Frankfurt -- Philosophical Certainty -- The Philosophical Review -- V71n3pp303-327

8/8/2019 Frankfurt -- Philosophical Certainty -- The Philosophical Review -- V71n3pp303-327

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Philosophical Review

Philosophical CertaintyAuthor(s): Harry G. FrankfurtSource: The Philosophical Review, Vol. 71, No. 3 (Jul., 1962), pp. 303-327Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2183430

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PHILOSOPHICAL CERTAINTYAMONG the arguments sedby philosopherso show that itis never reasonable to regard any empirical statement asaltogether certain, one of the most important runs something likethis. An empirical statement is tested by checking predictionsderived from it, predictionswhose falsity would render the state-ment doubtful in some degree. The relevant predictions areinfinite in number, and we can never be certain that the un-checked oneswill turnout to confirmthe statement.Sowe canneverbe altogether certain that the statement is true, for it is alwayspossible that something will happen to make it reasonablefor usto doubt the statement. Norman Malcolm calls this "the Verifi-cation Argument," and he maintains that it is unsound.' While Iam inclined to agreewith him about this, I believe that the pointshe offers against the argument are mistaken. My purpose in thisessayis to illuminate the problemof certaintythrougha discussionof the Verification Argument and of Malcolm's objections to it.

IMalcolm provides the following statement of the VerificationArgument, in which "S" refers to some empirical statement:

I. S hasconsequences.II. The numberof consequences f S is infinite.

III. The consequences f S may ail to occur.IV. If someof the consequences f S were o fail to occur,thentherewould be a reasonabledoubt that S is true.

1 Norman Malcolm, "The Verification Argument," in Max Black, ed.,Philosophical nalysis Ithaca, 1950), pp. 244-298. Rather than clutter the pagesof my essay with numerous footnotes, I have inserted, after quotations in thetext, numberswithin parentheses; numbers between 244 and 298 refer to pagesin "The Verification Argument"; numbers between i8 and 46 referto anotheressay by Malcolm entitled "Certainty and Empirical Statements," Mind, LI(1942), 18-46.

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HARRY G. FRANKFURTV. If at anytimethereshouldbe a reasonabledoubt that S is truethen at no previous ime did anyonemake absolutelycertain

that S is true.Conclusion:No one did make absolutelycertain that S is true[p. 264].

Apparently, Malcolm would accept the conclusion of the argu-ment if he were convinced that its premises are true, for hevindicates the argument of any flaw in its validity. "If all of itspremisses were true," he says, "the ... argument would prove thegeneral proposition that no empirical statement can be conclu-sively established" (pp. 265-266). Now Malcolm finds nothingobjectionable in the first, second, or fourth premise. But he doesobject to premises III and V.Malcolm claims that the fifth premise of the argument is false,and he is clearly correct in this claim. That there is a reasonabledoubt about a statement at one time does not entail that no oneat any earlier time knew for certain that the statement is true.There is a reasonable doubt about many statements concerningancient history, for instance, because we have very meagerevidence for these statements. But this does not exclude thepossibilitythat, at some point in the past, someonehad absolutelyconclusive evidence for some of these statements and knew themfor certain. As Malcolm puts it, there is no contradiction insupposing "thatsome person at one time should possess a body ofevidence that conclusivelyestablishedthat so-and-sowas the case,but that at a later time another person should possess none ofthat evidence but should posses otherevidence on the basis ofwhich it was reasonable to doubt that so-and-so was the case"(P. 258).Although Malcolm does not say so, there is not even a contra-diction in supposing that a person at one time should possessevidence conclusively establishingthat so-and-so was the case, butthat at a later time that sameperson hould possess none-of thatevidence (or only some of it) and should possess otherevidencewhich made it reasonable to doubt that so-and-so was the case.Evidence may be forgotten as well as lost, and if the availableevidence is weak or even negative at one time it may have beenvery strong at an earlier time. So it is a mistake, as Malcolm

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PHILOSOPHICAL CERTAINTrsays, to assume "that if something was accepted as a fact attime t1, but that at time t2 there arose a reasonable doubt as towhether this something was a fact, then it follows that it was notabsolutely verified at t1 that this something was a fact" (pp. 260-26I).

Having established this, Malcolm suggests a way of reformu-lating the Verification Argument so as to avoid the error containedin V. He proposes to strengthen the fourth step of the originalargument by substituting for IV the following statement, IVa,which he accepts as true: "If a sufficient number of the conse-quences of S were to fail to occur then it would be absolutelyconclusive that S is false." He also proposes to replace V by thefollowing statement, Va: "If at any time there should be absolute-ly conclusive grounds that S is false then at no previous timedid anyone make absolutely certain that S is true."

But with IV and V of the original argument replaced by IVaand Va, Malcolm argues that the argument loses its usefulness.This is because IVa "relies on the supposition that a particularstatement, the statement 'S is false,' can be conclusively establishedas true." Here is what Malcolm says about the revised argument:Since one premise assumes that an empirical statement can be conclu-sively established, it would be wrong to say that the revised argument,if its premisses were all true, would prove ... that no empirical state-ment can be conclusively established. No matter what statement wassubstituted for S, premise IVa would assume that the contradictory ofthat statement can be conclusively established. The revised argumenthas this peculiar logical character, that if all of its premisseswere trueit would prove, with regard to any empirical statement, that thatstatement cannot be completely verified, but it would not prove thatno empirical statement can be completely verified [pp. 265-266].I shall not discuss the "peculiar logical character" of the revisedargument. Instead, I shall show that the original argument neednot undergo the revisions that result in its acquiring this peculiarcharacter-that there is a way of reformulating the argumentwhich avoids the error in V, which is not subject to the criticismMalcolm makes of his own reformulation, and which is an accu-rate expression of what is intended by proponents -of the Verifi-cation Argument.

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HARRT G. FRANKFURTTo avoid the error in V, it is not necessary to alter IV at all,but only to substitute for V the following statement, Vb: "If at

any time t2 there should be a reasonable doubt that S is true,then at no previous time t1 did anyone make absolutely certainthat S is true, providedhat theevidenceossessed t t2 includes ll theevidenceossessed t t,." Let me clarify the meaning of Vb.Suppose that at time t4 someone who has a body of evidence(E1) in favor of some empirical statement claims, on the basis ofE1, that the statement is absolutely certain; suppose, in otherwords, that he regards E1 as absolutely conclusive evidence forthe statement in question. Now suppose that at a later time t2someone has another body of evidence (E2) concerning the samestatement, and suppose that (a) E2 includes E1, and (b) it isreasonable, on the basis of E2, to doubt the truth of the statement.Then the claim of certainty made at t, must have been mistaken,and it must also have been a mistake to claim that E1 constitutesabsolutely conclusive evidence for the statement in question. Theevidence in favor of a statement cannot be absolutely conclusiveiffurther vidence would renderthe statementsubject to a reason-able doubt. To say that evidence is conclusive is to say that it issufficient to justify the conclusion based on it no matter whatfurther informationis obtained.The originalpremiseV might have been formulatedas follows:"If at any time t2 someone has a body of evidence (E2) whichmakes it doubtful that S is true, then at no previous time t1 didanyone have a body of evidence (E1) which made S certain."This statement is false, as we have seen, because it does notpreclude the possibility that E1 includes evidence lacking in E2;it does not preclude the possibility that E1 is stronger than E2.But Vb does preclude this possibility, since it specifies that E2containsE1 and that, consequently,E1can be no strongerthanE2.It seems evident, then, that Vb is a true statement.The substitution of Vb for V does not affect the validity of theVerification Argument. It is implied by I, II, and III that E2may contain evidence against the truth of S plus all the evidencein E1 concerning S. Together with IV, this implies that E2 mayprovide reasonablegrounds for doubting S. PremiseVbsaysthatif E2 provides reasonable grounds for doubting S, and if the

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PHILOSOPHICAL CERTAINTYrelation between E1 and E2 is as the first three premises of theargument imply it may be, then no one ever made absolutelycertain that S is true. And the conclusionfollows validly as in theoriginal argument.Moreover, the substitution of Vb for V does not result in theacquisition by the argument of the "peculiar logical character"described by Malcolm as afflicting his revision of the originalargument. Thus, Malcolm has failed to disposeof the VerificationArgument by attacking its fifth premise. For his attack can easilybe met by a revision which leaves the force of the argumentundiminished.

IIRepelling Malcolm's attack on the Verification Argument'sfifth premise does not save the argument from his efforts toimpugn its soundness, for he alleges that the argument involvesother difficultiesas well. Indeed, he offers a criticism of its third

premise which he considersto be even more important than hiscriticism of V. To showwhat is wrong with the third premise,hesays, "is to expose the most important error in the VerificationArgument" (p. 292).Malcolm maintains that "in order for the Verification Argu-ment to be a valid deductive argument... III must be understoodin such a way that it implies the following proposition, which Iwill call 'I11a': 'It is not certain that the consequencesof S willoccur' " (p. 267). If III does not imply IIIa, he points out, thepossibility remains that it is certain that the consequences of Swill occur, and as long as this possibility remains the conclusionof the VerificationArgument cannot validly be deduced from itspremises.Proponentsof the Verification Argument seem to have thoughtthat I11a s implied by the following statement, which Malcolmcalls "1112": "No statement,p, which expressesa consequenceofS is entailed by any statement, q, which states the grounds forholding that p is true." For instance, in a passage quoted byMalcolm, C. I. Lewis says this:My belief must imply as probable, anythingthe failure of which Ishouldacceptastending o discredit his belief.... Suchfuturecontin-

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HARRT G. FRANKFURTgencies implied by the belief are not such that failure of them can beabsolutely precluded in the light of prior empirical corroborations ofwhat is believed. However improbable, it remains thinkable that suchlater tests could have a negative result. Though truth of the beliefitself implies a positive result of such later tests, the evidence to datedoes not imply this as more than probable ... [quoted p. 286].When Lewis says that the failure of the consequences of hisbelief to occur is not "absolutely precluded in the light of priorempirical corroboration of what is believed," he seems to besaying that the evidence for thinking these consequences willoccur does not entail their occurrence. This interpretation of hisposition is suggested again by his statement that the evidence thatthe consequences of his beliefwill occur "does not imply this as morethan probable." Lewis apparently bases his claim that it is notcertain that the consequences of his belief will occur on the factthat there is no deductively compelling evidence that they willoccur, but only evidence which renders their occurrence probable.In other words, Lewis apparently regards IIIa as established byIII2.Malcolm accepts III2 as a true statement. The soundness ofthe Verification Argument, then, turns on the question of whetheror not III2 entails IIIa. That is, it turns on the question of whetheran empirical statement can be certain if it is not entailed by theevidence for it, or whether any evidence can properly be regardedas conclusive which does not entail the conclusion based upon it.Malcolm's opinion is that III2 does not entail IIIa, but hisargument in behalf of this opinion is unsatisfactory.

In order to facilitate discussion of these statements and theirrelationships, Malcolm uses "R" to refer to the statement of thegrounds for believing that the consequences of an empiricalstatement will occur; and he uses "c" to refer to the statementthat those consequences will occur. Thus, II2 may be expressedas "R does not entail c"; and IIIa may be expressed as "It is notcertain that c." Now he acknowledges that "there is a tempta-tion" to believe that II12 implies IIIa and that "it is easy to bemisled" into thinking that it does. However, he asserts that "itdoes not . . . follow from the fact that R does not entail c eitherthat it is not certain that c is true or that R does not state the

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PHILOSOPHICAL CERTAINTYgrounds on the basis of which it is certain that c is true" (pp.277-278).

In view of the ease with which he thinks it possible to be misledabout the relation between II"2 and IIIa, Malcolm offers sur-prisingly little in the way of support for his view of the relation.Here is the entire passage in which he explains why "'2 does notimply IIIa:Whether it is certain that c is true depends upon the state of theevidence with regard to c. The statement "R does not entail c" saysno more about the state of the evidence with regard to c than doesthe statement "'c is false' is not self-contradictory." Both statementsare irrelevant to that matter. The statement "The fact that R is truemakes it absolutely certain that c is true" is in no way contradicted bythe statement "R does not entail c." The two statements are perfectlycompatible with one another. One statement describes the evidenceconcerning c. The other describesa logical relationship between R and cof which one could be aware even though one knew nothing whateverabout the state of the evidence concerning c. The fact that R does notentail c provides no ground for doubting that c is true. It is a mistaketo suppose that because it is possible that c is false even though R istrue, in the sense of "112, that therefore "It is possible that c is false,"where these latter words imply that it is not quite certain that c is true[p. 278].A number of the statements in this passage are merely reformu-lations of the claim that "'2 does not imply IIIa. In fact, Malcolmhere offers only one point in support of his claim-the point thatthe statement "R does not entail c" is irrelevant to any questionabout "the state of the evidence" with regard to c.

But what can we make of this point? The statement "R does notentail c" is obviously about the evidence for c. It says that theevidence does not entail c, and one question about the state ofthe evidence for c is the question of the relation between c andthe evidence for it. So how can III2 be supposed to be irrelevantto questions about the state of the evidence for c?

Suppose that c were not an empirical statement but a mathe-matical one, and suppose that R were a statement of the premisesin a purported proof of it. Then, as Malcolm would doubtlessagree, the statement that R does not entail c would not only be

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HARRT G. FRANKFURTquite relevant to the state of the evidence with regard to c;it would generally be supposed to imply that it is not certain thatc.In mathematics, when the evidence for a statement does notentail statement, this is generally taken to indicate that thestatement has not been proven, and that its truth is not certain.It is not only in mathematics that this is the case. Malcolm's ownefforts to raise a doubt about the truth of IIIa consist preciselyin an attempt to show that IIIa is not entailed by any true state-ment offered as evidence for it. In his own discussion,Malcolmsupposes that the fact that a statement is not entailed by theevidence for it is quite relevant to the question of whether or notthe statement is certain.Of course,Malcolm evidently believes that empirical statementsdiffer from other statementsin this respect. He believes not onlythat an empirical statement may be certain even though there isno deductively compelling evidence for its truth, but also that thelack of such evidence is irrelevant to questions about the state ofthe evidence with regard to an empirical statement. He may becorrect in believing this; nothing I have said demonstratesthathe is not. But he cannot establish the correctness of his beliefmerely by asserting it and without explaining how it is thatempirical statements come to differ in this respect fromstatementsof other types.Although Malcolm does not adduce it, there is an argumentwhich might be thought to support his claim that III2 is irrelevantto questions about the state of the evidence with regard to c.Since III2 is true no matterhowmuchevidence has been obtainedin favor of c, it is useless to know that III2 is true when onewishes to know how much evidence there is for c. And therefore,it might be argued, the truth of III2 is irrelevant to questionsabout the state of the evidence with regard to c. But Malcolmcannot make use of this argument without begging the questionof the soundness of the Verification Argument.The argument might be useful to Malcolm if there were aproblem of weighing evidence in order to distinguish cases inwhich it is certain that c from cases in which it is not certain thatc. But the very question at issue in the Verification Argument iswhether there is any such problem, and there is no such problem

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PHILOSOPHICAL CERTAINTYif the VerificationArgument is sound. For the VerificationArgu-ment purports to establish that no empirical statement can becertain no matter how much evidence for it there may be, andthat the evidence for an empirical statement is never conclusiveno matter how weighty the evidence is.Knowing that III2 is true does not, to be sure, enable one toknowwhetherthereis a greatdeal of evidence for c or only a little.But knowing III2 may still enable one to know that the evidencefor c is inconclusive, if the fact that the evidence is inconclusivedoes not depend on how much evidence there is. Thus, theargument I have describedcannot be used without assumingthefalsity of what the Verification Argument seeks to establish, andit would accordingly be fallacious to use it to support the viewthat III2 does not entail IIIa.In section V, I shall consider whether any other argumentoffered by Malcolm provides adequate support for the claimthat III2 does not entail IIIa, or for his claim that IIIa is false.But none of his argumentswhich I have discussedso far succeedsin any way in showingthat the VerificationArgumentis unsound.

IIIAnother charge that Malcolm levels against proponentsof theVerification Argument is that they misuse such expressions as

"certain,""absolutely certain," and "theoretically certain." Inshowing that the arguments with which he supports this chargeare inconclusive, I shall at the same time be preparing the wayfor the next section of my essay, in which I attempt to clarifythe meanings of expressionssuch as "certain."To call attention to what he regards as a misuse of language byproponents of the Verification Argument, Malcolm begins witha question: "What state of affairs, if it could be realized, wouldthey call 'theoretical certainty'?" (p. 297). The answer to thisquestion, he says, is that "it would be 'theoreticallycertain' thata given statement is true only if an infinitenumber of 'tests' or'acts of verification' had been performed" (p. 297). But it islogically impossible for an infinite number of tests to have beenperformed."Therefore,"Malcolm concludes, "thesephilosophers

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HARRY G. FRANKFURTmisuse the expression 'theoretically certain.' What they call'theoretical certainty' cannot be attained even in theory"p. 297).

Malcolm's conclusion that the expression "theoretically cer-tain" is misused by proponents of the Verification Argument isapparently based on the premise that they use the expression insuch a way that it is logically impossible for it to be correctlyapplied to any statement. At any rate, this is the only evidenceMalcolm gives for his conclusion. This premise, n turn, is support-ed by his statement that proponents of the argument use theexpression in such a way that it can be correctly applied onlywhen an infinite number of tests has been performed,a circum-stance whose occurrence is logically impossible.Now if they are taken strictly, he statements in which Malcolmgives the evidence for his conclusion are false. No proponent ofthe Verification Argument has held that "it would be 'theoreti-cally certain' that a given statement is true only if an infinitenumber of 'tests' or 'acts of verification' had been performed."What they haveheld is that it would be theoretically certainthat a given empiricaltatement is true only if an infinite numberof tests had been performed. Lewis and Carnap, as well as otherproponentsof the Verification Argument, have insistedrepeatedlythat there are many statements-for instance, statements oflogical truths, and "terminating judgments" or "protocolstatements"-which may be theoretically certain without aninfinite number of tests having been performed.To be sure, proponents of the Verification Argument arecommitted to the view that it is logically impossible for theexpression "theoretically certain" to be applied correctly to anyempirical statement. Indeed, it is precisely this view which theyseek to establish by their argument. But there is no inevitablemisuse of language in arguing that an expressionwhich is appliedcorrectly in some circumstances nvolves a contradictionwhen it isappliedin othercircumstances.Since proponentsof the VerificationArgument admit the logical possibility of circumstances n whichthe expression in question would be applied correctly, they donot appear to be open to the charge that they have provided itwith no conceivable correct use.These remarks depend on the supposition that Malcolm

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PHILOSOPHICAL CERTAINTYintended his statements to be taken strictly, but it is quite likelythat he did not. Instead of asserting falsely that proponents ofthe argument use words in such a way that theoretical certaintycannot be attained even in theory, Malcolm probablyintended toassert this: "When proponents of the Verification Argumentclaim that it is logically impossible for any empiricaltatement tobe theoretically certain, they are using the expression theoreticallycertain' in a special sense, and in that sense it is logically impos-sible foranystatementto be theoretically certain."Malcolm woulddoubtless admit that proponents of the Verification Argumentsometimes use the expression n otherenses, in which it is logicallypossible for it to be applied correctly. But he probably wished tosuggest that in the specialsense in which the expression is usedin the statement that no empirical statement can be theoreticallycertain, it is also true that no statement of any kind can be theo-retically certain.Supporting my conjectures s the fact that Malcolm has arguedthat the meaning of the expression in question (or a similarexpression) is not the same when philosophers assert that noempirical statement can be theoretically certain as it is whenthey apply the expression to statements of logical truths or toprotocol statements. In an article published in Mind in 1942,Malcolm says that "there are three senses of the expression'it iscertain' which are important" for the problem ofwhether empir-ical statements can ever be certain (p. 26). In the same article,he says: "When it is said that a sense-statement [i.e., protocolstatement] is certain, what this means is that it does not makesense to doubt or question it. And when it is said that an a prioristatement is certain, what this means is that the negative of it isself-contradictory" (p. 35). He also observes that "the doctrinethat empirical statements are never known with certainty hasbeen held by various philosophers, because these philosophershave been led to attach a self-contradictory meaning to theexpression'it is certain that,' as applied to empirical statements"(p. 46). Apparently, Malcolm believes that when philosophersuse the expression "theoretically certain" or similar expressionsin the course of the Verification Argument, they use it to mean"confirmedby an infinite number of tests."

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HARRY G. FRANKFURTIf he were correct, the expression would have a self-contradic-

tory meaning on such occasions and this would make plausiblethe view that it is misused. So the question is whether philosopherswho say that no empirical statement can ever be certain do meanby this merely that no empirical statement can ever be confirmedby an infinite number of tests. So far as I can see, Malcolmoffers no evidence which establishes that they mean this.

On the other hand, he does offer evidence that they sometimesuse the expression "theoretically certain" or similar expressionsto mean "has a self-contradictory negative." Since it will be ofinterest to consider what this evidence is like, I shall quote fromthe Mind article in which it is offered:Let us turn for a moment to the philosophers who say that a prioristatements can be known with certainty, but not empirical statements.They may argue the point by saying that ... the negative of an a prioristatement is self-contradictory.Their declaration. . . is a disguised rec-ommendation that the phrase "it is certain that" be applied to a state-ment if and only if the statement has a self-contradictory negative....So what they are really saying is that no empirical statement has aself-contradictory negative, while every a priori statement does....And this is an absolute tautology. For it is the defining characteristicof an a priori statement that it has a self-contradictory negative, andit is a defining characteristic of an empirical statement that it does nothave a self-contradictory negative [pp. 34-35].The philosophers in question do not, as Malcolm suggests, declarethat "only a priori statements can be known with certainty."Generally, they say that protocol statements can also be knownwith certainty. But deferring this point for the moment, considerthe following passage from the same article, in which Malcolmattempts to explain another use of the expression he is examining:When the philosopher says that sense-statementscan be known withcertainty, but that empirical statements cannot, what he is doing isrestricting the use of the phrase "known with certainty" in such a waythat a statement will be capable of being known with certainty, if andonly if it is an incorrigible statement. . .. But then his pronouncementthat sense-statements can be known with certainty, but empiricalstatementscannot, is a plain truism.For it amounts to saying that sense-statements are incorrigible, and empirical statements are corrigible.

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PHILOSOPHICAL CERTAINTrAnd incorrigibilitys the definingcharacteristic f sense-statements,while corrigibilitys a definingcharacteristic f empiricalstatements[PP.33-34].In each of these passages, Malcolm describesa philosopherwhocompares empirical statements with statements of another class,who asserts that empirical statements cannot be certain butstatementsof the other class can be certain, and who gives as thereason for his assertionthe fact that empirical statementslack acharacteristicpossessed by members of the other class. In eachcase, the characteristicis one which it is logically impossibleforempirical statementsto possessbut which is the defining charac-teristic of the other class.And Malcolm assertsthat in each casethe characteristicmentioned is one which a statement possessesif and only f it is certain.

At first glance, it may appear quite plausible for Malcolm tomake this last assertion. After all, if a philosopher says thatstatements of one type are uncertain merely because they lacksome characteristic,this suggestsstrongly that he regardsposses-sion of the characteristic as a necessary condition for certainty;and if the philosopher says that statements of another type arecertain merely because they have the characteristic,this suggestsstrongly that he regards possession of the characteristic as asufficient condition for certainty. If possession of some charac-teristic is both a necessaryand a sufficientconditionfor certainty,it is not unreasonableto supposethat it is equivalent to certainty,and that its name is a synonym for "certain."

Yet it seems to me quite likely that Malcolm has misrepre-sented the position of the philosophershe criticizes. In describingthose who claim that a priori statements can be known withcertainty but not empirical statements, he supposes that theyoffer as the reason for the uncertainty of empirical statements,that such statements do not have self-contradictory nega-tives. In describing those who claim that protocol statementscan be known with certainty but that empirical statementscannot, he supposes that they offer a different reason for theuncertainty of empirical statements, namely, that such state-ments are not incorrigible.But I doubt that any philosopherever

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HARRYoG. FRANKFURTintended to offer as the reason for the uncertainty of empiricalstatements the fact that they do not have self-contradictorynegatives; and I doubt that any philosopher ever intended tooffer as the reason for the uncertainty of empirical statementsthe fact that they are not incorrigible.For, to return to the pointwhose considerationwasdeferreda little while ago, no philosopherhas ever suggestedthat a priori statements are uncertain becausethey are not incorrigible; and none has ever suggested thatprotocol statements are uncertain because they do not haveself-contradictorynegatives. Yet it would be perfectly natural forthem to do so if they believed what Malcolm ascribes to them.Another interpretation of their position is available, and toconsider it will prove fruitful. Let us suppose, then, that thephilosopherswho argue in the way Malcolm describesintend toassert only that having a self-contradictorynegative and beingincorrigible are two sufficientconditions for certainty but thatneither of them is necessary for it. Then the possibility remainsthat they use the expression "theoretically certain" consistentlyand not, as Malcolm suggests, in three different senses. Theirposition would be that there are various ways in which a state-ment may attain theoretical certainty; that is, various conditionsmay satisfy the general criteria of theoretical certainty. Theirclaim that no empirical statement can ever be theoreticallycertain would rest on the belief that it is logically impossible forany empirical statement to satisfy hese general criteriaof theoret-ical certainty in any way at all. This interpretation seems quiteconsistent with what the philosophersin question say about theproblem of certainty.It does, however, burden them with a serious failing. That noempirical statement can be certain cannot be establishedmerelyby showing that empirical statements do not satisfy the generalcriteria of theoretical certainty in the same way that thesecriteria are satisfied by a priori statements. Nor can it be estab-lished by adding to this the fact that empiricalstatements do notsatisfy these criteria in the way they are satisfied by protocolstatements. For it remains open that there are other ways,besides these two, in which the general criteria of theoreticalcertainty can be satisfied. Clearly, the conclusion can only be

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PHILOSOPHICAL CERTAINTYestablished by showing that these general criteria cannot besatisfied by empirical statements in any way at all. But thephilosophers n question have never, to my knowledge, stated thegeneral criteria of theoretical certainty which they employ.Until they do so, they cannot hope to show that the criteriacannot be satisfied in any way by any empirical statement.It is not only the philosophers Malcolm criticizes, however,who are guilty of failing to say what they mean by expressionssuch as "theoretically certain." Indeed, one of the most strikingand curious aspects of the whole philosophical controversy overcertainty is that few of the participantsin it have ever attemptedseriously and precisely to say what certainty is and what itsgeneral criteria are. Lewis does not do so, and neither doesCarnap. Nor, for all their concern with clarifying the uses ofexpressions,do Malcolm or Moore. In the next section of myessay, I shall attempt to shed some light on these questions.

IVMalcolm is anxious to show that empiricalstatementsmay becertain, while other philosophers are equally anxious to showthat they cannot be. But what precisely is at issue in this contro-versy? What is the difference between being certain and being

uncertain? It is not of much use to answer by saying that astatement is certain if and only if it is supported by conclusiveevidence, for this only shifts the focus of attention to anotherexpressionwhose meaning is equally unclear. Instead of searchingfor expressionssynonymousto or correlativewith expressions ike"certain,"we must make our understandingmore concrete.I suggest that the "cash value" of a claim of certainty lies inthe claimant's willingness to take the risks he associates withaccepting the statementsfor which he claims certainty.Wheneversomeone understands a statement, he supposes that there aresome consequencesof action which will occur if the statement istrue and otherswhich will occur if it is false. If he adopts a beliefin the statement, therefore,he stakes something on its truth. Anerror on his part may result in nothing worse than trivial disap-

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HARRY G. FRANKFURTointment, mild embarrassment or minor inconvenience; or itmay have consequences far more grave than these. But there isalways somepenalty associated with a given error, even though apersonmaking an errormay escape the penalty and even thoughan error may also bring rewards.When a person adopts a belief, he accepts whatever risks herecognizes of being made to suffer the penalty for error. He may,of course,accept these riskseven though he believes the statementin question to be probably false. It may even be reasonable forhim to do so, if the alternative carries greater risks or if acceptingthe risk brings closer the attainment of some otherwise unlikelyreward. It is often reasonable to make a bet even though thereis not much chance of winning it. Thus, a person's willingness totake the risks he associateswith some statement does not meanthat he regardsthe statement as certain, or even that he regardsit as probably true.But what about the converse of this? Is regarding a statementas certain compatible with being unwilling to risk what arethought to be the penalties for being mistaken about the state-ment? Surely, a person who regards some statement as certaincan have no expectation of suffering a penalty arising from thestatement's falsity. It makes no sense for a person to claim thathe knows something for certain and yet at the same time toconfess, explicitly or by his actions, that he fears he may bemistaken. Why, then, should he be unwilling to take the risk?He might be unwilling to take the risk, despite his certainty,because he thinks it immoral, or because there is nothing to begained by it, or because there is more to be gained in anotherway. But consider the following hypothetical situation. A personhas a number of alternative ways of acting, only one of which isappropriate if he believes that some statement, T, is true. If hechooses any other alternative he suffersP-a penalty. If he actsas if T is true, then the consequencesare the same as for the otheralternatives except that he suffers no penalty if T is true andsuffers a penalty greater than P if T is false. Suppose that theperson is aware of all this, that he has no moral compunctionsabout any of the alternatives as such, and that he is not self-destructive. In such a situation, the person cannot be certain of

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PHILOSOPHICAL CERTAINTYT if he does not choose the alternative appropriateonly if T istrue.

If a person regardsa statement as certain, he is willing to takethe risks associatedwith the statement if there is nothing to begained by refusing to do so.2 Now it is reasonableor a person toregard a statement as certain only if his willingness to take therisks associatedwith accepting the statement is justified by theevidence he possesses n favor of the statement. And a statementis certain only if it would be reasonablefor anyone possessingtheevidence available for it to regard the statement as certain. Itwill be noted that none of these remarksconstitutesa definition,sincenone describessufficientconditions,but only necessaryones.They do, however, suggest an important relation betweencertainty and risk taking. That this relation exists is, I believe,implicit in the ordinary usage of terms like "certain," since it ischaracteristic of that usage that no one can sensibly claim toregard something as certain and at the same time fear that hemay be mistaken.As I hope to show, examination of this relationis helpful both in understandingthe Verification Argument andin evaluating some of Malcolm's critcisms of that argument.Before proceedingto show this, however, I want to call attentionto several facts which, while familiar and relevant, seem to havebeen overlookedat times in philosophicaldiscussionsof certainty.Sometimes a person regards a statement as being certain andthen discovers evidence against it which compels him to giveup as mistaken the claim that he knew it for certain. There isnothing noteworthy in this. But it is also not uncommon for aperson to claim at one time that he knows something for certainand then to abandon this claim at another time, even though hisknowledge of the relevant evidence is the same at both times. Itis noteworthythat apparent inconsistencyof this sort need not beunreasonable. When very little is at stake it is only natural toclaim all sortsof things, and then to become more cautious as thepenalties for error increase. What seems unsusceptibleto reason-able doubt under one set of conditions may properly appear to

2 Instead of repeating this qualification endlessly in what follows, I requestthe reader to assume it whenever it is appropriate.319


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HARRY G. FRANKFURTbe quite a risky matter when the danger of error has to be takenvery seriously because the stakes are high. A doubt that seemsfantastic or absurd when the stakes are relativelytrivial may bequitenaturaland appropriate n other circumstances,even thoughthe relevant evidence remains constant.Anotherpoint is this. When a certaintyclaim is revokedbecauseof new evidence, the original claim of certainty is generallyregarded as having been mistaken. This is not always the case,however, when a certainty claim is revoked because of a changein the anticipated penalty for error. Frequently,in such cases,theoriginal claim of certainty is not regarded so much as havingbeen mistaken but as being no longer relevant in the changedcircumstances.The explanation of these facts is, I think, as follows. Certaintyis generally thought to be susceptible of variations in degree:people say that statements are "sufficiently certain," "morecertain than ever," "quite certain," and so on. If a personregardsone statement as being more certain than another he naturallythinks it reasonable to risk more on the truth of the one state-ment than he thinks it reasonable to risk on the truth of the other.We can imaginebetsbeing madeon the truth ofvariousstatements.It would make no sensefor a personto be willing to bet one amounton a statement he regards as rather uncertain and to be willingto bet only a lesser amount on a statement he regardsas certain,assuming that all bets are made at the same odds and that theperson is interested only in maximizing the chances of winninghis bet. Indeed, a plausibleway of testingwhetheror not a personregards one statement as more certain than another is to deter-mine whether or not he is willing to stake more on the truth ofthe one than on the truth of the other. If he were not willing todo so, it would be difficult to understand what he meant byclaiming that the one is more certain than the other.People frequently make certainty claims without indicatingexplicitly the degree of certainty they are claiming; they say thatsomething is certain without saying how certain they think it is.At other times, a degree of certainty may be indicated explicitly,or it may be explicitly indicated that the degree is at least of aparticular order of magnitude. For instance, an attorney might

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PHILOSOPHICAL CERTAINTYsay this to a prospective witness:"You say it is certain that Smithwas present at the gathering on the evening in question. Doyou regard it as being so certain that you are willing to assertit in court under oath, knowing that your testimony may beresponsible for sending a man to prison?" Here, the attorneyis not attempting to find out precisely how certain the prospec-tive witness thinks his statement to be. He is only trying todiscover whether the witness thinks it certain enough to be will-ing to risk on its truth the penalties indicated-for instance, thepenalty of being responsible for sending an innocent man toprison.Claims that a statement is certain are best understood as beingelliptical-as being claims that the statement is certain nough ojustify a willingnesso risksuch-and-suchn the truthof the statement.Obviously, the evidence may be weighty enough to justify awillingness to take this risk without being sufficiently weighty tojustify a willingness to take a greater risk. And the statementthat the evidence is not weighty enough to justify a willingness totake the greater risk does not contradict the statement that it isweighty enough to justify a willingness to take the lesser risk.Let me illustratesome of the points I have been making. Thereis an object lying before me on my desk, and I believe it to bemy notebook. I habitually keep my notebook where the objectrests, I remember putting my notebook there not long ago, andI can plainly see, among numerous familiar signs, my own signa-ture near the top of its cover. If my wife Marilyn should ask mewhere my notebook is, I would assertwith no qualms at all thatit is here on my desk. If she asked me to make certain, becauseshe suspected that I had left the notebookin the car this afternoon,I wouldjustifiably tell her that I was quite certain of it. It wouldnot occur to me to doubt that I had sufficient evidence for thisconfident reply.But suppose that her question had a graver import. Supposeshe told me that a great deal depended on my being certain ofmy answer. Imagine her saying that my notebook had beendiscovered to possess remarkable properties of some kind, andthat she has just learned that our lives and the lives of manyothers-perhaps even the survival of a free civilization-depend

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HARRT G. FRANKFURTon my answer to her question. Imagine that I accept thesestatements of hers and do not take them to be part of some sillyjoke or insane fantasy. Then surely it would reasonable for me tobe far more hesitant in my reply, even though I have exactly thesame evidence as previously for believing that my notebook islying in front of me.Were such horrendous consequences due to follow a mistakeon my part, I would begin to consider possibilities that wouldnot even have entered my mind if my wife's question had beenonly a casual one. What possibilitiesI considered would dependpartly on the richness of my imagination and partly on the cir-cumstances in which the question was asked, insofar as thesegave me some clue as to the source from which the danger oferror might arise. In certain circumstances, for instance, Imight be preoccupied with the techniques of deception availableto political enemies. In others, perhaps, I would even considerthe possibility that beings from another planet, with an incom-prehensibly profound capacity for manipulating the laws ofnature, had been active without my knowledge. In any case, Ishould be extremely reluctant to risk so much on my answer aslong as I could conceive any way at all, however implausible orfantastic, in which I might be mistaken. Indeed, if I could do sowithout incurring severe penalties, I would decline to answer thequestion at all.

In this illustration, my first claim of certainty was a reasonableone. Moreover, the subsequent events described do not show thatthis first claim was mistaken, even though they do result in areasonable refusal on my part to repeat the claim. To the pre-sumably casual question-"Are you certain of the location ofyour notebook?"-the correct answer was affirmative, and itscorrectnessis not impugned by the fact that the same responsewas not reasonable when the question was no longer thought tobe such a casual one. For there is a difference in how the twoquestionswere understood,even though both were expressed inthe same words. The first question was understood as askingwhether I was certain enough to take the minor risks generallyassociated with being wrong about such things as the locationsof inconsequential objects. The second was understood as asking322


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PHILOSOPHICAL CERTAINTrwhether I was willing to take far greater risks on the same evi-dence.

VThis discussion of the relation between certainty and risktaking suggestsa way of conceiving the highestdegree of certainty.A statement enjoys the highest degree of certainty only if it issupported by evidence which justifies a willingness to risk thegreatest possible penalty on the truth of the statement. For aperson to regard a statement as being certain in the highestdegree, he must be willing to risk anything n its truth. If there issomethinghe is unwilling to risk on the truth of a given statement,it is clearly possible to imagine him regarding some other state-ment as more certain than the given one-namely, some otherstatement on which he is willing to risk what he is unwilling torisk on the first.Now the expression"absolutely certain" is not ordinarilyusedin such a way that to claim some statement is absolutely certainimplies that there is no penalty that the claimant is unwilling torisk on the truth of the statement. Whether consciously or not,one who claims absolute certainty often implies no more thanthat he is willing to risk on the statement in question all that hewould normally expect to have to risk on it. I propose to use the

term "philosophical certainty" to refer to the highest degree ofcertainty. In offering a criterion for his highest degree of cer-tainty, I believe I have preserved the standard for measuringdegrees of certainty that is implicit in the ordinary usage ofterms like "certain."In my opinion, when proponentsof the Verification Argumentmaintain that no empirical statement can be certain, they meanthat none can be philosophically certain; they do not intend todeny that empirical statements may enjoy lesserdegrees of cer-tainty. I think they also have philosophical certainty in mindwhen they discuss the certainty of a prioristatementsor protocolstatements.Thus, I believe they use the term "certain" consist-ently in the sense of "philosophicallycertain" and not in severaldifferent senses.They are concerned with the general question of

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HARRr G. FRANKFURTthe conditions in which it is reasonable to regard a statement asphilosophicallycertain, and with the more particularquestion ofwhether there is any way in which an empirical statement cansatisfy these conditions.Assuming that this interpretationof the VerificationArgumentis correct,do any of Malcolm'sobjectionssucceedin underminingthe argument? In addition to the objections I have alreadyexamined, Malcolm observes that if the Verification Argumentwere sound, it would always be a mistake to claim certainty foran empirical statement, and he points out that such claims arefrequently made in the ordinary course of life and frequentlyaccepted as reasonable and correct. This shows, in his opinion,that III2 does not entail IIIa-that is, that an empiricalstatementmay be certain even though it is not entailed by the evidencefor it. For if III2 did entail IIIa, the VerificationArgumentwouldin his view be sound, and the argumentcannot be sound becausethat would involve the absurdity that people are always wrongwhen they claim to know some empirical statement for certain.But the undoubted fact that people frequently claim correctlyto know empirical statements for certain does not mean thatthey ever regardsuch statementsas philosophicallycertainor thatthey would ever think it reasonableto do so. It is not obvious thatpeople commonlyclaim empiricalstatementsto be philosophicallycertain, and if they do not then the ordinary usage of termslike "certain" is not all relevant to the position maintained byproponents of the Verification Argument. In fact, it is verylikely that people ordinarily claim to be certain of empiricalstatements without being aware that their claims are elliptical,and that they expressby these claims only that they are certainenough of various statementsto stake on them the limited penal-ties they suppose to be associatedwith them.

On the whole, people do not think in terms of philosophicalcertainty but in terms of lesser degrees of certainty. When con-frontedwith a question a personmay try to estimate the penaltiesfor giving a wrong answer, but he does not normally take intoaccount whether or not he would be willing to risk an answer ifthe penaltieswere much greaterthan these. A personmay believehe regards a statement as quite certain without realizing that324


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PHILOSOPHICAL CERTAINTYthere is some penalty he would not be willing to risk on hisbelief in its truth. And when someone thinks there is no reasonableground for doubting the truth of a statement, he may be correctthat no grounds for doubting it are reasonable in the circum-stances in which he finds himself. Nonetheless it may be thatgrounds for doubting the statement would be reasonable inother circumstances, n which a great deal depended on avoidingerror.Indeed, it is not at all easy for someone to know either that hehimself or that another regards a statement as philosophically cer-tain. For it is generally very difficult to knowwhat a person wouldor would not be willing to do when the stakes are very high-ashigh as can be imagined-and when the alternatives are unlikewhat is ordinarily encountered in life. There is no reason forsupposingthat the ordinary man is competent to decide questionsof philosophical certainty, since he is altogether without expe-rience in making such decisions.

That the ordinary usage of terms like "certain"is irrelevant tothe Verification Argument does not, of course, mean that theVerification Argument is sound. Nor does it mean that Malcolmis wrong in his view that III2 does not entail IIIa, for his viewmay be correct even if his attempts to establish it fail. I confessthat I cannot see clearly whether Malcolm is right or wrongabout this. While admitting that his view may be correct, how-ever, I wish to make a few remarkswhich suggestthat it may bemistaken.The question is whether a statement can be philosophicallycertain although it is not entailed by the evidence for it. Now ifa statement is not entailed by the evidence for it, it is possible toconceive circumstances in which, even with this evidence, itwould be reasonable to regard the statement as false. The forceof Malcolm's denial that III2 entails IIIa derives from the factthat it is often unreasonable to take these conceivable circum-stances into account. In the ordinarycourse of life it is unreason-able to take into account such logical possibilities as that thelaws of nature may change or that there are forces operating inthe universe with which we are unacquainted and which arecapable of producing effects altogether outside our previous

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HARRr G. FRANKFURTexperience. To take such possibilities into account would beunreasonablebecause it would cripple our capacity for action.

But philosophical certainty is not greatly relevant to the practi-cal demands of life, since the necessity to act probably neverrequires a decision about philosophical certainty. The problemof making such a decision is a philosophical problem, not apractical one. However, it is possible to imagine being faced withthe necessity of deciding whether or not a statement is philosophi-cally certain. Suppose I am offered the following bet. If I assertincorrectlythat some empirical statement is true (or false), E willoccur, where "E" refersto what I regard as the greatest possibleevil. If I assertcorrectlythat the statement is true (or false), thenE will not occur. In all other respects the consequences of acorrect answer and of an incorrect one will be identical.Obviously the bet is an unfair one, since I have nothing togain by taking it and everything to lose. But if my opinion of thestatement's truth-value is correct, I can take the bet and losenothing. Now suppose I regard the truth (or falsity) of the state-ment as philosophically certain. Then I can have no expectationof losing, and if I were to decline the bet it would have to be forreasons altogether extraneous to the likelihood of winning orlosing it. If an empirical statement can be philosophically certain,even though it is not entailed by the evidence for it, then theremay be situations in which the only reasons for declining a betsuch as this would be reasons having nothing to do with the like-lihood of winning or losing the bet.If the evidence that the bet would be won leaves open thelogical possibility that it would be lost, would not that aloneprovide reasonable grounds for declining to take the bet? IfMalcolm believes that an empirical statement may be philosoph-ically certain even though it is not entailed by the evidence forit, he must suppose that the answer to this question is negative.While this answer may be correct, it is surely not obviouslycorrect, and none of Malcolm's arguments supports a negativeanswer to the question. The evidence that the bet would bewon might be so strong that only a change in the laws of naturewould result in its being lost. But if the stakes were high enough,

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PHILOSOPHICAL CERTAINTTit would not be implausible to suggest that even this possibilityought to be taken into account and that it would be unreasonableto accept the bet in view of the logical possibility of losing it.

HARRY G. FRANKFURTHarpurCollege

Documents

Frankfurt -- Philosophical Certainty -- The Philosophical Review -- V71n3pp303-327