theaetetus on how we think

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The "Theaetetus" on How We Think

Author(s): David BartonSource: Phronesis, Vol. 44, No. 3 (Aug., 1999), pp. 163-180Published by: BRILLStable URL: http://www.jstor.org/stable/4182617 .Accessed: 18/02/2011 10:42

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The Theaetetus on how we ThinkDAVID BARTON

ABSTRACTI argue that Plato's purposein the discussion of false belief in the Theaetetus isto entertainand then to rejectthe idea thatthinkingis a kind of mentalgrasping.The interpretationallows us to make good sense of Plato's discussion of 'other-judging' (189c-190e), of his remarksabout mathematicalerror(195d-196c), andmost importantly,of the initial statement of the puzzle about falsity (188a-c).That puzzle shows that if we insist on conceiving of the relation between thoughtand its objects on the model of holding or grasping somethingin our hands, wewill be unable to account for the possibility of false identity judgments:For noone who is literally grasping two things in his hands would seriously entertainthe idea that one of the things is numericallyidenticalwith the other.

At Stephanus page 187 of the dialogue bearing his name, Theaetetus pro-poses his second definition of knowledge, that it is true belief (a&XniO50'a). He contrasts this with the proposal that all belief counts as know-ledge, which he says cannot be right since there are, of course, falsebeliefs. But Socrates professes not to understand how there could be sucha thing as falsity, and he suggests that they pause to discuss the problem.He then lays out a brief and puzzling argument which allegedly showsthat there can be no such thing as false belief. Plato takes this argumentseriously, spending twelve pages and considerable ingenuity and imagina-tion in an ultimately unsuccessful attempt to answer it. Yet it is not at allclear how we are meant to understandthe key moves in the argument, andconsequently it is not clear exactly why or how it is thought to threatenfalsity. Recently, scholars have suggested that we can understandPlato tobe concerned with a serious and philosophically interesting problemif we take him to be making implicit use of a principle about judgmentthat Bertrand Russell was also known to have held.' According to thatprinciple, judgment is possible only when we are acquainted with everyterm of the judgment. I think that this recent turn of scholarship is helpfuland points us in the right direction, but I do not believe that Russell's

Accepted March 1999' John McDowell presses the point in "Identity Mistakes: Plato and the LogicalAtomists," pp. 181-96 of Proceedings of the AristotelianSociety N.S. 70, 1969-70, andmore briefly in his commentary on his own translationof the Theaetetus. See Plato:Theaetetus(Oxford: ClarendonPress, 1973). Myles Burnyeatflirts with the idea in hisX Koninklijke Brill NV, Leiden, 1999 PhronesisXLIV13


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164 DAVID BARTON

principle is in play in Plato's argument. I shall argue, nonetheless, thatPlato is working with a principle similar in some respect to Russell's,and that attention to this fact shows that there is a philosophical point ofthe first importance to be gleaned from the discussion of falsity in theTheaetetus, a point about the nature of the relationship between self andworld.

Here is the crucial stretch of text:Socrates: Well now, aren't there just these possibilities for us, in the

case of everything and with each individual thing: either toknow it or not to know it? Because at the moment I'm leav-ing out learning and forgetting, as being in between thesetwo: at this stage they aren't at all relevant to the argument.

Theaetetus: Well, Socrates, there's no other alternative, in the case ofeach thing, besides knowing it or not knowing it.

Socrates: Now it follows immediately that if someone thinks, he thinkseither something which he knows or which he does not know.

Theaetetus: Yes.Socrates: And it's impossible for someone who knows something notto know that same thing, or for someone who doesn't know

something to know that same thing.Theaetetus: Of course.Socrates: Well now, take someone who thinks false things. Does he

believe that things he knows are not these but some otherthings he knows, and knowing both he is ignorant of both?

Theaetetus: No, that's impossible, Socrates.Socrates: Well, is it that he supposes that things he doesn't know are

some other things which he doesn't know? Is this possible: thatsomeone who knows neither Theaetetus nor Socrates shouldgrasp into his mind (ri; tiiv 68avouav kappIiv) that Socrates isTheaetetus or Theaetetus Socrates?

Theaetetus: Of course not.Socrates: But surely it isn't that he believes that things he knows are

things he doesn't know, or that things he doesn't know arethings he knows.

Theaetetus: That would be monstrous.

commentaryon M.J. Levett's translation.See The Theaetetusof Plato (Indianapolis:Hackett, 1990), esp. pp. 73-7. I shall be concentrating,however, on Gail Fine's "FalseBelief in the Theaetetus,"Phronesis, 1979, pp. 70-80.


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THE THEAETETUSON HOW WE THINK 165Socrates: Well then, how can it still be possible to think falsely? Becauseoutside of these situations it's surely impossible to think, since,

in the case of everything, we either know it or don't know it.But it doesn't seem to be possible to think falsely anywherewithin these situations. (188a-c)

This is a puzzling argument, and it is unlikely to convince any modernreader that there is a serious problem about falsity. One of its curious (andoften noticed) features, which I mention only so that I can set it aside, isthat although it seems to be concerned exclusively with a small sub-classof false beliefs, cases of false identity judgments, Plato takes it to showthat all false beliefs are problematic. This does seem to be a mistake onPlato's part, perhaps originating in a hope that if he could get clear aboutfalsity in a restricted domain of cases he would thereby shed light on otherkinds of cases as well. That would be a reasonable hope, especially inlight of Plato's view, articulated in the Sophist,that identity statementsare really not fundamentally different in kind than statements whichattribute some property to a subject. Both kinds of statement get cashedout in terms of participation relations: To say that Socrates is identicalto Socrates is to say that Socrates participates in Sameness, one of theSophist'sfive great kinds, with respect to Socrates.2

Another curious feature of the argument, which I shall not simply setaside, is that it relies on the undefended and unelaborated principle thatone either knows an object or does not. Plato clearly wants the reader tounderstand that the principle is at the heart of the argument: He hasSocrates secure Theaetetus' assent to it explicitly, and in his conclusionhe states the principle again. There is also a second principle indispens-ably at work in the argument, that a thing cannot figure in one's thoughtsif one does not already know the thing. I'll call the first of these principlesP and the second Q. The argument can be reconstructed as follows:1. P: "There's no other alternative, in the case of each thing, besides

knowing it or not knowing it."2 Anotherinterestingpossibility (I am grateful to the editors of Phronesis for bring-ing it to my attention) is that Plato finds it naturalto understandall mistakenjudg-ment as, at bottom,a matter of mistakenidentity: In judging falsely we mean to pick

out some actually existing thing or state of affairs, but what we actually end uppicking out is something different- and so in effect we mistake the first for the sec-ond. This would clear Plato altogether of the charge that he is falsely generalizingfrom the problematiccharacterof one class of false beliefs to the problematiccharacterof all of them.


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166 DAVID BARTON2. Therefore, when someone thinks, he thinks either something he knows

or something he does not know.3. Someone who thinks falsely must think either (a) that things he knows

are other things he knows, or (b) that things he doesn't know are otherthings he doesn't know, or (c) that things he knows are other things hedoesn't know, or finally (d) that things he doesn't know are other thingshe knows.

4. (a) is impossible because it implies that he both knows and does notknow the same things.

5. (b), (c), and (d) are impossible because (Q) it is impossible for some-thing to figure in one's thoughts if one doesn't know that thing.

6. Therefore it is impossible to think falsely.This is a valid argument, but as it stands it is really just a shell of anargument, partly because we lack any understanding of what the realcontent of P and Q is. For the moment I shall concentrate on P. The mostobvious interpretationsof P render it false or else leave us without a gen-uine puzzle about falsity. We could take the import of the principle to bethat one either knows everything about a thing or else one knows nothingabout it. If this principle were true, it would indeed be difficult to see howwe could ever make false identity judgments; but of course no such prin-ciple is true, or even tempting. Alternatively, we could understandP toassert that one either knows something about a thing or one does not. Thisprinciple has the advantage of being true, but it leaves us without a puz-zle: For if I know something about Socrates (but not that he is distinctfrom Theaetetus) and I know something about Theaetetus (but not that heis distinct from Socrates), nothing prevents me from judging, incorrectly,that Socrates and Theaetetus are one and the same. Finally, we might thinkthat P claims that one either knows what a thing is or one does not. Idon't know whether P, so interpreted,would be true or not - that dependson what is involved in knowing what a thing is - but it again leaves uswithout a puzzle. Perhaps in my childhood I knew a person, call him Joe,quite well. I played with him regularly, knew a lot about him, and couldeasily pick him out of any crowd. In short, I clearly knew who he was.Suppose now that later in my life I meet anotherJoe, and I come to knowhim quite well: I talk with him regularly, know a lot about him and caneasily pick him out of a crowd. Even in a case like this, it is perfectlyreasonable for me to ask myself whether this Joe whom I know as anadult is the same as the Joe whom I know from childhood, and even toconclude incorrectly on the basis of the available evidence that he is.


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THE THEAETETUSON HOW WE THINK 167There really is no puzzle here at all. It might be objected that in a caselike this I don't really know who either Joe is, since ex hypothesi I don'tthat they are distinct from each other. But this certainly won't do: Fornow we have strengthened P to such a degree that the whole force of theargument at 188a-c is lost. Plato is certainly right if he is claiming that Iwill not think to myself, "x is identical with y" when I know already thatx and y are distinct, but that truism hardly counts as a puzzle - and it hasno tendency to show that there is anything puzzling about the kinds ofmistaken identity judgments that people actually do make.3

Gail Fine's TheaetetusHow then are we to understand Plato's argument? Gail Fine and othershave sought help in a thesis about judgment that Russell held at one stageof his career. The thesis employs his notion of acquaintance, which heunderstands as a kind of direct awareness of an object. In "Knowledge byAcquaintance and Knowledge by Description," Russell states the thesisthis way: "Whenever a relation of supposing or judging occurs, the termsto which the supposing or judging mind is related by the relation of sup-posing or judging must be terms with which the mind in question isacquainted."4Earlier in the same work he formulates what is evidently thesame principle somewhat differently: "Every proposition which we canunderstand must be composed wholly of constituents with which we areacquainted.""Russell thought that this principle was self-evident if prop-erly understood - for "it seems scarcely possible to believe that we canmake a judgment or entertain a supposition without knowing what it isthat we are judging or supposing about."6 The principle is nicely suitedfor application to Plato's argument: First, on Russell's view, acquaintanceis an all or nothing matter;one either is or is not acquainted with a thing.Thus Plato's principle P comes out true, at least according to Russell, ifwe understand it as follows:

I If the fact that I knew the one Joe early in life and the other later in life is thoughttroublesome here, it is easy enough to constructexamples where this kind of timedifferenceplays no role. I may wonder whether the coffee cup on my desk is mine orSarah's, and then conclude incorrectly on the basis of good evidence that it is mine.And here I of course know what my coffee cup is and what Sarah's coffee cup is.I "Knowledge by Acquaintanceand Knowledge by Description,"in MysticismandLogic (New York: Longmans, Green and Co., 1918), pp. 220-1.5 "Knowledge by Acquaintance and Knowledge by Description," p. 219.6 "Knowledge by Acquaintance and Knowledge by Description,"p. 219.


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168 DAVID BARTONP* There's no other alternative, in the case of each thing, besides beingacquaintedwith it or not being acquaintedwith it.

Second, it is clear that one of the key steps of the argument, step 5,depends uponat least something like Russell's thesis aboutjudgment. Plato'sidea here is clearly that we cannot have a thought in which a particularthing figures unless we already have knowledge of, or on the currenthypothesis, acquaintance, with that thing. Thus Q comes out true as well,on the following reading:

Q* It is impossible for something to figurein one's thoughtif one is not alreadyacquaintedwith it.Fine then attributes to Russell the implausible view that if one is ac-quainted with a thing one "knows all there is to know about it."7 In factRussell did not hold such a view, a point we shall come back to in amoment. For now, we should simply note that this additional point givesFine all the materials she needs to make sense of Plato's puzzle, as follows:(a) P*: There's no other alternative, in the case of each thing, besides

being acquainted with it or not being acquainted with it.(b) Therefore, when someone thinks he is either acquainted with theconstituents of his thoughts or he is not.

(c) Someone who thinks falsely must think either (1) that something heis acquainted with is something else he is acquainted with, or (2) thatsomething he isn't acquainted with is something else he isn't ac-quainted with, or (3) that something he is acquainted with is some-thing else he isn't acquainted with, or (4) that something he isn'tacquainted with is something else he is acquainted with.

(d) (1) is impossible, because anyone who is acquainted with both thingsknows everything there is to know about each of them, including thatthey are distinct from each other.

(e) (2)-(4) are impossible because, by Q*, it is impossible for somethingto figure in one's thought if one is not already acquainted with it.

To put the point of the argument more briefly: I cannot think falsely thatA is B unless I am acquainted with both A and B, but having this ac-quaintance is a sufficient condition for knowing that A and B are in factdistinct. No one, therefore, would ever mistake one thing for another.

If this is Plato's puzzle, it is easily solved. All we need to do is reject

I "False Belief in the Theaetetus,"p. 72.


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THETHEAETETUSON HOWWE THINK 169the model of knowledge on which it is founded. Fine thinks that this isprecisely the moral Plato wants his readers to draw. On her view, Platointends the discussion of false belief as a reductio ad absurdum of whatshe calls the 'acquaintance model of knowledge' - a model according towhich knowledge is a kind of "grasping or hitting"8 that confers totalknowledge of the thing grasped.

We may still wonder, however, why Plato would expend so much philo-sophical energy and imagination in discrediting the acquaintance model.What point would Plato have in demonstrating the obvious point thatknowing a thing doesn't imply knowing everything about it? Here Finereminds us that the discussion of falsity occurs in the context of Theae-tetus' claim that true belief is knowledge. Her idea is that the acquaint-ance model supports Theaetetus' definition by dissolving any distinctionbetween true belief and knowledge: I cannot believe truly, say, thatSocrates is snub-nosed unless I know everything about Socrates, includingthat he is snub-nosed - thus any true belief turns out also to be a pieceof knowledge:

Onthatmodel [the acquaintancemodel],any graspof athingamountstoknowledgeand so true belief, since it involves a grasp of a thing, is knowledge. But ofcourse Theaetetusshould welcome this result, since he suggests that there is nodistinctionbetweenknowledge and true belief. Thus, the underlyingacquaintancemodel, although it precludesa satisfactoryexplanationof false belief, supportsTheaetetus' suggestion, by obliteratingany distinction between knowledge andtruebelief.9By refuting the acquaintance model, Fine claims, Plato has successfullyremoved one line of support for Theaetetus' definition. This allows Fineto conclude that the long discussion of false belief is not a mere digres-sion, but an indirect argument against Theaetetus' claim that knowledgeis true belief.

Such, in broad outline, is Fine's reading. I find myself in agreementwith much of what she says, but I also think that there are some seriousproblems in the details of her analysis. I want now to identify these, sothat I can clear them away and find a common core of agreement on whicha satisfactory reading of the Theaetetus can be built. I shall be concernedmostly with the acquaintance model of knowledge and the role Fineassigns to it. That model is certainly central to Fine's account, for her ver-sion of Plato's argument will not go through without the claim that

8 "False Belief in the Theaetetus,"p. 70.9 "False Belief in the Theaetetus,"p. 70.


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knowing a thing confers knowledge of everything about the thing (step(d), above, is essential to her reading). But this idea is sufficiently implau-sible to rob Plato's puzzle of any independent philosophical interest, so Iwould be disappointed to find that the puzzle turns on it. Fine tries to mit-igate this disappointment by alleging a connection between the acquaint-ance model and Theaetetus' claim that knowledge is true belief. I shalltry to show, however, that there is no such connection. This will removethe temptation to read the acquaintance model into Plato's puzzle aboutfalsity and pave the way for a fresh interpretation.

First, it should probably be noted that Fine has seriously misunderstoodRussell's notion of acquaintance. Of course, nothing in her interpretationof the Theaetetus requires that the concept of acquaintance she finds thereshould be in Russell as well. But her attribution of the acquaintance modelof knowledge to Russell does give that model a certain aura of respect-ability, which then makes it seem more likely that a great thinker suchas Plato would take an interest in it, even if his interest lies mostly inrefuting it. So it is perhaps not gratuitous to point out that Russell neverthought, as Fine claims, that acquaintance with a thing confers knowledgeof everything about the thing. For Russell, knowledge by acquaintance isa kind of direct mode of cognitive access to objects, to be understood incontrast with an indirect mode of access, knowledge by description. I amacquainted with an object "when I have a direct cognitive relation to thatobject, i.e. when I am directly aware of the object itself."'0 I know anobject by description, on the other hand, when I know that there is oneand only one object that satisfies a certain description. I know, for exam-ple, that there is one and only one object who is the author of theTheaetetus, and thus I know this object, Plato, by description. Without tak-ing a stand on whether the distinction Russell is after is a real one, wemay express it as follows: To be acquaintedwith an object is to know theobject itself, whereas to know something by description is to know some-thing about it.

Because knowledge by description and knowledge by acquaintance arefundamentally different modes of access to objects, they are in Russell'sview "logically independent."" This means that it does not follow logi-cally from the fact that I am acquainted with a thing that I have anydescriptive knowledge of it at all, though Russell claims it would be

10 "Knowledge by Acquaintanceand Knowledge by Description,"p. 209.11BertrandRussell, The Problemsof Philosophy (London: Oxford UniversityPress,1952), p. 46.


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THE THEAETETUSON HOW WE THINK 171"rash" to suppose that one is ever in fact acquainted with a thing withoutalso knowing something about it.'2

Russell, then, acknowledges at least the logical possibility that I couldknow something by acquaintance and yet know nothing about it at all.Fine reaches the opposite conclusion, that knowing something by ac-quaintance confers omniscience about the thing, by conflating Russell'sview that acquaintance is an all or nothing affair, that one either is oris not acquainted with a thing, with the quite different view that oneeither knows everything about a thing or nothing about it. She writes,"Acquaintance ... is ... a hit or miss, all or nothing, affair. Either one isacquainted with something, and so knows all there is to know about it, orelse one is not acquainted with it, and so has total ignorance."'3But if wekeep firmly in mind that knowledge by acquaintance sharply contrastswith knowledge by description it is easy to avoid this conflation: Russelldoes hold that acquaintance is an all or nothing affair in the sense thatone either is or is not acquainted with a thing, but since knowing some-thing by acquaintance is quite different than knowing anything about it(having knowledge by description), it does not follow from this that oneeither knows everything or nothing about a thing. Fine is tempted to theconflation by Russell's misleading remark, which she quotes, that whenone is acquainted with a particular color "no furtherknowledge of it itselfis even theoretically possible."'4 The fuller context of this remark makesit clear that Russell is referring here to knowledge by acquaintance, andis claiming only that no further knowledge of this kind is theoreticallypossible - for one either is or is not acquainted with a thing. The quotedremark is immediately preceded by the following: "So far as concernsknowledge of the colour itself, as opposed to knowledge of truths aboutit, I know the colour perfectly and completely when I see it."'5 ThusRussell does not commit himself hereto the view that when one is acquaintedwith a thing one knows everything about it. Indeed, in The Philosophy ofLogical Atomism, he explicitly disavows any such view: "When you haveacquaintance with a particular,you understand that particular itself quitefully, independently of the fact that there are a great many propositionsabout it that you do not know .*. .6

2 The Problems of Philosophy,p. 46."3 "False Belief in the Theaetetus,"p. 72.14 The Problems of Philosophy, p. 47.'5 The Problems of Philosophy, p. 47. Italics my own.16 "ThePhilosophyof LogicalAtomism,"inThe CollectedPapersofBertrandRussell,v. 8, ed. John G. Slater (London:Allen & Unwin, 1986).


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172 DAVID BARTONNow that the acquaintance model has been stripped of its association

with Russell, it is perhaps a little easier to see how deeply implausiblethat model is, and how unlikely it is that Plato had any independent inter-est in it. According to the model, one either knows nothing or everythingabout any given thing. To refute this, Socrates need only have pointed outthat they have been assuming all along that he knows Theaetetus (it hasbeen a favored example), and then add that he plainly does not knoweverything there is to know about him, such as the number of hairs onhis head. If, as Fine claims, the ten page discussion of falsity is really areductio of the acquaintance model, it is a pointlessly complicated andlengthy one. To explain why Plato would spend so much philosophicalenergy on the refutation of the model - a model he has never previouslyshown any interest in, and which is never stated in any Platonic dialogue,including this one - Fine must lean hard on her claim that Plato's refu-tation removes one line of support for Theaetetus' definition of knowl-edge. That claim can now be seen to bear the full weight of her argument.

I do not see how it can bear that weight. One problem, not the mostserious, is that the acquaintance model is less plausible than the definitionit is meant to support. That definition, that knowledge is true as opposedto false belief, is a promising one, and it represents an obvious advanceover Theaetetus' first definition, that knowledge is perception. It is, I sus-pect, meant to be a definition that any attentive reader might be temptedto propose, and to propose at just the moment that Theaetetus does. Bycontrast, the claim that we know everything or nothing about an objectdoes not look very promising, and so it would be at least peculiar to enlistits support in defense of the new definition.

But the real problem is that the refutation of the acquaintance modelwould not in fact undermine Theaetetus' definition. Fine emphasizes thatthe acquaintance model dissolves the distinction between having truebelief about a thing and having knowledge of it, but the problem is thatit does more than just that - it dissolves the distinction between havingtrue belief about a thing and having omniscience about it. On Fine'sacquaintance model, to be acquainted with something is not just to knowit, but to know everything about it. If Plato refutes this view he hasremoved one reason for holding the strong view that true belief is omni-science, but it's hard to see how he's removed any support for the muchweaker claim that is actually in question, that true belief is knowledge.Plato cannot undermine the weaker view by undermining the strongerview, at least not by the argument Fine attributesto him, which turns onjust that feature of the stronger view that distinguishes it from the weaker


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THE THEAETETUSON HOW WE THINK 173one: Plato's argument, according to Fine, shows that false belief is impos-sible if having a belief about a thing amounts to having total knowledgeof it. (Step (d) is essential in Fine's version of the argument.) Since Theae-tetus' view is that true belief amounts to knowledge, not that it amountsto total knowledge, this leaves his real claim untouched. If Plato succeedsin refuting the acquaintance model, he will have shown that it is possibleto believe truly that, say, Socrates is snub-nosed without knowing every-thing there is to know about him. But this does nothing to undermineTheaetetus' claim that it is not possible to believe truly that Socrates issnub-nosed without knowing, simply, that he is snub-nosed. To put all ofthis another way: If the acquaintance model constitutes the foundationfor the claim that knowledge is true belief, then that foundation is muchwider than the structurebuilt on top of it, and since Plato's discussion offalse belief (on Fine's reading) removes just that part of the foundationthat is unneeded, the structureitself stands firm.

So I believe Fine's reading of the Theaetetus cannot be right, at leastnot in its details. Russell's thesis about judgment, Q*, does not help us torecover a genuine puzzle about falsity unless we add to it the implausi-ble idea that acquaintance confers total knowledge about an object. Andwhen we do add that idea, thus generating Fine's acquaintance model,Plato's puzzle turns out to be philosophically uninterestingnot only for usbut for him, since its force depends entirely on a thesis that ought to temptneither us nor him. Nor can we fix this problem by supposing that Plato'sreal interest in the acquaintancemodel lies in its connection with Theaetetus'definition of knowledge; for as I've just tried to show, that connection isnot there. Russell's thesis about judgment thus does not seem to providethe key needed to decipher Plato's puzzle.

Thinking as GraspingNonetheless, Fine's approach is suggestive, and there are several strandsin it I want to follow and which I think point us in the right direction.First, on Fine's reading, Plato's principle P asserts something very generalabout the relation between the mind and its objects. P*, Fine's reading ofP, is only incidentally about knowledge, for knowing is just one of therelations that a mind might bear to an object. This may seem like a strikeagainst P*, since the Theaetetus is at least ostensibly about knowledge.But the current discussion is about falsity, and since falsity is at bottoma kind of malfunction in the relation between the mind and its objects, weshouldn't be surprised that a puzzle strong enough to cast doubt on its


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174 DAVID BARTONvery possibilityshould rest on a generalprincipleaboutwhat the relationbetween the mindand its objects is like. It may be that Plato casts theprinciplein terms of knowledgeonly because this makesdramaticsense,given the subjectof the dialogue.Second, step5 of Plato's argumentcer-tainly does seem to make use of somethinglike Russell's thesis aboutjudgment.SurelyPlato's idea here is that if we do not alreadybear someappropriatecognitiverelationto an object we cannot so muchas have athought about it. Indeed, Plato's remark,in his initial statementof thepuzzle, that someone who knew neither Socrates nor Theaetetuscouldnever 'grasp into his mind' (e4; Ti1v Sauvotlcv ka?Eiv) that the one is theother,leaves little doubton this point.The question is what cognitive relation to an object makes thoughtaboutit possible,if notacquaintance.I believe thatpartof Plato'spurposein the discussionof falsityis to test a certainnaturalway of understandingtherelationbetweena thinkeror a knowerand thethingsshe thinksabout,accordingto whichcontemplatingsomethingis like holdingit orgraspingit. Languagescatteredthroughoutthe Theaetetussuggests that this con-ceptionis very muchin the forefrontof Plato's mind. There is a particu-larly strikingexample at 190c,where Platosays thatno one wouldjudgeone thingto be anotherwhenhe is "layinghold of boththingsin his soul."(E'pwanTovo;aE0 poa vni Tn) The whimsicalproposalintroducedat 197d,that the soul containsa kind of aviary,is somethinglike an enshrinementof this view: Bringinga piece of knowledgeto one's mind is here likenedto the actual catchingof a bird in one's hand, and keeping it there islikened to keepingit in one's hands. Plato uses a remarkablyrich vocab-ularyto describethe processesof holdingand laying hold of a thinginone's mind - variants of kai4a'vo, flpao), 'i%w, and ?pact6o'at all appearin this context,and in the case of kapavw, they appearfrequently.If this is right, then we should read P as follows:

P** There's no other alternative,in the case of each thing, besides mentally'grasping' it or not mentally 'grasping' it.Notice that,if mentalgraspingis to be understoodon the analogyof lit-erally grasping things with one's hands, then P** is true, since it is truethatin the case of each thingone is eitherholdingit in one's hands or isnot. Supposenow that we recast the Russellianthesis aboutjudgmentsothat it concerns the notion of mentalgraspingratherthan the notionofacquaintance.It then reads:

Q** Every propositionwhich we can understandmust be composed wholly ofconstituents which we mentally grasp.


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THE THEAETETUSON HOW WE THINK 175If this thesis is in play in Plato'sstatementof the problemof false belief,we can at last recovera genuinepuzzle fromit: We cannotthinkthatAis B, whereA and B are distinct,unlesswe graspbothA and B (by themodifiedRussellianthesis, Q**). But if graspingis understoodon themodelof literalgrasping,thenclearlyanyonewho graspedbothA andBwould know thatthey are distinct,for it is difficultto see how someonewho was literallyholdingtwo objects in his hands could thinkthatoneof them is identicalwith theother.Thusfalse identityjudgmentsareinex-plicable.Somewhatmoreformally:(a) P**: There'sno otheralternative,in the case of each thing,besidesmentallygraspingit or not mentallygraspingit.(b) Therefore,when someone thinks, each of the constituentsof histhoughtis eithersomethinghe is mentallygraspingor somethingheis not mentallygrasping.(c) Someonewho thinksfalsely must thinkeither(1) that somethingheis graspingis somethingelse he is grasping,(2) that somethingheisn't graspingis somethingelse he isn't grasping,or (3) that some-

thinghe is graspingis somethinghe isn't grasping,or (4) thatsome-thing he is not graspingis somethinghe is grasping.(d) (1) is impossibleif mentalgraspingis understoodon the modelof lit-eral grasping.For someone who was literally graspingtwo distinctthingsin his handswould not supposethatthe one is the other.(e) (2)-(4) are impossible,becauseby Q** it is impossiblefor somethingto figurein one's thoughtsif one does not have a mental graspof it.Notice that this puzzledoes not dependon the unpromisingidea thatwemusthave completeknowledgeof each of the thingsgrasped.It dependsonly on takingthe analogybetween thinkingand graspingseriously."7

1" Ronald Polansky, in Philosophy and Knowledge: A Commentary on Plato'sTheaetetus (Lewisburg:Bucknell University Press, 1992), claims that Plato's use ofthe concept of grasping indicates that he is operatingon the assumptionthat we musthave complete knowledgeof anythingwe thinkabout: "ThatTheaetetusstill holds thatwe must have complete knowledge of what we think is indicatedby the reference to'grasping (?paxrt6jsvo;)both things by the soul' (190c6-7) and by the speaking ofopining 'in no way' (o,qa4i - 190d7-8), because this latter suggests that we eitherhave a knowledgeable grasp of things or none at all." (p. 183, n. 18) But when wespeak, in the ordinaryparlance of English or of Greek, of having a mental grasp ofsomething, we certainly do not imply that we know every last one of the infinitelymany things that are true of it, so it seems to me quite clear that Plato's talk of grasp-ing underminesratherthan supportsthe idea that Plato is making use of this strongassumption.As for Plato's use of 'in no way' at 190d7-8, here Plato is simply noting


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176 DAVID BARTONIf what I have been saying is right, then the puzzle at 188a-c can bereadas a reductioad absurdumof the idea thatthinkingabout a thingislike holdingit or graspingit, only with one's mind ratherthanwith one'shands. The thinking as grasping metaphoris worth refuting,for unlikeFine's acquaintancemodel it is a view that has real intuitive pull, evennow. Indeed,this conceptionof thoughtis latent in our everydayspeech:We speakof holdingsomethingto be true,of graspinga concept,of beingunableto get a handleon an idea. In the Theaetetus,Plato has done usthe valuableserviceof showing that these metaphorscannotbe pressed.

If we insist on conceivingof the relationbetweenthoughtand its objectson the modelof holdingor grasping,we will be unableto makesense offalse identity judgments:For no one who literally grasps two distinctthingsin his handswill supposethatone of thethingsis numericallyiden-tical with the other.'8One key piece of evidence in favor of the currentreadingis that itenablesus to makegood sense of the otherwisepuzzlingpassageat 189c-190e, in which Platoproposesandthenquickly rejectsthe idea thatfalsebelief maybe understoodas a kind of 'interchangedthinking'(CaXo&otEivor XTepo6oteiv).The proposal,to put it as vaguelyas Platodoes, is thata

that if someone does not think about a thing at all he could not mistakenly supposethat it is something else. The full sentence reads, "But surely he who thinks the onething only, and the other in no way, will never think the one is the other." This ispretty close to a logical truth, and it needs no supportfrom any strong assumptionsabout knowledge.18 To all of this it might be objected that a person could grasp one end of a thingwith his left handand anotherwith his right and mistakenlysuppose (becausehis eyes

are closed, perhaps)that he is holding two distinct things. But this would not be acounterexample:Plato's puzzle is not about the possibility of thinkingthat one thingis two distinct things, it is about the possibility of thinkingthat one thing is identicalwith another.Significantly,whenever Plato gives an exampleof the kind of judgmentshe thinks are problematic,he cites a case of this kind. And here it is substantiallymore difficult to constructa counterexample.If I am holding a pen in my left handand a coffee cup in my right, I will not make the mistakeof thinkingthat one of thesethings is numericallyidentical with the other. (Notice thatthe descriptionunderwhichI thinkof these objects does not matter:I will not thinkto myself 'this pen is identi-cal with this coffee cup,' nor 'this thing in my left hand is identical with this thing inmy right,' nor 'this light thing is identicalwith this heavier thing.')A couple of other cases: I might grasp a part of one thing, x, with my left handand a partof another thing, y, with my right and still mistakenly suppose that theseparts belong to the same object. In such a case I mightbe said to mistake x for y (ory for x, dependingon how the case is further described). But here I am inclined to

say that what I grasp in each of my hands, in the sense of 'grasp' that Plato has in


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THE THEAETETUSON HOW WE THINK 177

person may think falsely that a thing, x, is what it is not, y, by somehowexchanging, in his mind, x for y. In this way "he misses what he was aim-ing at" (189c) and thus it is, apparently, possible "for the mind to set upsomething as another and not as itself." (189d) But Plato then dismissesthe proposal, reasoning as follows: Someone who thinks that x is y, wherex and y are not identical, "must necessarily think either one or both"(189e) of x or y. But if he thinks only one of them, then it is not possi-ble for him to have the thought that this one is the other - for he is noteven thinking of the other. To think that the one is this other it would benecessary, Theaetetus says, "to lay hold of" (?paitsa) this item "whichone does not think." (190d) This is a direct application of the principleQ** - Theaetetus' claim is that one cannot have the thought that x is yunless one grasps, somehow or other, both x and y. If, on the other hand,someone does lay hold of both x and y, then he will not have the falsethought that the first is really the second: "no one who thinks both andlays hold of (?pranT6gvoq) both with his soul could say and think that theone is the other." (190c) If Plato is understanding the act of laying holdof something as anything like literally laying hold of something with one'shands, he is right: no one who grasps two things in his hands would eversay or think to himself that the one is really the other. Thinking that onething x is another thing y is thus impossible whether one thinks (graspshold of) both x and y or whether one grasps hold of just one of them. SoPlato concludes that "anyone who sets out to define false thought as inter-changed thinking would be saying nothing." (190e)

mind, is not a whole object, but a part of an object, for each hand is enclosing onlya part. (Plato speaks of taking or grasping things into the mind, ci; tiiv 6ulivotav XaP;iv(188b), suggesting that the kind of grasping he has in mind is a kind of envelopingor enclosing.) The relevant question, then, is whether I would mistake the partI graspwith my left hand for the part I grasp with my right. And clearly I would not do this.Finally, I could easily make the mistake of supposing that I am grasping one objectin one of my hands when I am actually grasping two: If I am holding two neatlystacked coins in my left hand, I might mistakenly judge that I am holding just one.But this is, again, not a genuine counterexample,for here I would be making the mis-take of supposing that two objects are one, but I would not be making the kind ofmistake Plato has in mind - I would not be mistaking one of the coins for the other.To construct a genuine counterexample,we'd need to find a case where a personhas his hands wrapped around two distinct objects and still manages to mistake oneof the objects for the other. I cannot show that it would be impossible to constructsuch a counterexample, but surely the extreme rarity of such cases would still beenough to show that the thinkingas grasping metaphorhas to be rejected, since casesof false identity judgmentsare not extremelyrare.


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178 DAVID BARTONThe current reading also renders Plato's remarks about mathematicalerror intelligible and even compelling. Plato notes that people often make

errors in addition, thinking, for example, that the sum of seven and fiveis eleven, but he claims not to understand how such a thing is possible.The worry comes in the context of the proposal that the mind contains akind of wax block on which impressions of thoughts and perceptions arestamped, and Plato takes the worry to be grounds for the rejection of thatmodel of mind. It is nonetheless possible to abstract from this context andto retrieve from Plato's discussion the following worry about mathemati-cal error: If I think that the sum of seven and five is eleven, then I seemto think that twelve is eleven, since the sum of seven and five is, in pointof fact, twelve. But surely, Plato worries, no one would ever think thattwelve is eleven. Now, to the modem mind Plato's worry will seem todepend on a gross fallacy, a willful flouting of the rule that intentionalcontexts are opaque - the rule that says that in intentional contexts sub-stitution of co-referential terms does not always preserve truth value. Fromthe fact that John believes that Cicero is a great orator it does not followthat he believes that Tully is, even though 'Cicero' and 'Tully' in fact referto the same person. If John happens to be ignorant of the co-referentialityof these terms, nothing prevents him from believing one thing of the per-son he knows as Cicero and another of the person he knows as Tully. Justso, from the fact that John mistakenly believes that the sum of seven andfive is eleven it does not follow that he believes twelve is eleven, eventhough 'the sum of seven and five' and 'twelve' are co-referential terms.For here John is obviously unaware of the co-referentiality, else he wouldnever have made his mathematical error. It appears, then, that Plato isguilty of a none too subtle fallacy. But we are now in a position to acquithim of the charge.The key is to see that terms like 'grasp' and 'lay hold of' do not intro-duce opaque contexts. In these contexts, the principle of the substitutivityof co-referential expressions salva veritate is actually preserved. If it istrue that I am laying hold of Cicero - literally grasping him - then whetherI am aware of it or not, it is also true that I am laying hold of Tully, forthat is who Cicero is, and in grasping the one I cannot help but grasp the'other'. Now, if we are operating with a conception of thought accordingto which thinking of something is understoodas a kind of grasp of it, thenwe shall have to say that intentional terms do not introduce opaquecontexts either. From the fact that I am thinking of, laying hold of, thesum of seven and five it will follow that I am thinking of, laying hold of,twelve - for that is what the sum of seven and five is. It will then be


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THE THEAETETUSON HOW WE THINK 179genuinely mysterious how I could think that seven and five is eleven, forthis can no longer be distinguished from the thought that twelve is eleven- a thought nobody would have. Plato is not guilty of a fallacy; he hasin fact confirmed the result of the argument at 188a-c, that mistaken judg-ments of identity become incomprehensible if we understand thinking ofa thing as a kind of mental grasp of it.

There is an obvious solution to Plato's puzzle, and the fact that Platodoes not articulate it in the Theaetetus has sometimes been taken to showthe depth of his confusion. Plato seems to be unaware that when we thinkof a thing we think of it under one or more of its aspects. We do not thinkof a thing, so to speak, full stop, we think of it, rather, as having somequality or other, as being beautiful, or ugly, or small - we think some-thing about it. This point immediately dissolves Plato's puzzle about fal-sity: For it is simply not true that thinking of two things is tantamount tothe awareness that they are distinct. Since we think of things underaspects, it is quite possible to think of x under one aspect and y underanother and yet fail to realize that it is the same thing that presents thesedifferent aspects. Why does Plato ignore such an obvious point?

The answer, I think, is not that Plato is confused, but that the point isincompatible with the conception of thought that Plato is testing in theTheaetetus. If thinking is to be understood on the model of touching orgrasping, then it is hard to see how we could think of something underone of its aspects rather than another. When we grasp something in ourhands, we do not grasp it under one of its aspects, we do not grasp it asbeautiful or as small, we simply grasp it full stop."9(Of course, I maygrasp a beer in my hands as a thirsty person, but here 'thirsty person' isan aspect of me, not of the beer.) If Plato is indeed testing to see how farthe metaphor of grasping can be pressed, then it is hardly surprising thathe does not press it farther than it will go. Incidentally, this explains anotherwise puzzling feature of the discussion of false belief - Plato's tendencyto attach direct objects to verbs of thinking, to speak simply of 'thinkinga thing' rather than of 'thinking something about a thing.' (One example

'" Of course, we could grasp somethingby a part,but this is not usefully analo-gous to thinking of something under an aspect. This is not only because there areaspects of things (like theirbeauty) which are not partsof them. It is also because thelogic of the expression 'grasping by a part,' is unlike the logic of the expression,'thinkingunder an aspect'. To take a silly example: If I literallygraspSocrates by hisnose it follows that I grasp him by his snub-nose. But if I thinkthat Socrates has anose (if I think of him underhis nasal aspect, as it were), it obviously does not fol-low that I think of him as having a snub-nose.


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180 DAVID BARTONis found at 188a in the original statement of the puzzle, and there arenumerous examples at 189a-b and in the discussion of interchangedopin-ion at 189c-190c.) This is just the way Plato ought to speak if he is tak-ing the grasping metaphor seriously. If thinking is grasping, then some-how or other we are able simply to think a thing (full stop), just as weare able simply to grasp it (full stop).

There is a closely related point that I want to emphasize here. The factthat we do not grasp things under aspects can serve to highlight just howmysterious it is that we do think of them under aspects. It shows us thatthought is unlike anything we are familiar with from our bodily interac-tions with everyday objects. If we look at things in this way, we come torealize that Plato would not think that a mere statement of the fact thatwe think things under aspects would be sufficient to solve his puzzle aboutfalsity. This would be to explain one mystery in terms of a still greaterone. This sort of solution will be intellectually unsatisfying until we havesome account of how it could be that thought, unlike grasping, picks thingsout under some aspects rather than others - or, to put it another way,under some concepts ratherthan others. Significantly, just such an accountis developed in the Sophist, the sequel to the Theaetetus, where Platoabandons the grasping metaphor in favor of a new one which he intro-duces explicitly and defends in detail, the thinking as 'weaving' metaphor.The idea is that thinking is an activity in which a subject is 'woven'together with a predicate in such a way that the predicate says somethingaboutthe subject,thatis, picks it ourunderone of its aspects.The metaphysicsneeded to underwrite and explain such a picture is not yet in place in theTheaetetus, and one of the central tasks of the Sophist is to supply it.

The task of the section on false belief in the Theaetetus is, by contrast,a more limited and destructive one, but Plato accomplishes it brilliantly:He shows us, decisively, that thought cannot be understood as a kind ofmental holding or grasping.Department of PhilosophySwarthmore College

theaetetus on how we think

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