particularly tolerant of the beliefs of others when it comes to the truth

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about truthand cant be. But even with beliefs that are not about truthRelativism falls short. If B says that God exists and A responds by sayingthat this is just true-for-B, B is entitled to feel annoyed. For B does notthink that it is just true for him, he thinks its true. If he didnt think thathe wouldnt bother believing it. When someone believes something theymostlybarring bizarre irrational beliefs that the person retains whileknowing that they are irrationalbelieve it because they think they havegood evidence. So if someone believes that God exists they will think thattheir belief is truenot just true-for-them. (Or course, that is not enoughto ensure that their belief is true, but that is a commonplace.)

The tolerance defence also sits very ill with the most commonRelativist views. As I noted in the previous section, most people who areRelativists are so on matters of valuesit is a view that is, so to speak,weighted heavily over the evaluative part of our discourse. Thus theusual Relativist cry is: All morality is just relative (to our culture)! But if that is so how can a moral evaluationtolerance is goodact as anobjective evaluation that justies Relativism? On the Relativist view it isnot true simpliciter that tolerance is good, it is only true- for-the-one-who-believes-it. So, on this view, intolerance is good, is true for the one whobelieves that . The upshot is that there can be no moral justication of Relativism.

(It is perhaps worth adding at this point that in my experienceRelativists are a little inclined to use Relativism to selectively neutralisethe views of others and to forget the view when it comes to their ownpositions. Thus it seems to be tacitly asserted that your beliefs are justtrue-for-you, whereas mine are simply true. And perhaps this accountsfor the oddityand I am not the rst one to have observed thisthatRelativists are often inclined to hold their Relativism as though it were adogmatic, uncriticisable, fact.)

2.6 Relative Truth and Relativity

If the idea that truth is relative has its origins anywhere it is probably in a

confused misunderstanding of the ideas of Relativity Theory. RelativityTheory (specically, Einsteins Special Theory of Relativity (STR))makes the claim that an objects velocity is relative. That is, somethingcan be said to be travelling at a particular velocity only relative to a par-ticular (inertial) frame of referencethere is no such thing as the realor absolute velocity of an object. In fact in STR it is also true that the timethat elapses between two events is also relative to a particular frame of

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referencetwo observers measuring with respect to different frames of reference will measure different elapse times for the same pair of events.Thus there is no such thing as the real elapse time. But even thoughvelocity and elapse time are relative in STRindeed the former is rela-tive even in Newtonian kinematics, where it is called GalileanRelativityit is not the case that everything is relative. It is a strange anddifcult to grasp fact that even though velocity is only relative, change invelocity, also known as acceleration, is absolutethat is, it is the same forall observers.

Perhaps the doctrine that all truth is relative arose originally fromsomeone hearing of Einsteins theorywhich, by the way, has beenborne out by all subsequent experimentsand drawing from it thewrong conclusion. Perhaps someone clumsily paraphrased the theorywith the slogan Everything is Relative! and, once started, the misunder-standing proved impossible to stop, eventually seeming to be conrmedwhen someone else turned mistake into philosophy by claiming that thiswas the correct view of truth. It is impossible to know. All that is knownis that a view that was nowhere espoused in the history of philosophysuddenly, in the middle of the Twentieth Century, acquired the status of a philosophy among people who were not themselves philosophers. Astrange fate for a simple mistake to enjoy!

2.7 Truth and RedundancyAn Advanced Topic that may be skipped

In recent years there has grown up a view about truth that declares it tobe redundant, in the sense that whatever can be said with it can be saidwithout it. This view is variously called, following Ramsay, the

Redundancy Theory; following Quine, the Disquotational view ; or follow-ing Horwich, the Minimalist view . (There are slight differences herewhich will be described below.)

Consider the two schema, described in 2.4 above.

(1) For all sentences p, p is true if and only if p

(2) For all sentences p, it is true that p if and only if p.

In essence the disquotational view (DT) is that (1) is all that there is to theconcept of truthit is nothing more than a device for making assertionsthat could perfectly well be made without it. If I say: Grass is green istrue, I could have said it disquotationally by just saying grass is green.

On the redundancy view (call it MT) (2) is all that there is to the con-cept of truth. It is an operator that just yea-says any proposition. So it is

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true that grass is green just says the same thing as grass is green. This is alsocalled the Minimal Theory of Truth.

The idea here can be, has been, variously expressed by saying thattruth is not a substantive notion, that the concept adds nothing, that it istrivial, or that it could be eliminated without loss. Indeed if someonewere of a mischievous natureand there have been such peopleitmight even be claimed that this is a precise statement of the Nihilistsbasic idea: there is no truth.

So is it true? Do either DT or MT express all that there is to truth?To answer this question it is necessary to put it slightly more precisely.Take DTwe could ask whether a theory expressed in a language thatcontains no truth predicate would be deductively equivalent to the sametheory with a language enriched by a truth predicate. Would this exten-sion be, what is called, a conservativeextension? (We could ask the samething about a language augmented with a truth operatoras in MT.)The next thing to ask is whether a language in which a full theory of truth is denedas in Alfred Tarskis seminal 1936 paper On theConcept of Truth in Formalised Languageswould also be a conserva-tive extension. Obviously if one augmentation is a conservative extensionand the other isnt then they cant be equivalent and the rst could not beidentical to a full theory of truthit couldnt be everything there is to

the concept of truth.The answer to this question was given by the same Tarski in that1936 paper. It is no, they are not equivalent. Our concept of truth is notexhausted by the equivalences in (1) or (2). Moreover, in PeanoArithmetic (PA) augmented by a full truth theory, the consistency of PAis derivablebut not without, by Gdels second incompleteness theo-rem. (For the readdressing of these questions in a modern context, seeJeffrey Ketlands excellent Deationism and Tarskis Paradise in Mind,vol.108, 1999, 6994.)

We could say that a full Tarskian truth theory employing the con-cept of satisfaction, is not empty or non-substantive, or any one of the

other belittling epithets that Minimalists have attempted to hang on it.And moreover this should have been obvious from the efforts of Tarskiover sixty years ago!to dene the conditions under whichintroducing the predicate does and does not engender paradox. One hasto say that much recent writing on this topic has provided a far from edi-fying spectacle.

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2.8 Some Questions and AnswersLet us return to the relation between knowledge and truth. There are anumber of matters that come up frequently that need simple clarication.So here, to end this chapter, we have a compendium of frequently askedquestions and answers.

Q: If I believe that I know something does that mean that I know it? A:Noyou can be wrong.

Q: If I know that I know something does that mean that I know it? A:Yes.

Q: If I believe that I know that I know something does that mean that Iknow it? A: No.

Q: If I believe something must it be true? A: No.

Q: If I know something must it be true? A: Yes.

Q: If something is true must I know it? A: No.

Q: If I know something must I know that it is true? A: Yes.

Q: If I know something will I never know that I know itbecause I cannever verify that it is true? A: (This is a tricky one) No. If I know some-thing, say p, then I have a true justied belief, and I could quite reason-

ably have a justied true belief that I have a justied true belief that p. (Iwill go into more detail on this one in a later chapter.)

Q: Could we just do without the condition that the thing known must betrue? A: No. We have a perfectly serviceable concept of rational belief and it is not the same as our concept of knowledge. If we drop the truthcondition we will not be able to make the distinction between justiedtrue belief and justied false belief. We need the concept of a rationalbelief that succeeds in its aim that is knowledge. (Just as we need theconcept not only of trying to win a race, but of actually winning it!)

Q: Were there truths before there were any peoplewhen the Universewas, say, three seconds old? A: (Again tricky) This is called theTruthbearer Issue . I think most philosophers would say yestherewould be many things true back then, including the simple claim thatthere are no humans alive yet. For there to be truths there do not need tobe actually uttered sentences. Other philosophers might be of a moreNominalist bentthey may insist that though there are plenty of factsback then, there were no true sentences until they were uttered. I am

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inclined, for present purposes, to be agnostic on this issuethough Ithink the latter option requires us to speak in an unnecessarily cumber-some way. So I will say that when there were dinosaurs there were manystatements that were true about those dinosaurseven though thedinosaurs themselves were not capable of uttering them.

That concludes our discussion of truth and its relation to knowledge.There are many other aspects that can be considered, but we can savesome of those for later chapters when we have a lot more philosophyunder our belt.

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Chapter 3. Descartes Meditation One

Let us now return to the question: what do we know? If the argu-

ment against the global sceptic in chapter one has as its conclusionthat we must know something, then the obvious thing to ask is:

what is it that we know? And before we can answer that question weneed to know how we can nd out what we know. Ren Descartes(15961650) attempted to answer both questions and presented thoseanswers in a number of works, beginning with the Discourse on Methodin1637, continuing with the Meditations in 1641, and also in Principles of

Philosophy in 1644. His work has often been seen as the beginning of modern philosophy, and whether that is true or not he certainly present-ed a compelling picture of himself as sweeping aside all prejudice andattempting to reinvent the theory of knowledge single-handed. And itmust be said that there is an economy and show of precision in his workwhich subsequent generations have found instructive and refreshing.

Here I want to examine the foundation of his foundation of knowl-edge: the First Meditation, which repeats in economical form the positionof the Discourse on Method. It is arguably his single most important con-tribution to the theory of knowledge and it will repay examination indetail.

3.1 The Method

The starting point is to try to establish how we can know what we know.

Descartes appears to reason that I know that I know something if it is notopen to doubt. Thus we nd him at the beginning of Meditation Oneannouncing that if we want to discover what is knownand what canstand as the foundation to the rest of our knowledgewe should try tond out what is doubtable. Here is what he says.

It is now several years since I rst became aware how many falseopinions I had from my childhood been admitting as true, andhow doubtful was everything I have subsequently based on

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them. Accordingly I have ever since been convinced that if I amto establish anything rm and lasting in the sciences, I must oncefor all, and by a deliberate effort, rid myself of all those opinionsto which I have hitherto given credence, starting entirely anew,and building from the foundations up. But as this enterprise wasevidently one of great magnitude, I waited until I had attainedan age so mature that I could no longer expect that I should atany later date be better able to execute my design. This is whathas made me delay so long; and I should now be failing in myduty, were I to continue consuming in deliberation such time foraction as still remains to me.

Today, then, as I have suitably freed my mind from all cares,and have secured for myself an assured leisure in peaceful soli-tude, I shall at last apply myself earnestly and freely to the gen-eral overthrow of all my former opinions. In doing so, it will notbe necessary for me to show that they are one and all false; that isperhaps more than can be done. But since reason has already per-suaded me that I ought to withhold belief no less carefully fromthings not entirely certain and indubitable than from thosewhich appear to me manifestly false, I shall be justied in settingall of them aside, if in each case I can nd any ground whatsoev-

er for regarding them as dubitable. Nor in so doing shall I beinvestigating each belief separatelythat, like inquiry into theirfalsity, would be an endless labour. The withdrawal of founda-tions involves the downfall of whatever rests on these founda-tions, and what I shall therefore begin by examining are theprinciples on which my former beliefs rested.

Not everything here is clear, but the main idea is plain enough. The foun-dations for our knowledge of the world are to be discovered by a processof elimination: we eliminate everything that is dubitable to discover whatis certain.

Note, parenthetically, that Descartes uses the image of foundationsin two ways: rstly for the basis of his proposed new construction, andsecondly for the principles that underlie his old set of beliefs. Thus heintends to isolate his new foundation by pulling the foundations out frombeneath of his old set of beliefs. This image of foundations really comesfrom the mathematics of the time, from the axioms in a geometric theo-ry, say. Thus a better name for Descartes theory would really be An

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Axiomatic Theory of Knowledge. The idea is that, what we derive, by log-ical means, from the axiomsthese derived claims are called theoremsare as certain as the axioms themselves. In fact, understanding this moti-vating analogy will take us a long way to seeing what works and whatdoes not in Descartes account.

Our second parenthetical remark is to note that Descartes does notseem entirely clear whether he is trying to winnow out the dubitable toisolate the certain, or whether he is trying to winnow out the false to iso-late the true. At this early stage this vacillation does no damage but laterwe will see that this masks a serious confusion in his thought.

But we can now see Descartes answer to his rst question: how canwe know what we know? The answer is that we know what is beyonddoubt, and that which follows logically from what is beyond doubt. Thuswe may conclude that, for Descartes, we know what is certain.

3.2 The Arguments for Doubt

What then is beyond doubt? Descartes attempts to answer that questionby producing three arguments for doubt that are of increasing strength,or at least increasing scope.

The rst argument is from the unreliability of the senses. Here isDescartes statement.

Whatever, up to the present, I have accepted as possessed of thehighest truth and certainty I have learned either from the sensesor through the senses. Now these senses I have sometimes foundto be deceptive; and it is only prudent never to place completecondence in that by which we have even once been deceived.

This argument is a generalisation from known factthe fact that oursenses have sometimes, in some circumstances, led us astray. It invites usto be prudent and not to completely trusti.e. not in other circum-stancesthat which has once misled us.

How compelling is this argument? Descartes hardly gives us time toconsider for he immediately supplies a counterargument, the import of which is that this is in fact a non-prudent overgeneralisation.

But, it may be said, although the senses sometimes deceive usregarding minute objects, or such as are at a great distance fromus, there are yet many other things which, though known by wayof sense, are too evident to be doubted; as, for instance, that I amin this place, seated by the re, attired in a dressing gown, having

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this paper in my hands, and other similar seeming certainties.Can I deny that these hands and this body are mine, save perhapsby comparing myself to those who are insane, and whose brainsare so disturbed and clouded by dark bilious vapours that theypersist in assuring us that they are kings, when in fact they are inextreme poverty; or that they are clothed in gold and purplewhen they are in fact destitute of any covering; or that their headis made of clay and their body of glass, or that they are pump-kins. They are mad; and I should be no less insane were I to fol-low examples so extravagant.

So this rst argument for doubt is awed. (Just how awed it can reallybe, given Descartes later acceptance of a doubt that is even more encom-passing, is a point to which we will return.)

Descartes then proposes a second argument for doubt, which is oftencalled The Dreaming Argument.

None the less I must bear in mind that I am a man, and amtherefore in the habit of sleeping, and that what the insane rep-resent to themselves in their waking moments I represent tomyself, with other things even less probable, in my dreams. Howoften, indeed, have I dreamt of myself being in this place, dressed

and seated by the re, whilst all the time I was lying undressed inbed! At the present moment it certainly seems that in looking atthis paper I do so with open eyes, that the head which I move isnot asleep, that it is deliberately and of set purpose that I extendthis hand, and that I am sensing the hand. The things whichhappen to the sleeper are not so clear nor so distinct as all of thesethings are. I cannot, however, but remind myself that on manyoccasions I have in sleep been deceived by similar illusions; andon more careful study of them I see that there are no certainmarks distinguishing waking from sleep; and I see this so mani-festly that, lost in amazement, I am almost persuaded that I amnow dreaming.

The emphasis in that last sentence should fall on certain. The idea is thatwhen I am dreaming I have an experience as if of sitting by the re, justas when I am awake I have an experience of an actual re. There are no

certain marks to distinguish the ersatz from the genuineand so it is pos-

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sible that I am now dreaming though I think myself awake. This is theDreaming Argument.

(Think of it via an analogy: there are no certain marks to distinguisha counterfeit Van Gogh painting from a genuine onetherefore it is pos-sible that this Van Gogh that I am now looking at is a forgery.)

This argument seems quite convincing. The only real source of worry is the qualitative gap between the dreaming experience and thewaking one. Even Descartes acknowledges that they are not that close.And if they are not very close then I am not likely to be lost in amaze-ment and almost persuaded that I am now dreamingas Descartesrhetorically adds. (Think what a shrug would greet the counterfeitingargument if all Van Gogh counterfeits were terriblelittle more thanchildrens doodles. Then we would say, yes, we cannot be certain

absolutely certainthat this Van Gogh is not a counterfeit, but we canstill be pretty damn sure!)

Descartes has other worries. The dream experience is, he feels,always simply a recombination of the elements of waking life, and thus isparasitical on waking experience.

Let us then suppose ourselves to be asleep, and all these particu-larsnamely, that we open our eyes, move the head, extend thehandsare false and illusory; and let us reect that our hands

perhaps, and the whole body, are not what we see them as being.Nevertheless we must at least agree that the things seen by us insleep are as it were like painted images, and cannot have beenformed save in the likeness of what is real and true. The types of things depicted, eyes, head, hands, etc.these at least are notimaginary, but true and existent. For in truth when paintersendeavour with all possible artice to represent sirens and satyrsby forms the most fantastic and unusual, they cannot assign themnatures which are entirely new, but only make a certain selectionof limbs from different animals. Even should they excogitatesomething so novel that nothing similiar has ever before beenseen, and that their work represents to us a thing entirely cti-cious and false, the colours used in depicting them cannot besimilarly cticious; they at least must truly exist. And by thissame reasoning, even should those general things, viz, a body,eyes, a head, hands and such like, be imaginary, we are yet boundto admit that there are things simpler and more universal whichare the real existents and by the intermixture of which, as in the

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case of the colours, all the images of things of which we have anyawareness, be they true and real or false and fantastic, areformed. To this class of things belong corporeal nature in gener-al and its extension, the shape of extended things, their quantityor magnitude, and their number, as also the location in whichthey are, the time through which they endure, and other similarthings.

Dreams, then, are essentially recombinations of the fundamentals of real-ity. Logically, this point should be used by Descartes to suggest that theDreaming Argument is still rather limitedthat it does not captureeverything that is open to doubtyet he does not in fact use it in thatway. Instead he suggests that this fact explains the supposed certainty thatis often thought to attend studies of the fundamentalsarithmetic andgeometryas opposed to studies of the composites, i.e. physics, chem-istry, biology, etc. This is rather implausible. If physics discovered funda-mental particlestruly fundamental particlesit is hardly likely that atthat moment physics would become certain. We must look elsewhere forexplanations of the difference between arithmetic and geometry on theone hand, and physics, chemistry and medicine, on the other.

Still, Descartes does not linger over this point and neither should we.

He immediately points out that the possibilities of recombination afford-ed by dreams is limited, for arithmetic and geometric facts are constantacross both dream and reality. Here are both points together.

This perhaps is why we not unreasonably conclude that physics,astronomy, medicine, and all other disciplines treating of com-posite things are of doubtful character, and that arithmetic,geometry, etc., treating only of the simplest and most generalthings and but little concerned as to whether or not they are actu-al existents, have a content that is certain and indubitable. Forwhether I am awake or dreaming, 2 and 3 are 5, a square has nomore than four sides; and it does not seem possible that truths soevident can ever be suspected of falsity.

He goes on to try to extend the method of doubt to these things as well.

Yet even these truths can be questioned. That God exists, thatHe is all-powerful, and has created me such as I am, has longbeen my settled opinion. How, then, do I know that He has notarranged that there be no Earth, no heavens, no extended thing,

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no shape, no magnitude, no location, while at the same timesecuring that all these things appear to me to exist precisely asthey now do? Others, as I sometimes think, deceive themselvesin the things which they believe they know best. How do I knowthat I am not myself deceived every time I add 2 and 3, or countthe sides of a square, or judge of things yet simpler, if anythingsimpler can be suggested? But perhaps God has not been willingthat I should be thus deceived, for He is said to be supremelygood. If, however, it be repugnant to the goodness of God tohave created me such that I am constantly subject to deception, itwould also appear to be contrary to His goodness to permit me tobe sometimes deceived, and that He does permit this is not indoubt.

So if God exists and is all-powerful then He could cause my calculationsand my reasoning to go awryeven if to do such things might appear tobe contrary to His goodness. This clearly is an enlargement of the scopeof doubt. It should now be capable of taking in the truths of reason aswell as the truths of experience. But Descartes is not entirely happy withitbecause even though the argument only requires that such an all-powerful God be possible, it may not be possible for a wholly benevolent

being to deceive me in this way. So Descartes has to imagine a very pow-erful being who would not suffer from this moral impediment. This is hisfamous Evil Demon. Before conjuring up this possibility, however,Descartes rst worries about Mans capacity for error and its relation tohis origins.

There may be those who might prefer to deny the existence of aGod so powerful, rather than to believe that all other things areuncertain. Let us, for the present, not oppose them; let us allow,in the manner of their view, that all that has been said regardingGod is a fable. Even so we shall not have met and answered thedoubts suggested above regarding the reliability of our mentalfaculties; instead we shall have given added force to them. For inwhatever way it be supposed that I have come to be what I am,whether by fate or by chance, or by a continual succession andconnection of things, or by some other means, since to bedeceived and to err is an imperfection, the likelihood of my beingso imperfect as to be the constant victim of deception will beincreased in proportion as the power to which they assign my

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origin is lessened. To such arguments I have assuredly nothingto reply; and thus at last I am constrained to confess that there isno one of all my former opinions which is not open to doubt, andthis not merely owing to want of thought on my part, or throughlevity, but from cogent and maturely considered reasons.Henceforth, therefore, should I desire to discover something cer-tain, I ought to refrain from assenting to these opinions no lessscrupulously than in respect of what is manifestly false.

This last sentence is puzzling. Descartes says therefore but it is not obvi-ous what this claim actually follows from. Moreover it doesnt seem true.What good could it do in the discovery of certainties to refuse to assent tothat which is not certain?(It is a little like saying that if you want to catchlions you must pretend that everything that is not a lion doesnt exist! Itsall very zen, but not, ultimately, that helpful.) In fact, the philosopherLeibniz complained on just this point. In part of his commentary onDescartes he said: I do not see what good it does to consider what isdoubtful as false. This would be not to lay aside prejudices but to changethem. To which we might add that it is hard to see how these new false-hoods could aid in the discovery of certainties: self-deception is not usual-ly thought to be the best way of discovering the truth!

In fact Descartes tries to justify this strange manoeuvre in the nextparagraph.

But it is not sufcient to have taken note of these conclusions; wemust also be careful to keep them in mind. For long-establishedcustomary opinions perpetually recur in thought, long andfamiliar usage having given them the right to occupy my mind,even almost against my will, and to be masters of my belief. Norshall I ever lose this habit of assenting to and conding in them,not at least so long as I consider them as in truth they are, [myemphasis] namely, as opinions which, though in some fashiondoubtful (as I have just shown) are still, none the less, highlyprobable and such as it is much more reasonable to believe thandeny. This is why I shall, as I think, be acting prudently if, tak-ing a directly contrary line, I of set purpose employ every avail-able device for the deceiving of myself, feigning that all theseopinions are entirely false and imaginary. Then, in due course,having so balanced my old-time prejudice by this new prejudicethat I cease to incline to one side more than to another, my judge-

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ment, no longer dominated by misleading usages, will not behindered by them in the apprehension of things. In this coursethere can, I am convinced, be neither danger nor error. What Ihave under consideration is a question solely of knowledge, notof action, so that I cannot for the present be at fault as being over-ready to adopt a questioning attitude.

This paragraph presents a tangle of issues, that it will take us some timeto sort out. We may note immediately, however, that there is really noexplanation of Descartes perverse decision forthcoming: we ought tobelieve that which it is more reasonable to believe than deny; however,for the purposes of the method he intends to employ every availabledevice for the deceiving of [himself]. And having announced this, heassures us that there can in this be neither danger nor error! One is tempt-ed to say that there will be as little of the former as there is as much of thelatter. However, more of this later.

Following this disclaimer Descartes goes on to state his well-knownEvil Demon Hypothesis.

Accordingly I shall now suppose, not that a true God, and whoas such must be supremely good and the fountain of truth, butthat some malignant genius exceedingly powerful and cunning

has devoted all his powers in the deceiving of me; I shall supposethat the sky, the earth, colours, shapes, sounds and all externalthings are illusions and impostures of which this evil genius hasavailed himself for the abuse of my credulity; I shall considermyself as having no hands, no eyes, no esh, no blood, nor anysenses, but as falsely opining myself to possess all these things.Further, I shall obstinately persist, in this way of thinking; andeven if, while so doing, it may not be within my power to arriveat the knowledge of any truth, there is one thing I have it in meto do, viz. to suspend judgement, refusing assent to what is false.[ Authors note: and also to what is true!] Thereby, thanks to thisresolved rmness of mind, I shall be effectively guarding myself against being imposed on by this deceiver, no matter how pow-erful or how craftily deceptive he may be.

After this we have Descartes weary resignation that such extreme doubtis not maintainable for long.

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This undertaking is, however, irksome and laborious, and a cer-tain indolence drags me back into the course of my customarylife. Just as a captive who has been enjoying in sleep an imagi-nary liberty, should he begin to suspect that his liberty is adream, dreads awakening, and conspires with the agreeable illu-sions for the prolonging of the deception, so in similar fashion Igladly lapse back into my accustomed opinions. I dread to beawakened, in fear lest the wakefulness may have to be laborious-ly spent, not in the tranquilising light of truth, but in the extremedarkness of the above suggested questionings.

It is easy to miss the strangeness of this rhetorical ourish. The peacefuldream is the supposition that he is being deceived by an Evil Demon. Thewaking world is the darkness of his former opinions. The former is thetranquilising light of truth, whereas the latter, being in some fashiondoubtful, is now completely repugnant. Descartes has here talked him-self into a very inverted position, where black is white and white is black!It is hard to see how all of this self-deceiving can end but in false philoso-phy.

3.3 The Missing French-Remainder Theorem

The purpose of the Method of Doubt was to suspend belief in all that isdoubtful in order to isolate that which is certain. What is certain will bethe remainder once the doubtful is removed. So what does Descartesthink is the certain remainder? The answer is: that I exist. And the argu-ment that convinces him that this is certain is the famous Cogito ergo Sum:I think therefore I am. Even if there were an Evil Demon trying todeceive me I must exist in order to be deceived. When I attempt to doubtthat I exist it is obvious that I must exist to do the doubting. So I exist.

The argument does not tell me who or what I am, nor does it tell methat you exist: all of that is open to doubt. But the argument does tell methat it is certain to me that I exist. We might think of this as Descartes

rst isolated axiom.But one axiom alone is not likely to take us very far. In Meditation

III Descartes argues that it is also certain that God exists and that He is allgood. With these two foundational axioms Descartes attempts to deriveour knowledge of the world.

I do not intend to say much about this positive, constructive, phase of Descartes philosophy. It is audacious and venturesome but it is also

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unconvincing and of mainly historical interest. Instead I want to focus onMeditation I and the Method of Doubt to see whether it is a cogent start-ing point. And it is also true that philosophers who have been impressedby Descartes arguments there have seen themas Descartes did notasan argument for scepticism. We want to know if that scepticism gen-uinely follows.

The rst thing to say may seem unimportant but is not. OstensiblyDescartes uses the Method of Doubt to nd that which is insusceptible of doubt. But in order to do this he needs to show that the doubt that henally arrives at is maximal i.e. that everything that is capable of beingdoubted is now within its ambit. Otherwise he cannot conclude that theremainder will be that which is certain. But there is no hint of such aproof in Descartes. Moreover, as we shall see, there are good reasons whyhe cannot answer this question.

This need for the doubt to be maximal has shaped, howeverin ahalf-conscious waythe structure of Meditation I. Descartes has pro-gressed through the three arguments for doubt trying to nd the mostencompassing. He is enlarging the scope of doubt at every turn. But thismakes his response to the rst argument for the unreliability of the sens-es quite wrong. For he suggests there that my mistrust of my senses willbring me perilously close to those who are mad i.e. to those whose sens-

es do in fact deceive them. But this is not the correct reservation for himto have: it should not be that such doubt is too extreme but that it is notextreme enough. It is not maximal. And, of course, by the time we reachthe Evil Demon hypothesis we are well beyond those poor simple soulswho think that they are pumpkins. In fact, by comparison they seemmodels of sanity.

But even though Meditation I is structured around this progressiontoward a maximal doubt there is no proof that we have arrived at it. Noris it at all clearas we will see in the next sectionwhat falls within thescope of the doubt that has been arrived at. Because of this Descartes can-not be sure that the remainder will be certain. This is perhaps why, when

he comes to the Cogito, and then to his arguments for the existence of God, he separately, and independently, argues for their certainty. But thismeans that the Method of Doubt was redundant all along: if we wantedto know what was certain we should have simply gone straight to the par-ticular candidates; we didnt need to approach them stealthily throughthe doubtful. The method of Doubt is a path that just peters out and wethen just jump to what we could have jumped to all along. But this ismore than just a slipfor it conceals a problem that goes to the heart of

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Descartes entire enterprise. What that problem is we turn to in the nextsection.

3.4 The Symmetry of Doubt.

The Evil Demon hypothesis goes beyond the Dreaming Argument, buthow? Certain truths of reason are constant across dreams and reality andtherefore are not cast into doubt by the fact that we might be dreaming.The Evil Demon Hypothesisor, in the rst form, God Himselfistherefore meant to show that even these things can be doubted.Moreover, we could adapt the Unreliability of the Senses Argument toshow that all truths of reason are open to doubt.

I have sometimes found my reasoning to be deceptive; and it isonly prudent never to place complete condence in that bywhich we have even once been deceived.

However, by the time we have come to the conclusion of Meditation I thepossibility that our reasoning is open to doubt, just as much as our senso-ry experience, has been lost. The doubt that Descartes runs throughseems to be little different to what was open to doubt at the end of theDreaming Argument. We havent progressed beyond it after all.

This omission allows Descartes to discover the certainties that he

nds in Meditations II and III, for these are arguments that depend onthe slenderest fact: that I am thinking. As arguments they seek to drawconclusions from that fact, and these conclusions are that I exist, and soalso does a perfect being.

If reasoning is open to doubt as much as experience what would bethe consequences for Descartes enterprise? Well, at the very least,Descartes would not be able to conclude that the consequence of anyargument is certain. He might have to rest content with the bare assertion

I am thinking , and perhaps not even that. He would, at any rate, not be theprincipal representative of 17 th Century Rationalism that we know today.

I am suggesting that the only reason Descartes is hopeful of con-structing our knowledge of the world on the basis of the Method of Doubt is that he is treating that method asymmetrically. He takes it toundermine our belief in experience, but not our belief in reasoning. Butthe arguments for doubt are symmetrical and cut against both if they cutagainst one. If even reasoning is open to doubt then no argument issecure, no matter how certain it seemsfor I cannot conclude from thefact that an argument seemscertain that it really is.

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Someone might conclude that I am suggesting that a complete scep-ticism follows from Descartes argument; and that moreover I amendorsing that scepticism. Not so. My view is that the Method of Doubtis in error and that it is this error that leads to conclusions so disastrous.Or to be cute: the Method of Doubt is open to the severest doubt.

3.5 Possible Errors and Evidence of Errors

We may note that Descartes does not believe that there is an Evil Demon,or even that it is remotely probable; he merely thinks it is logically possi-ble that there be one. What weight should be given to that possibilitythat is, how should it affect my belief that there is an external world? Ata minimum Descartes believes that if my experiences could be caused byan Evil Demon rather than an external world of independent objectsthen I cannot be logically certain that there is such an external world. Letus grant him this much. But he is normally taken to go much further thanthis. He is normally taken to believe that we know only that which is cer-tain (one has to say, however, that he himself is never so forthright) andthat therefore we do not know that there is an external world. This is avery strong claim. From the mere possibility of the existence of an expla-nation for our sensory experience other than the usual one, Descartesconcludes that we do not know that the usual explanation holds.

If we try to distil a principle out of this claim it might be the follow-ing:

If we believe an explanation E for X then it cannot be that we know that E holds if there is some other conceivable explanationE* for X.

It is very hard to say that this principle is true. It puts such a stringentcondition on knowledge that it is fairly clear that it rules out the possibil-ity of our knowing anything. If it looks plausible that may be because weare inclined to confuse it with something weaker.

To see what that other thing is, think again of the Unreliability of theSenses Argument. There we cite evidence of error and argue from thoseerrors to the conclusion that we could be in error elsewhere. In a sense theargument is inductiveand to the extent that it seems to be overgeneral-izing it is rather unconvincing. However, the general principle on whichthe argument runs is undoubtedly right: evidence of error does make onesuspicious that such errors could exist elsewhere, hitherto undetected.Thus if I know that I have been fooled by fake paintings before I shouldbe a little worried that this Van Gogh before me is a fakeeven if I have

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no reason to believe that there are any counterfeit Van Goghs in exis-tence. I may even be able to make a judgement of the likelihood of thatevent. But what would someone think if there are no couterfeits in exis-tence at all and we have no idea how it could be done; what estimatecould that person make on the likelihood of the Van Gogh before thembeing a fake? At best we could say that they are not certain that it is not,but it is unlikely that we would say that such a person does not know thatthey are looking at a Van Gogh.

In fact Descartes Dreaming Argument is poised half-way betweenan evidential argument and a mere possibility argument. It cites evidenceof past errorthose times in which we have been asleep and believedourselves to be awakeand, again unconvincingly, tries to suggest thatthere is some likelihood that though we now think ourselves awake wemight be asleep. But the evidence is insufcient; and indeed my wakingthought that I am awake has never proven to be wrong. (This shouldmake us think that when, or if, we ever think ourselves awake when weare dreaming that some part of us knows that it isnt true.) We are simplynot deceived by dreams to the extent that Descartes argument requires.

But suppose, someone might say, that what we were having now is aSuper-Dream , in which the experience has all the features of waking real-ity. How do we know that we are not now having a Super-Dream?

The reply is that we have no idea how to estimate the likelihood of aSuper-Dream, since weve never had onenor to our knowledge hasanyone else. We can conceed that the possibility existsthe logical possi-bilityand that therefore we cannot be certain that we are not having oneright now, but that is about as much as anyone could say.

We could summarize this in the following rubrics: possibility arguments show that we are not certain; evidential arguments show that there is some probability that we are mistaken. In the next section we will look athow the the two different kinds of arguments match up with two differ-ent conceptions of knowledge, both of which can be found in MeditationI nestled uncomfortably alongside one another.

3.6 The True or the Certain

If we reect back on the beginning of Meditation I we see that Descartesmentions the possibility of doing something entirely different to what heends up doing.

I shall at last apply myself earnestly and freely to the generaloverthrow of all my former opinions. In doing so, it will not be

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necessary for me to show that they are one and all false; that isperhaps more than can be done. But since reason has already per-suaded me that I ought to withhold belief no less carefully fromthings not entirely certain and indubitable than from thosewhich appear to me manifestly false, I shall be justied in settingall of them aside, if in each case I can nd any ground whatsoev-er for regarding them as dubitable.

This, as already noted, is a strange passage. He considers the possibility of winnowing out his false beliefs, thus leaving those that are trueandrejects this approach only because it would be more than can be done.And it is clear what this means: it would be an endless labour, becausethere is no short-cut method that would simplify the task. Because of thishe goes on to adopt a completely different project: that of winnowing outthe doubtful to reach the certain. This, fortunately, does have a methodattached to it. And to justify this transition from one undoable project toa separate doable one he says something that seems spectacularlyfalsethat nal sentence above that begins: But since reason has alreadypersuaded me

But suppose that Descartes had taken the rst indicated way; whatwould he have ended with? The answer is: if one winnows out the false

one ends with the true. And since we are considering our beliefs we willend up with our more-probable-than-not true beliefsor in other words,knowledge, under our usual denition. But our only way of winnowingout the false to leave the true is to consider the evidence or reasons we hadfor believing our beliefsand that is just to consider again why webelieve them. This is also Leibnizs view.

Descartes dictum that everything in which there is the leastuncertainty is to be doubted might have been better and moreexactly formulated in the precept that we must consider thedegree of assent or dissent which a matter deserves, or, moresimply, that we must look into the reasons for every doctrine.

Just so (though Leibniz does not point out that this would be to do some-thing entirely different to what Descartes does; it is no mere reformula-tion). But doing this is, we must note, a rather more conservative activitythan the one that Descartes pursues. For if we examine the justicationsfor our beliefs to see which are true we are likely to leave them almostuntouched. For if we hold beliefs then we generally hold them because

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we think them true. A scrupulous examination may cast out some irra-tional beliefs that we holdand we would be well rid of thembut if wehad always tried to hold beliefs for good reasons, there may be very littleweeding to be done. At any rate we are not likely to turn the world upsidedown,

concept of knowledge

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