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Philosophical Review

Vlastos and "The Third Man"Author(s): Wilfrid SellarsSource: The Philosophical Review, Vol. 64, No. 3 (Jul., 1955), pp. 405-437Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2182209

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VLASTOS AND "THE THIRD MAN"IN HIS recent article on "The Third Man Argument in the

Parmenides"'Professor Vlastos raises anew the classic questions:"Is the Third Man Argument a valid objection to the Theory ofForms?" "Did Plato believe that it was valid ?"2 He reminds usthat "one can find acute and learned critics on both sides of boththese questions"3 and soundly concludes that "if any progress inagreement is to be made at this juncture, it must come from someadvance in understanding the logical structure of the argument."4He proposes, therefore, to "pursue its analysis further than Ithink anyone has yet found it profitable to push it."5 And heproceeds to give us what must be admitted to be a patient andpainstaking reconstruction of Plato's argument. Furthermore, ifthis reconstruction is sound, and if we allow him one or two addi-tional premises of reputable standing, Vlastos has struck a rich veinindeed. It not only yields clear-cut answers to the questions withwhich he began, but also reveals for our admiration and wonder aPlato who faced an intellectual, indeed spiritual, crisis in a manner"absolutely without parallel in the pages of Western Philosophy."6

There is much in Vlastos' paper with which I should like to takeissue, for in the course of a rich and complex argument he takes astand, to my mind not always a wise one, on many of the moreexciting issues of Plato interpretation. On the present occasion,however, I shall limit myself to criticizing (i) his reconstructionof the Third Man Argument, (2) his conception of the place ofwhat he calls "Self-Predication" (Triangularity is a triangle) inPlato's later metaphysics, and, consequently, (3) his interpreta-tion of Plato's frame of mind when composing the first part of theParmenides.

IVlastos opens his assault on this Everest of scholarship byquoting Parmenides I 32a i-bi, which he translates as follows:"I suppose this is what leads you to suppose that there is in every

1 Philosophical Review, LXIII (95i4), 3 19-349 id., P. 319.3lbid. 4Ibid. 5lIbid. 6Ibid., P. 349.405

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THE PHILOSOPHICAL REVIEWcase a single Form: When several things seem large to you, itseems perhaps that there is a single Form which is the same inyour view of all of them. Hence you believe that Largeness is asingle thing."'

He calls this passage "the first step of the Argument"8 and tellsus that it "may be generalized as follows: (Ai) If a number ofthings, a, b, c, are all F, there must be a single Form, F-ness, invirtue of which we apprehend a, b, c, as all F."9 He explains the"generality" of (Ai) by saying that " 'F' stands for any discerniblecharacter or property."10 He adds that "the use of the samesymbol, 'F,' in 'F-ness,' the symbolic representation of the 'singleForm,' records the identity of the character discerned in theparticular ('large') and conceived in the Form ('Largeness')through which we see that this, or any other, particular has thischaracter.'"11

Now (Ai) as formulated by Vlastos tells us that the role ofF-ness is that of making possible the apprehension of a, b, c as all F.But surely the point of the Theory of Ideas is that F-ness makespossible the apprehensionf, say, a, b, c as F, because F-ness is thatby virtue of which (i.e., by virtue of participating in which) a, b, call are F. Thus, at the very least, (Ai) should read "If a numberof things, a, b, c, are all F, there must be a single Form, F-ness, byvirtue of which a, b, c are all F and can be apprehended as such."But does a reference to our apprehension of a, b, c as F belong in(Ai) at all? Granted that the text reads "when several thingsseem large to you, it seems perhaps that there is a single Formwhich is the same in your view of all of them," can we not takethe "seeming" and the "viewing" to pertain to the discovery f theprinciple which is to function as a premise of the Third ManArgument, rather than as constituent elements in the principleitself? Why does Vlastos think that the reference to apprehensionbelongs in the principle? The answer is that Vlastos, like Taylorbefore him, sees that even if the Third Man establishes an infiniteseries of Largenesses as a consequence of the Theory of Ideas, this

I Ibid. p. 320. At no point does my criticism of Vlastos' reconstruction hingeon a difference in translation. As a matter of fact, his translation avoids atleast one pit into which others have fallen. See below, n. 22.

8 Ibid. 9 Ibid. 10 Ibid. 11 Ibid.406

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VLASTOS AND "THE THIRD MANJ"fact as such would not suffice to refute the Theory in the strictsense of showing it to be logically absurd.12 For there is no logicalabsurdity in an infinite series as such. On the other hand, if thisseries could be shown to involve a viciousregress, the job wouldindeed be done. But would not Plato himself have regarded theinfinite series as already unacceptable, and sufficient to refute theTheory if it could be shown to be a consequence of it? Vlastosrecognizes that this is the case,13 but since he thinks that Plato isanyway committed to an epistemological principle which, whencombined with the infinite series of Largenesses, does yield avicious regress, he feels justified in putting it into the argument.14This principle, which Vlastos nowhere carefully formulates, is tothe effect that we apprehend an item as F in virtue of apprehend-ing the F-ness in which it participates as being what it, in turn, is.Thus, on the assumption that all F-nesses are F, the principlebecomes: We apprehend an item as F in virtue of apprehendingthe F-ness in which it participates as also F. But while F-ness mustindeed be apprehended to play its epistemological role, need it beapprehended as beingF? There is an important distinction betweenthe apprehension of X, and the apprehension of X as so-and-so.And if Vlastos sees this distinction, but is convinced that the formercannot take place without the latter, he has given no reason forfoisting this conviction on Plato.15

But whether or not Plato (however "implicitly") mobilized anepistemic premise to insure the unacceptability of an infiniteseries of Largenesses, it is clear that it is not necessary to the esta-blishing of the series itself. And in his reconstruction of this aspect

Ibid., p. 328, n. I2. 13Ibid.14 Ibid., p. 327. "Wei could thus get a bona fide infinite regress, logically

vicious, since it is assumed that we discern F particulars in virtue of F-nessF-ness in virtue of F1-ness ..., and so on ad infinitum, the discernment of eachsuccessive Form being required for the discernment of its immediate prede-cessor, a requirement which can never be fulfilled, since the series is infinite."15 That Vlastos is on dangerous ground is shown by the fact that even atheory of Forms or universals which d-nies that F-ness is F (e.g., Russell's inThe Problems of Philosophy) would yield a vicious regress when combined withVlastos' epistemic principle. For eveni if F- Imss is not F, it is at least changeless.And if in order to apprehend a particular az F one had raot only to apprehendF-ness but also to aDprehend it a Iei g -vhat it is, e.g., changeless, one wouldindeed be faced with a task that c; ill never be begun.

407

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THE PHILOSOPHICAL REVIEWof Plato's argument, Vlastos makes no use of this premise. Since itis this reconstruction which I shall be criticizing, I shall, in thefollowing, omit from (Ai)-and later from (A2)-all reference toapprehension.

One other comment before we turn our attention to Vlastos'reconstruction of what he takes to be "the second step." In thepassage which follows his formulation of (Ai), Vlastos lays down aplausible procedural rule. He tells us that "Plato's argumentprofesses to be a deductive argument and I propose to treat it as aformal structure of inference from premises, stated or implied.For this reason, I raise no questions about the Theory of Formsand presume no more information about it than I can extractfrom the text before me."'16But whether or not this procedure is aviable one, Vlastos has already violated it by importing into hisexplication of (Ai)-quoted above-a distinction between largeas a "character or property" of large things and the Form Large-ness in which they participate. Plato does, indeed, distinguish inthe Phaedo17 between a large thing, the large in the thing, and TheLarge Itself (Largeness), and he even recalls this distinction earlyin the Parmenides(I 3oB), when Parmenides asks Socrates:have you yourself drawn the distinction you speak of and separatedapart on the one side Forms themselves, and on the other the thingsthat share in them? Do you believe that there is such a thing as Like-ness itself apart rom the ikeness hatwepossess,and so on with Unity andPlurality and all the terms in Zeno's argument... ?18

Nevertheless, while all this is true, the trichotomy in questionjust cannot be found in the passages which constitute the ThirdMan Argument. Vlastos asserts "that F and F-ness are logicallyand ontologically distinct is crucial to the argument."19 But whathe must mean is that it is crucial to his (Vlastos') explanation ofwhy Plato offered the Third Man Argument which he (Vlastos)attributes to him, and of why he (Plato) failed to refute it. Forthis "crucial" thesis does not occur in the Third Man Argumentitself, even as Vlastos reconstructs it. We will find it wise tointerpret "large" not as "standing for" a "character" (whereas

16 Op. cit., p. 320. 17 I 02 ff.18 F. M. Cornford, Plato and Parmenides (London, 1939), p. 8i. Italics mine.19 Op. cit., p. 320, n- 5.

408

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VLASTOS AND "THE THIRD MAN""Largeness" names a Form), but rather, more neutrally, as theadjectival expression corresponding to the abstract noun "Large-ness," which latter, according to Platonic theory, is the name ofan Idea.

IIIn the light of these remarks, let us reformulate (Ai) to read:(Ai) If a number of things, a, b, c, are all F, there must be asingle Form, F-ness, in virtue of which they are all F.Let us now turn our attention Vlastos' reconstruction of what

he calls the "second step." This he translates as follows:What then if you similarly view mentally Largeness itself and theother large things? Will not a single Largeness appear once again, invirtue of which all these (sc. Largeness and the other large things)appear large?-It seems so.-Consequently another Form of Large-ness will appear, over and above Largeness itself and the things whichparticipate in it.20He then boils it down and "generalizes" it into the followingprinciple, from the formulation of which, as before, we haveomitted his reference to apprehension:

(A2) If a, b, c, and F-ness are all F, there must be another Form,F1-ness, in virtue of which a, b, c, and F-ness are all F.

But why does Vlastos write "F1-ness" instead of "F-ness1"??Bydoing so, he introduces an unnecessary queerness into the argu-ment, making it look as though Plato had in mind a principle ofwhich the following would be an illustration: If a, b, c, and Redo-ness are all redo (say scarlet), then there must be another Form,Red1-ness (say, Harvard Crimson) in virtue of which a, b, c, andRedo-ness are all redo. But not only is there nothing in the textwhich requires him to attach the subscripts to the "F" in"F-ness,"'21 nothing in his formal reconstruction of the argumenthinges on this placing of the subscripts. And while there wouldbe no objection to so attaching them if it were clearly understood

20Ibid., p. 32I.21 It is interesting to note that Vlastos never writes "Large1-ness" butalways "Largeness," even when it is intended as an illustration of "Fl-ness,"e.g., p. 322, 1. 14-

409

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THE PHILOSOPHICAL REVIEWthat it was to have no other force than if it were attached to the"ness," actually the temptation to construe "F1-ness" and "F2-ness" as standing for two different specific or determinate formsof a generic F-ness is so strong as to rule out this placing of thesubscripts. Vlastos, indeed, lays great stress (e.g., in n. 7, p. 323)on the determinables and determinates which, as he sees it, arelurking in the Argument. He sees that the Theory of Ideas againstwhich it is directed (and which he mistakenly believes to be thetheory Plato actually held) involves that the Form F-ness issuperlativelyF, particulars being by contrast humdrumlyF. Heconcludes that being superlativelyF and being humdrumlyF are twodeterminate ways of beingF. It is doubtless this reasoning whichunderlies his choice of "F1-ness" in the formulation of (A2). Butit fails to justify the placing of the subscript after the "F" in"F-ness." For these metaphysically different ways of being F arenot, in the usual sense, specific or determinate ways of being F. Thesubscripts would belong to the "being" rather than to the "F" in"being F."One more comment before we watch Vlastos rub (Ai) and (A2)together. Even a casual reading of the passage which Vlastos boilsdown to (A2) shows that something is wrong. For the text(Vlastos' translation) actually gives us two steps: (i) When oneviews Largeness itself and the other large things, a single Large-ness appears once again, in virtue of which all these are large.(2) Thereforewe discover a new Largeness which is over andabove the Largeness already noted. And if we ask, What doesthe second of these steps add to the first? the answer is that theLargeness which "appears" in (i) is other than the Largenesspreviously discerned.22 The significance of this point will emergeat the conclusion of our critique of Vlastos' reconstruction.

IIIAfter reconstructing the text of the Third Man Argument into

two steps, (Ai) and (A2), and before he introduces the two22 Note that there would be a radical redundancy if in (i) instead of "asingle Largeness appears onceagain"the translation read (mistakenly) "anotherLargeness appears" (compare the translations of Fowler in the Loeb ClassicalLibraryedition and Cornford in his Plato and Parmenides.

4IO

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VLASTOS AND "THE THIRD MAN"additional premises which he finds implicit in the text, Vlastospauses to make the following comment:Merely to compare (A2) with (Ai) above is to see a discrepancy in thereasoning which, so far as I know, has never been noticed before,though it leaps to the eye the moment one takes the trouble to trans-cribe the full content of the two steps in symbolic form. In (Ai) we aretold that if several things are all F, they are all seen as such in virtueof F-ness. But (A2) tells us that if several things are all F, they are allseen as such not because of F-ness, but because of a Form other thanF-ness, namely Fl-ness. To be sure, there is a difference in the protasisof (Ai) and (A2), and this is doubtless what has misled patrons orcritics of the Argument: (A2) includes, while (Ai) does not, F-ness,among the things which have the property F. The significance of theassumption which prompts this inclusion will be discussed directly,and will indeed remain the most important single issue throughout thewhole of this paper. But if we simply stick to the logical form of thetwo statements, the disparity of reasoning as between (Ai) and (A2)remains glaringly abrupt and unwarranted.23Vlastos, in this comment, is pointing out that whereas accordingto (Ai) the members of the class of F particulars, a, b, c, etc., are Fby virtue of F-ness, according to (A2) these same particulars (andF-ness as well) are F by virtue of the different Form F1-ness.24 This,according to Vlastos, is a glaring inconsistency,25 so that we cansay straight away that if the Theory of Forms commits us to (Ai)and (A2) we are in a position to reject it without waiting toderive further consequences (in particular, a regress) from (Ai)and (A2).

Two comments are in order. In the first place, it must, indeed,be granted that the Third Man Argument, as formulated by

23 Op. cit., p. 32 I.24 The soundness of this point is independent of the exact sense in which

Fl-ness is different from F-ness-that is, if sound, the point would remainsound even if "Fl-ness" were replaced by "F-nessl."25 That we have not misinterpreted the point which Vlastos is making isborne out by a reading of the footnote to this passage (n. 6) in which he offersa formal demonstration of the inconsistency by means of the propositionalcalculus. This demonstration, as he points out, rests on the assumption that"It cannot be true that x,y, z are seen as F in virtue of F-ness and also in virtueof a Form other than F-ness." It is this assumption that I am examining inthe text above.

4II

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THE PHILOSOPHICAL REVIEWPlato, involves that each large item, whether it be a particular ora Form, participates in an infinite number of Largenesses, andthat it is large many times overby virtue of participating in thesemany Largenesses. But notice that as being large by virtue ofparticipating in a given Largeness, an item is a member of acertain class of large items. Thus, a, b, c, etc., would be membersof the class of large particulars by virtue of the fact that eachparticipates in the first largeness. On the other hand, a, b, c, etc.,together with this first Largeness are members of a more inclusiveclass by virtue of their common participation in the secondLargeness, and so on. Thus it does not follow from Plato's premisesthat the members of one and the same class of large items, e.g., theclass of large particulars, are members of that class by virtue oftwo different Largenesses. The latter would indeed be a grossinconsistency. Therefore, unless we are going to rule out of courtas absurd the idea that a large item participates in many Large-nesses, all we are entitled to do at this stage is note that theregress as Plato sets it up requires that it be incorrect to speak ofthe Form by virtue of which an item, x, is large, without going onto specify the class of large things26 with respect to which it isbeing considered.27

If it is pointed out that the class whose members are largeparticulars can be different (as it must be) from the class whosemembers are large particulars plus Largeness, only if "large"connotes a different property in each case, whereas the Theory ofForms that is under attack clearly involves that "large" is not

26 E.g. the class whose membership consists of large particulars; the classwhose membership consists of large particulars, plus Largeness; the classwhose membership consists of large particulars, plus Largeness, plus Lar-geness1; ...27 It should be noted that the Third Man Argument can easily be set up insuch a way as to avoid (at least prima facie) this participation of each large

item in an infinite number of Largenesses. For instead of bringing in the secondLargeness to account for the (presumed) fact that a, b, c, etc., and Largeness areall large, it can be brought in simply to account for the (presumed) fact thatLargeness is large. Yet as soon as the question is raised, "Are not a, b, c, etc.and Largeness all large, and if so, must not a, b, c, etc., and Largenessparticipate in a common Form?" it would seem that an affirmative answercan be avoided only at the expense of denying that Largeness is large in thesame sense of "large" in which a, b, c, etc., are large.4I2

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VLASTOS AND "THE THIRD MAN"ambiguouslyapplied to both large particulars and Largeness, thismust indeed be granted. But must it also be granted that thedifference between the properties,which is necessary to make thetwo classes different, is such as to entail that the word "large" isambiguous in the ordinarysense of "ambiguous" (That the regressinvolves that "large" be ambiguous in an odd metaphysical enseis clear.) There is, indeed, an absurdity in the idea that largeparticulars are many times large in the same sense of "large."What I have been concerned to show is that the absurdity is nomatter of a simple contradiction.

My second comment on this "discrepancy" is that Vlastos con-ceives of both (Ai) and (A2) as premises of Plato's argument(though not of the one he reconstructs with premises mined fromPlato's philosophical unconscious). He therefore finds it necessaryto explain why Plato failed to notice this discrepancy. It is mypurpose to show that (A2) is not a premise of Plato's argument,and therefore that Vlastos has not, as he supposes, given a goodreason for holding that Plato was a puzzled spectator of hisargument. III

If we now ask, How does Vlastos conceive the role of (A2) in theargument? the answer seems to be that it is the hypothetical fromwhich, by modusponens, we are to draw the conclusion, There isanother Form, Fl-ness .... From this point of view, two questionsarise: (i) What authorizes the hypothetical? (2) What authorizesthe affirmation of its antecedent?

Vlastos sees the first of these questions in terms of the problem,how to get from (Ai) to (A2). And as it is immediately clear that(A2) does not follow logically from (Ai) by itself, he looks foradditional premises which, when combined with (Ai), will dothe job and which can reasonably be said to be implicit in Plato'sformulation. But before "rummaging into other texts to discoverwhat further assumptions Plato made about the Theory of Forms,"Vlastos asks the purely logical question, "What are the simplestpremises, not given in the present Argument, which would haveto be added to its first step, to make (A2) a legitimate conclu-sion ?"28

28 op. Cit., p. 324-4I3

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THE PHILOSOPHICAL REVIEWHe finds two additional premises to be necessary. The first of

these is the Self-Predication Assumption, which he formulates asfollows: "(A3) Any Form can be predicated of itself. Largenessis itself large. F-ness is itself F."29

Now the phrase "self-predication" is a misleading one. Tobegin with, there is the obvious point that it is not Largenesswhich is predicated of Largeness, but rather "large" or (materialmode) being large. What is needed is, indeed, a principle ofpredication, but to speak of self-predication in connection withForms is to run the risk (a clear and present danger) of confusingthe principle needed with a principle of self-participation, .e., toconfuse Largenessis large with Largenessparticipatesin itself. Sincethe second additional premise required by the Argument willturn out to be a principle of non-self-participation, i.e., the verydenial of self-participation, it is clear that the above confusionwould lead to the "discovery" of inconsistent premises in Plato'sargument. Vlastos does, indeed, "discover" an inconsistencybetween the two additional premises required by the Argument,and it is confusion which leads him to do so. But it is a moreradical confusion, in which the danger to which we have beencalling attention plays at most an auxiliary role.

The assumption Vlastos has in mind would be formulated morecorrectly as "The adjective corresponding to the name of anyForm can correctly be predicated of that Form." This might wellbe called the "F-ness is F" Assumption. However, there is enoughappropriateness to the name "Self-Predication Assumption" towarrant its use, provided the above points are kept in mind.

Now (A3) seems more relevant to the question (2) above,"What authorizes the affirmation of the antecedent of (A2) ?"than to the establishing of (A2) itself. Let us therefore turn ourattention to the second of the additional premises. This he callsthe Nonidentity Assumption, and formulates as follows: (A4) Ifanything has a certain character, it cannot be identical with theForm in virtue of which we apprehend that character. If x is F,x cannot be identical with F-ness."30 I shall not comment specific-ally on this principle at this time, as what I should say about it

29 Ibid. 30 Ibid., p. 325.4I4

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VLASTOS AND "THE THIRD MAN"is, in part, implicit in what I have already said about the otherpremises of Vlastos' reconstruction, and the rest is a matter of afundamental flaw in all his formulations which will be pointedout in the next section.

IVVlastos is clearly correct in saying that both Self-Predication

and Nonidentity are essential to the Third Man Argument.Are they also sufficient, when joined with (Ai) to generate (A2) ?Vlastos thinks so, though he qualifies this by adding "though in avery odd way."'31 And the reason for this is that he has just shown,to his own satisfaction, that these two additional premises aremutually inconsistent, "so that we should not be surprised to seethem justify all kinds of contradictory conclusions."32 Let us lookat his demonstration of this inconsistency. He begins by giving aterse formulation of (A3), namely, "F-ness is F" ;33 he follows thiswith a terse formulation of (A4), namely, "if x is F, x cannot beidentical with F-ness," where x is a variable which includes notonly particulars, but also Forms, in its range of values. He con-tinues:Substituting F-ness for x in (A4) we get

(A5) If F-ness is F, F-ness cannot be identical with F-ness.And since the consequent of (A5) is plainly false, because self-contra-dictory, at least one of the premises from which it follows-(A3),(A4)-must be false.34Convincing? Yet this "demonstration" is a tissue of confusions.The passage which is most clearly diagnostic of these confusionsis that in which Vlastos analyzes the way-the "odd" way-inwhich, as he sees it, (Ai), (A3), and (A4) are jointly sufficient toestablish (A2): "Since these premises warrant the proposition thatF-ness is not identical with F-ness, they will warrant the proposi-tion that F-ness is identical with Fl-ness, which is a Form notidentical with F-ness, and (A2) will then follow from (Ai)."3At this point Vlastos relegates to a footnote his formal analysisof this reasoning:

31Ibid., p- 327- 32 Ibid. 33 Ibid., p- 326- 34 Ibid.35Ibid., p. 327.415

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THE PHILOSOPHICAL REVIEWFor we know from (Ai) that if a number of things are F there must bea Form, F-ness, through which they are apprehended as F. Whenceit follows that(A2b) If a, b, c, and F-ness are all F, there must be a form, F-ness,through which they are apprehended as F.But if F-ness is identical with F1-ness, we may substitute F1-ness forF-ness in the second clause of (A2b), which will produce (A2).36But notice the use that is made of (Ai) in this argument! Whereas(Ai) as initially formulated told us that if a set of particulars,a, b, c,etc., are F, there must be a form F-ness by virtue of which theyare F, it is now being used as a more general principle to the effectthat if a number of "things" are F, there must be a Form, F-ness,where the "things" in question may be either particulars orForms. Let us call this more general principle "(G)." Clearlysomething like the original (Ai) results from applying (G) to thecase where the "things" which are F are particulars. Thissuggests that (A2) might be the result of applying (G) to thecase where the things which are F are F particulars together withthe Form, F-ness, in which they all participate. Clearly, however,(A2) requires, in addition, the use of an Assumption of Non-identity.

But it is even more important to note the role played by theexpression "F-ness" in (Ai) as it is used in the above footnote.An expression such as "F-ness" may be a variable in either of twosenses. (i) It can serve as a representativeymbol.In this use, "F-ness"would represent the name of a Form. To assert a formula whichincludes a representative name is, in effect, to assert each andevery sentence which results from the formula by replacing therepresentative name by a name. Consequently to formulate anargument in terms of "F-ness" where "F-ness" represents thename of a Form is, in effect, to propound a class of arguments ineach of which there occurs not "F-ness," but the name of a singleForm, e.g., "Largeness."(2) "F-ness" can serve as a variable proper. The distinctivefeature of a variable proper is that it makes sense to say "for allvalues of v," "for some values of v," etc. Thus, where "F-ness"is an variable proper, it makes sense to say "All F-nesses ...,"

36 Ibid., n. I I.4I6

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VLASTOS AND "THE THIRD MAN""Some F-nesses " "The F-ness which ...," "There must be anF-ness which ...," etc. These contexts are improper for repre-sentative names.

Now, I wrote above that "an expression such as 'F-ness' maybe a variable in either of two senses." I did not say "either or bothof two senses," but it can readily be seen that, provided care istaken, these two modes of variability (representative ymbol andvariable proper) can be embodied in one and the same symbol.In this case a formula involving "F-ness" would represent class ofsentences in each of which there would occur, instead of "F-ness,"one of the following: "Largeness," "Triangularity," ..., where thelatter, however, are to be construed not as names of single Forms,but rather as variables.In other words, the latter would be used insuch a way as to admit of such contexts as "All Largenesses ...,""There is a Triangularity ...," etc. And the substituends for thesevariables, e.g., "Largeness," would be designated by some suchdevice as the use of numerical subscripts, e.g., "Largeness,,""Largeness2," etc. Note that it would be obviously inappropriateto put the subscripts "inside" the variable, e.g. "Large1ness,""Large2ness."

If we now ask, "Which of these uses of 'F-ness' is appropriate to(G) ?" the answer is obvious. "F-ness," here, must be a symbolwhich representsa class of variables. Indeed, (G), correctly for-mulated as

(G) If a number of entities are all F, there must be an F-nessby virtue of which they are all F,is a formula which represents a class of propositions, one of whichwould be

(G-Largeness) If a number of entities are all large, theremust be a Largeness by virtue of which they are alllarge.

And an application of this proposition to the case of largeparti-culars, would yield

(HI -Largeness) If a number of particulars, a, b, c, are all large,there must be a Largeness by virtue of which they are alllarge.

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THE PHILOSOPHICAL REVIEWThis, in turn, must be carefully distinguished from

(L) If a number of particulars, a, b, c, are all large, they are soin virtue of a Form, namely Largeness.

For in the latter, "Largeness" appears as the name of a singleForm, whereas in (Hi -Largeness) it is a variable.

VIf we approach the Third Man Argument in the light of these

distinctions, puzzles and perplexities melt away like thawing ice.The movement of thought is from (L)-by "induction"-to(G-Largeness) and from (G-Largeness) to the series of hypothetic-als which are its applications. These hypotheticals would be:

(Hi-Largeness) as above.(H2-Largeness) If a number of particulars, a, b, c, etc., and the

Largeness they jointly exemplify are all large, there mustbe a Largeness by virtue of which they are all large.

(H3-Largeness) If a number of particulars, a, b, c, etc., theLargeness they exemplify, and the Largeness exemplifiedby all the preceeding items are all large, there must be aLargeness by virtue of which they are all large.

Indeed, since the Third Man Argument, though phrased in termsof "Largeness," is intended to have a more general validity,"Largeness" has a representative function and, at a certain stagein the logical movement of thought, plays the role of "F-ness"in the last paragraph of the preceding section. Much more, then,than Self-Predication and Nonidentity must be found implicit inParmenidesI32ai ff. if it is to embody a cogent argument.

But what of the charge that Self-Predication and Nonidentityare mutually inconsistent? A quick review of these principles in thelight of the distinctions we have drawn exposes the groundlessnessof this claim. For properly formulated, the Self-PredicationAssumption becomes

(SP) All F-nesses are F.and the Nonidentity Assumption

(NI) If x is F, then x is not identical with theF-ness by virtue ofwhich it is F.

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VLASTOS AND "THE THIRD MAN"And a moment's reflection makes it clear that Vlastos found aninconsistency, because he treated the "F-ness" in his formulationsas a representative name.Once it is realized that what is needed areformulae in which "F-ness" functions as a representative variable,it is seen that the Self-Predication and Nonidentity Assumptionsare to be formulated as above, and the inconsistency vanishes.

VIWhat, then, does the Third Man Argument look like when all

these points have been taken into account?Premises: (G); (SP); (NI); (P) = a, b, c, etc., particulars, are F.(G) (i) = (Hi) If a, b, c, etc., are F, there is an F-nessby virtue of which they are F.(I), (P) (2) There is an F-ness by virtue of which a, b, c, etc.,are F.

(3) [Call this F-ness, "F-nessl."](2), (3), (SP) (4) F-ness1 is F.(4), (P) (5) a, b, c, etc., and F-ness1are all F.(G) (6) = (H2) If a, b, c, etc., and F-ness1 are all F, thenthere is an F-ness by virtue of which they are all F.(6), (5) (7) There is an F-ness by virtue of which a, b, c, etc.,and F-ness1 are all F.(8) [Call this F-ness, "F-ness2."](NI) (9) If F-ness1 is F, then F-ness1 is not identical withthe F-ness by virtue of which it is F.(4), (8), (9) (io) F-ness1 is not identical with F-ness2.(G) (i i) = (H3) If a, b, c, etc., and F-ness1 and F-ness2are all F, then there is an F-ness by virtue ofwhich they are all F.(SP) (1 2) F-ness2 is F.(I2) (5) (13) a, b, c, etc., and F-ness1 and F-ness2 are all F.

ad libitum.VII

Is the argument we have just constructed to be found in theParmenides?Certainly not "in so many words." Implicitly, then?But there are many ways in which formally complete argumentsare "found" in arguments as actually propounded, and I would

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THE PHILOSOPHICAL REVIEWbe willing to say that the above is "merely implicit" in the textof the Parmenides only if this phrase is so understood as to becompatible with the idea that this argument is a fair (albeitidealized) representation of Plato's thought, and, in particular,with the idea that its premises can be said to have been Plato'spremises.37 But it is not my aim, in this second part of my paper,to make a detailed case for the claim that the above is a satis-factory reconstruction of Plato's Third Man Argument. Indeed, Ithink that a careful reading of the complete argument as Platogave it is sufficiently convincing. I say complete, because nowherein his article does Vlastos reproduce, let alone analyze, what Isuppose he would have called the "third step" of the Argument.I suppose this is what leads you to suppose that there is in every casea single Form: When several things seem large to you, it seems per-haps that there is a single Form which is the same in your view of allof them. Hence you believe that Largenessis a single thing....What then if you similarly view mentally Largeness itself and theother large things? Will not a single Largeness appear once again,in virtue of which all these appear large-It seems so.-Consequentlyanother Form of Largeness will appear, over and above Largenessitself and the things which participate in it. And again, coveringall these,yet another,whichwill makeall of them arge.So eachof yourFormswill nolongerbeone, butan indefinite umber.38

If Vlastos had devoted as much care and attention to bringingout the logical form of the "third step" as he did to the two other"steps," he must surely have been led to the distinction between amatrix of general principles and the specific steps in the regressconstituted by their recurrent application. And this, in turn, musthave led him to appreciate the diversity of roles played by"largeness"-failure to discern which is responsible for most ofthe confusions in his analysis.

It is Vlastos' diagnosis of Plato's philosophical frame of mind at37By "Plato's premises" I mean, of course, "propositions used by Plato as

premises in the Third Man Argument," not "premises which Plato thoughtto be true." For, as I shall argue below, the whole point of the first part of theParmenides is that the key premise of the Third Man Argument is false.

38 J have used Vlastos' translation as before (op. cit., pp. 320, 321), save forthe italicized passage-which he neglects-in which I have followed Cornford,Plato and Parmenides, p. 88.

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VLASTOS AND "THE THIRD MA N"the time of writing the Parmenides which is the target of thisportion of my paper. This diagnosis occupies the second, andlarger, part of his paper, and if Vlastos is right in his maincontentions, then Plato could not have had in mind the argumentwith which we concluded Section VI above. Fortunately thispart of his paper rests on a few key premises in the discussion ofwhich we can be quite brief.

Vlastos summarizes as follows the conclusions to be drawn fromwhat he takes to be the fact that Plato presented the Third ManArgument with no clear indication of a refutation.If Plato had identified all of the premises which are necessary (andsufficient) to warrant the second step of the Third Man Argument, hewould not have produced the Third Man Argument at all, unless hewere simply pursuing a logical game for its own sake, which is not whathe is doing in the first part of the Parmenides.n stating the Third ManArgument, and in leaving it unrefuted, he is revealing (a) that he didnot know all of its necessary premises, whence it would follow that (b)he had no way of determining whether or not it was a valid argument.39

The crucial step in this reasoning is the contention that ifPlato had realized that Self-Predication and Nonidentity areindispensable premises of the Argument, he would have detectedtheir inconsistency, and would therefore, instead of playing with aregress, have turned directly to the problem "Does my Theory ofForms involve a commitment to these inconsistent principles? Andif not, what would remain if one or the other were abandoned ?"But we have undercut this step by showing that the idea on whichit rests-namely that Self-Predication and Nonidentity arepatently incompatible-is mistaken. Up to this point, therefore,Vlastos has given no good reason for supposing that Plato had not"identified all of the premises" and therefore "had no way ofdetermining whether or not it was a valid argument."

But Vlastos has another string to his bow. He claims to haveindependent evidence-evidence, that is, which does not springfrom his analysis of the Third Man Argument-for the thesis thatPlato had not identified all of the necessary premises.40 Specifically

39Ibid., p. 329.40 Thus, immediately following the passage just quoted he writes, "(a) canbe independently verified, and it will be in Section II."

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THE PHILOSOPHICAL REVIEWhe proposes to establish (a) that Plato's Theory of Ideas, even inits later form, is through and through committed to Self-Predi-cation-; but also (b) that Plato never came to an explicit recogni-tion of this fact. (a) is clearly the crucial step, for unless it weretrue, the fact-upon which Vlastos lays such stress-that Platonowhere explicitly formulates a Principle of Self-Predication4'could scarcely mean that Plato failed to recognize an essentialfeature of his theory; nor could evidence be found in the factthat Plato, in the later dialogues, arrives at conclusions about theRealm of Ideas-e.g., its genus-species structure; the existenceof a Form of Motion (or Change)-which must have been seento be incompatible with an explicitly entertainedprinciple of Self-Predication. On the other hand, if Vlastos can establish thatPlato's Theory of Ideas, even in its later form, is committed toSelf-Predication, then one can hold that Plato was cognizantof the logical force of the Third Man Argument as we havereconstructed it, and therefore that he recognized that Self-Predication is its key premise, only at the expense of supposingthat Plato believed either that the argument refuted his Theory ofIdeas or that it could be saved by dropping the generalizedAssumption of Nonidentity.

VIIIVlastos has little difficulty in showing that the language of the

earlier dialogues is fraught with Self-Predication. And it isscarcely plausible to discount the (familiar) evidence he bringsforward by claiming that Plato's language was self-consciouslymetaphorical. For in what language would Plato have formulatedto himself a distinction between the philosophical claims he wasmaking, and the literal meaning of the language in which he waspublishing these claims? Certainly it would be a mistake tosuppose that when Plato began his philosophical speculations hefound ready to hand a vocabulary whose literal meanings were the

41 Vlastos himself points out, however, that Plato comes very close indeedto such a formulation in the text of the Third Man Argument. Thus, afterpointing out that Self-Predication is essential to the Argument, Vlastos writes,"Plato's actual wording of the second step comes as close to asserting it as onecould without stating the Self-Predication Assumption" (p. 325). And thisis no understatement, as a glance at the passage in question will confirm.

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VLASTOS AND "THE THIRD MAN"concepts and distinctions of the Theory of Ideas, a vocabularywhich he could use inforo interno in the process of contriving therhetorically more effective metaphors of the dialogues. Rather,the creation of the Theory of Ideas was identical with the creationof the language of the Theory of Ideas. The differences betweenthe philosophical and the everyday meanings of words, as well asthe awareness of these differences, was the slowly ripening fruit ofphilosophical argumentation about the Ideas, and of catch-as-catch-can wrestling with the perplexities they were introduced toresolve (as well as the perplexities which inevitably arise wheneveryday language is put to philosophical use).I think it is fair to say that when Plato was writing the earlierdialogues, he had not yet been led to question the Self-Predica-tional force of the language of his Theory. But this is by no meansequivalent to the idea that he was "implicitly" thinking of hisForms as Self-Predicational, i.e., "taking" this (in Cook Wilson'ssense) "for granted." To establish this, we would have to showthat significant features of the early Theory of Ideas, or of thearguments developed in connection with it, imply a commitmentto Self-Predication. In other words, one would have to show thatSelf-Predication plays a role in the philosophical use to whichPlato put the language of the theory. To do this is no simpletask, and I shall not attempt to settle the matter one way or theother on the present occasion. I do, however, want to call atten-tion to at least two considerations which contribute to an explana-tion of the fact that Plato used language with Self-Predicationalforce, yet do not require us to say that he (even implicitly) thoughtof the Ideas as Self-Predicational.

In the first place, there is the obvious fact that the names ofthe Ideas had to be formed from the roots of the class terms andadjectives, the applicability of which to particulars was to beexplained by the Theory. Thus, anglice, the name of the Idea interms of which statements of the form "... is triangular" or"... is a triangle" are to be explained, would be a noun or noun-phrase built from the root of "triangular" and "triangle." Onlywhen the concept of a universal had been hammered out inphilosophical debate would it come to be seen that there issomething queer about the use of "The Triangle Itself" to design-

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THE PHILOSOPHICAL REVIEWate this Idea. And until the concept of a universal had beenhammered out, the distinctive expressions which philosophers useto designate them (e.g., "Triangularity," "Redness," etc.) did notexist. In short, Plato did exactly what we should expect. He tookthe existing noun "triangle" and put it to a new use. But the factthat by referring to the Idea as "The Triangle Itself" he wasusing language which implies that the Idea is a triangle, does notsuffice to establish that Plato thought (even "implicitly") thatThe Triangle Itself was a triangle. To show this, as we havepointed out, one must show that this implication of the languageis put to philosophical use.In the second place, the early dialogues stress the role of theIdeas as standards or norms which objects in the World of Becom-ing strive to realize, but necessarily fail to realize fully because ofthe inherent fuzziness of Becoming. Now, if we thought along theselines, we should carefully distinguish between the Idea or universaland the (nonexistent) Ideal which it specifies, e.g., between Straight-Linearity and a perfectlystraight line. But this distinction was nota datum for Plato, and he could have been led to draw it only bythe pressure of the perplexities which arise from a failure to drawit. Did Plato ever draw, in his own mind, this distinction betweenIdeas and Ideal Particulars? One immediately thinks of ta mathe-matika. Note, however, that, as usually conceived by those whofind them in Plato, they are existent Ideal Particulars which areother than the Ideas they exemplify. As for a distinction betweenIdeas and non-existent deal Particulars, Plato was not in a positionto draw it, until he had acquired the insight into "Not-Being,"which is embodied in that most wonderful of the dialogues, theSophist. Fortunately, the resolution of this problem is not mypresent concern. The point I wish to make is that to say thatPlato's language embodies no distinction between The CircleItself and an ideal circle, and, in general, between an Idea and theIdeal it specifies, is not the same as to say that Plato "implicitly"thinks of The Circle Itself as an Ideal Circle. The latter statementis much stronger in its force than the former. That Plato failedto draw an explicit distinction is, indeed, a reason or supposing thathe "implicitly" thought of the Ideas as Ideal Objects. But it is nota compellingreason, as is made clear by the fact that we can con-

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VLASTOS AND "THE THIRD MAN"ceive of considerations which would lead us to say that althoughPlato drew no such explicit distinction he "implicitly" distin-guished between Ideas and Ideals. These considerations wouldspring from an examination of the different philosophical uses towhich such expressions as "The Circle Itself" were put in thecontext of different problems.

IxBut whether or not a careful examination of the evidence would

lead us to the conclusion that in the early dialogues Plato thoughtof the Ideas as Self-Predicational, I am convinced that by thetime he wrote the first part of the Parmenides,he had faced up tothe question, "Is, e.g., The Large Itself large?" and answered itin the negative. This thesis is by no means a novel one. As Vlastoshimself points out it is the orthodox view.42 On what grounds doeshe reject it?If Plato never stated it [the Assumption of Self-Predication], whatreason can be given for saying that he did make it after all ?-Thereason is that it is certainly implied by various things he said andbelieved. It is implied, first of all, both by his Degrees of RealityTheory and by his Copy Theory of the relation of things to Forms.43

Postponing comment on the idea that Plato ever held a "CopyTheory of the relation of things to Forms," let us first take upthe question of a Platonic "Degrees-of-Reality" theory. Vlastosapproaches this topic from a number of directions. To begin with,he claims to find in Plato the "assumption" "logically thecostliest assumption that Plato made"-"that the verb 'is' andall its substantival, adjectival or adverbial variants have a singlemeaning."44What Plato means by saying ... that "x is," in the strict sense of "is,"becomes clear when we see that he understandsthis to entail:

(i) x is intelligible;(ii) x is changeless;(iii) x is not qualified by contrary predicates;(iv) x is itself the perfect instance of the quality or relation whichthe word for 'x' connotes.45

42 Op. Cit., p. 337, n- 33; p. 346, n- 48.43 Ibid., pp. 336-337. 44 Ibid., P. 334. 45Ibid.425

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THE PHILOSOPHICAL REVIEWNow it is certainly true that we find no hint in the early dialoguesthat Plato is aware of the different meanings of "is" and also truethat he thinks of the Ideas as the things that are, and also true thathe is not yet able to give the reply direct to Parmenides, who canbe said to have made the assumption in question. But this falls farshort of establishing that Plato himself makes this assumption.Indeed, Plato's refusal to commit himself to Eleatic monism, aswell as the elusive flexibility of his discussions of Becoming, andhis willingness-noted by Vlastos46-to speak of objects in theWorld of Becoming as "beings" (onta), things that are, all indicatethat Plato refused to postpone the solution of specific ontologicalproblems until he had come to terms with the Parmenideanproblem.47 As for the later dialogues, surely a good case can bemade for saying that once the Stranger of the Sophist has made itclear that "Being" has its puzzles no less than "Not-Being,"and that we can scarcely hope to solve the latter until we havemastered the former, he embarks upon a course of reasoning theheart of which consists exactly in drawing distinctions between themeanings of the word "is" and its cognates as they occur indifferent contexts.

Vlastos nowhere clearly brings out what he conceives to be therelation of this "costliest assumption" to Plato's "Degrees ofReality Theory." As a matter of fact, it would seem obvious thatif "is" had for Plato the meaning Vlastos says it did, then Platocould not, without inconsistency, have held such a theory. Vlastostacitly acknowledges this, for immediately after ascribing this"costliest assumption" to Plato, he writes:Plato did not thereby revert to the Eleatic view that the sensible worldis wholly unreal. His view was a Degrees-of-Reality theory whichpermittedhim, in compliancewith his nativetongue,to say that sensible thingsare, as logical subjects of assertions of existence and ascriptions ofproperties and relations. They were halfway real, "between the purelyreal and the totally unreal" (Rep.478d).48

Surely, however, this gives the show away. For to admit that46 Ibid., p. 335, n- 29.47 And he was by no means the only philosopher who continued to philoso-phize in the shadow of "Being alone is, Not-Being is not."48 Ibid., pp. 335-336. Italics mine.

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VLASTOS AND "THE THIRD MAN"Plato, in the discussion of particular problems, was willing to use"is" and related words "in compliance with his native tongue"is to grant that Plato's philosophizing was not limited by thestrait jacket of the "assumption" that "the verb 'is' and all itssubstantival, adjectival and adverbial variants have a singlemeaning."

Yet there is, indeed, a connection between Vlastos' attributionof this assumption to Plato, and the Degrees-of-Reality Theorywhich he finds in the dialogues. For if "is" has one meaning, andif this meaning involves Self-Predication (item iv in the list quotedabove, p. 425) then degrees of "being" or "reality" could beexpected to involve degrees of being F,-particulars beinghumdrumly F to various degrees, F-ness, however, being super-bly F. That some such reasoning is at the back of Vlastos' mindis shown by the fact that he fails even to consider the possibilitythat Plato might have had a degrees-of-reality theory withoutbeingcommittedo Self-Predication.

We have not yet, however, plumbed the depth of Vlastos'thought. For if we ask "Why does Vlastos so confidently includethe F-ness of F-ness in the very meaning of Plato's 'is' ?" it strikesus that this inclusion would be a bald petitio unless there were atleast the sketch of an argument to back it up. And clearly theargument would have to be more than a rehash of the evidencethat Plato (implicitly) thought F-ness to be F. For what is neededis an argument which would show that Self-Predication is sointrinsic to Plato's conception of being, that he couldn't abandonthe former without giving up the latter. And evidence that Platoat one time or another thought F-ness to be F would not servethis purpose.

There is indeed such an argument, and it is to be found in thefollowing passage:Did not his Theory of Formscall attention, and for the first time, to the"reality" of universals as distinct from that of material existents?This of course isperfectly true. But what is no less true is that the Pla-tonic ontology inadvertently blurs the very distinction it was devisedto express. It compels Plato to thinkof the differencebetween empiricalexistents and their intelligible properties as a difference between"deficiently" real and perfectly real things, i.e., as a difference in

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THE PHILOSOPHICAL REVIEWdegree between beings of the same kind, instead of a difference inkind between different kinds of being. To say that the differencebetween a white thing, like wool or snow, and the universal, Whiteness,is a difference in degree of reality, is to put Whiteness in the same classwith white things, albeit as a pre-eminent member of that class,endowed in a pre-eminent degree with the character which its fellowmembers possessin various deficient degrees; it is to think of Whitenessas a (superlatively) white thing, and thus to assimilate it categoriallyto white things, instead of distinguishing it from them.49

Now, in reproducing this argument, I have italicized a certainlittle word. It plays so important a role that it deserves thisdistinction. For to say that thedifference between an F particularand F-ness is a difference in degree of reality is indeed tantamountto saying that the F particular and F-ness are both F. For if theyweren't, then this would be an additional difference between themover and above their different degrees of reality. On the otherhand, if the F-particular and F-ness are both F, there must besome difference in the way they are F, for F-ness is not justanother F particular. And this difference would be the differencein degree of reality which is thedifference between them.

But why in the world should we suppose that (for Plato) thedifference between F particulars and F-ness is a difference indegree of reality? And without this premise, the argument doesn'tget off the ground. Let me emphasize that I have no objection tosaying that Plato throughout his philosophical career divided thethings that are into the more and the less real. I think it a seriousmistake however, to suppose that the way in which Plato con-ceives of degrees or levels of reality involves a commitment to thePrinciple of Self-Predication. Indeed, as I have said before, I amconvinced that the first part of the Parmenides s a deliberate andsustained critique of Self-Predicational interpretations of theIdeas.

One more comment on "is" before we turn to consider whatwould remain of a Platonic Degrees-of-Reality Theory if Self-Predication were dropped. After attributing to Plato the assump-tion that "is" has one single meaning, he writes, "The Aristotelianaxiom that 'things can be said to be in many different senses' was

49 Ibid., p. 340.428

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VLASTOS AND "THE THIRD MAN"not a commonplace in its day, but a revolutionary discovery."50

To this he adds as a footnote:[A discovery] which, among other things, offersa direct way of trackingdown the source of the Third Man Argument, as Aristotle himselfclearly saw. In his own language, the confusion of the sense which"is" has in the first category with its sense in one of the other categoriesis what "creates the 'third man.' " Soph.El. I78b37 ff; cf. Met.1038b34 ff.51This is an ancient legend. It overlooks the sad extent to whichAristotle had to manhandle Plato's thought before he couldconvince himself that he had refuted it. It is indeed true that ifyou think of universals as substances in Aristotle's sense (whichthey obviously an't be) then you are committed to thinking of themin Self-Predicational terms. For, let us face it, it is an analyticconsequence of Aristotle's conception of substance that no univer-sal can be a substance. Universals are necessarily predicable ofsomething, otherwise they wouldn't be universals. (Primary) sub-stances are not. Consequently, to suppose that a universal is asubstance (always in Aristotle's sense) is to suppose that it is aparticular. But to suppose that F-ness is a particular is tantamountto supposing that it is F, for clearly this particular has somethingto do with being F, and what could this something be but theparticular's being itself F. To all this it suffices to reply that onlythe Plato of Aristotle's (and Vlastos') imagination thinks ofF-ness as an Aristotelian substance.

Rather than saying that Platonists have thought of F-ness as Fbecausethey thought of F-ness as a substance in the Aristoteliansense, it would be more correct to say that when (if ever) Plato-nists have thought of F-ness as F, they have, in effect, treatedF-ness as a substance in the Aristotelian sense (i.e., as a particular).But this reformulation amounts to abandoning the claim thatAristotle has traced the genealogy of the Third Man. Much moreto the point is Vlastos' observation that the Greek language maytrap the unwary into confusing the tautology "Justice is justice"with the absurdity "Justice is just." I think it can be shown,however, that Protagoras 330c-d, "which, since first noted by

50 Ibid., pp. 334-335. 51 Ibid., p. 335, n. 25.429

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THE PHILOSOPHICAL REVIEWGoblot in 1929, has become the star instance of Self-Predicationin Plato," is capable of an interpretation (in the light of the dialec-tical structure of the dialogue as a whole) according to whichPlato usesrather than commits his confusion. (And as for the claimthat Plato must be guilty of the Assumption of Self-Predicationbecause he has Socrates say [Phaedo iooc], "If anything else isbeautiful, besides Beauty itself," and because "the whole pointof Diotima's speech is that the Form of Beauty is superlativelyfair,"52 it is sufficient to reply that Plato thought of all the Ideasas beautiful to the contemplation of the philosophically trainedmind, as have many other thinkers, including one of the manyBertrand Russells, who have not been guilty of the Assumption ofSelf-Predication.) However this may be, the point I wish to makeis that the confusion in question is between the "is" of predicationand the "is" of identity, rather than between two of the meaningsdistinguished by Aristotle, which are actually all special casesof the "is" of predication.

XWhat remains of Plato's hierarchical conception of reality if we

omit the Assumption of Self-Predication ? Items i-iii of Vlastos' listof what is entailed by "x is" in Plato's philosophy provide anexcellent starting point. The Ideas are changeless, objects ofmind, and consistent. In the early dialogues, Becoming is inconstant flux, the object of sense perception, and, above all,inconsistent. Yet Plato didn't know quite what to say about thestatus of Becoming, for he had not yet resolved to his own satis-faction the puzzles relating to "is not." In the Republic(478d) heplaces Becoming "between" Being (the Forms) and the utterlynonexistent. But there are, prima facie, two ways in which Platocould have interpreted this "intermediate" status. On the onehand, he could have viewed Becoming as somehow a mixtureofBeing (the Forms) and a Not-Being conceived as an ontologicalprinciple or, better, stuff. In favor of this interpretation would bethe fact, emphasized by Plato, that to describe a change we mustuse both "is" (or "was") and "is not" (or "was not"). On theother hand, he could have taken Becoming to be an ultimate and

52Ibid., p. 338.430

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VLASTOS AND "THE THIRD MAN"irreducible mode of existence, one which, indeed, dependson Being(the Forms) but does not contain Being as an ingredient.On thewhole it is the latter interpretation which comes closest to Plato'sthought, even in the Republic.It finds its clearest expression in theAnalogy of the Line, where the relation of Becoming to Being iscompared to the relation (within the world of becoming) ofshadows and reflections to physical things.

By the time of the Timaeusand the Sophistan important changehas taken place. Becoming is no longer thought to be internallyinconsistent. This revolution (and revolution it was) is signalizedin the Sophistby the recognition of an Idea of Change. The failureof Becoming to be "truly real" could no longer be traced to itssupposed self-contradictory character. Nor could the fact that itcannot be described without using "is not" suffice to give it alower status, for the Sophist shows this to be equally true of theIdeas. It is, therefore, the categories of dependencend independence(or self-sufficiency)which now take over the major part of the jobof ranking the levels of reality. Thus, although the Realm of Ideasand the World of Becoming are both self-consistent,the latterdepends on the former (and on the Receptacle or Place as well).The Ideas are taken to have an Olympian self-sufficiency. Afterall, if there were no Triangularity, there could be no triangles;but if there were no triangles, would there not still be Triangular-ity? To be sure, the Receptacle appears to be as self-sufficient asthe Ideas, but this only means that its place at the bottom of thescale must be justified by other criteria. Again, to account for theplace of Soul within the hierarchy would require a detailedanalysis of the Timaeus.53 But I have already said enough tovindicate the idea that the Great Chain of Being is possible withoutSelf-Predication.

But, it will be said, it is exactly in the course of developing theDegrees-of-Reality Theory of the Timaeusthat Plato most clearlycommits himself to a Copy Theory of the relation of things toForms. Does not Plato speak of the world of Becoming as con-sisting of "likenesses" of the Ideas? Do not both the Sophist andthe Timaeusecho the assimilation, in the Republic,of the relation

63An excellent account of the status of Soul in the metaphysics of theTimaeus is to be found in Cornford's Plato's Cosmology (London, 1937).43'

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THE PHILOSOPHICAL REVIEWbetween Becoming and Being to that between image and thing,painting and subject, imitation and original? Once again it justwon't do to jump from the fact that Plato uses language withSelf-Predicational implications to the conclusion that Platothought of the Ideas in Self-Predicational terms. "But can itseriously be maintained that Plato didn't think of things as like-nesses or imitations of the Ideas?" One good question deservesanother. What philosophical purposes could the language ofimitation have been serving for Plato if he didn't think of theIdeas as Self-Predicational? And what advantages (and dis-advantages) does it have as compared with the language of"sharing"? Until these questions have been answered, any dis-cussion of the former question is premature.

I shall make the essential points briefly. The first and mostobvious advantage of the copy-likeness-semblance-imitation ter-minology is that it is admirably suited to give expression to theinferior status of the World of Becoming. Then there is the fact,of greater technical interest, that "likeness" does not, as such,imply an internal diremption of the F thing; whereas if we speakof F things as "sharing" in The F Itself, we confront a distinctionwithin each F thing between a sharerand its portionof the shared.54Likeness is a two term relation between copy and original. Sharingis a tetradic relation between sharer,portion,shared tem, and anothersharer. In this respect, "likeness" is much closer than "sharing"to such contemporary terms as "exemplifies" and "is an instanceof."

The Phaedo is a key document in the interpretation of thelanguage of the Theory of Ideas. There we find passages which, byspeaking of the Ideas as Ideals which things strive to realize,suggest that it is the language of "likeness" or "imitation" whichis appropriate to express the relation of things to Ideas. On theother hand, the final and most metaphysical argument forimmortality is built on the distinction between an F thing, the F

64 This must not be pressed too far; even as used by the man in the street,"sharing" does not always imply that the shared item is dividedamong thesharers. (Thus two people may share a common goal.) Whether this is alsotrue of the corresponding Greek words I leave to the philologists. If so, thelanguage of "sharing" gains an additional flexibility which makes it possibleto use it cheek by jowl with the language of "likeness."432

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VLASTOS AND "THE THIRD MAN"in the thing and The F Itself, which, at first sight, is the frameworkof "sharing," pure and simple. If we ask what there is to a thingover and above "the large in the thing," "the sweet in thething," etc., we find, of course, no answer. The temptation is toread into the Phaedo a substratum theory55 by something likethe following line of thought. In the naturalistic philosophy ofEmpedocles, each object has its share of Earth, Air, Fire, andWater, yet contains no sharer over and above the shares. ButPlato's shared objects are the Ideas; and since Becoming canscarcely be made up of shared Beings, there must be in things asubstratum or sharer. We have already pointed out that untilPlato made substantial progress in clarifying the puzzles "is not"which were exploited by the Eleatics and Sophists alike, he wasbound to be tempted, on occasion, to think of changing asmixturesof Being and Not-Being-roughly, Form and non-Form.

Yet the fact remains that Plato drew no such conclusions.Nowhere do we find even a hint of a substratum analysis. Andif we take this seriously, and ask ourselves "Can sense be made ofthe trichotomy 'F thing,' 'the F in the thing' and 'The F Itself,'without a commitment to a substratum?" we note that if "the Fin the thing" were a copy or reflectionor imitation of the F Itself,a substratum would no longer be necessary, since the thing couldconsist of these copies or reflections or imitations, namely the hotin the thing, the sweet in the thing, etc., without consisting ofForms (or "parts" of Forms). And it is a significant fact that asPlato's metaphysics of Becoming matured, it is the Heracleiteanrather than the Ur-Aristotelian picture of physical things whichprevails. Enduring things are constituted by a binding of theflux of Becoming to order and recurrence. Plato rejects in advancethe Aristotelian dichotomy Form-Matter and replaces it by thedichotomy Process-Place.56

55 On this interpretation, "the large in the thing" would be a reificationof the fact that the substratum is related in a unique way to Largeness. Indeed,this interpretation calls for a conception of Largeness as a componentof largethings-a conception which entails that the Separation (chorismos) of thePlatonic Ideas must be a mistake.

56 Plato, indeed, places process in a context of active and passive powersfrom which they arise,-and this might make it seem as though process isbeing subordinated to the "causal" or "dispositional properties" of "conti-

433

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THE PHILOSOPHICAL REVIEWThe distinction between "the F in the thing," and "The F

Itself" is appropriate to both the "sharing" and the "likeness"terminologies. But clearly the Separation (chorismos)of the Forms-that is, the fact that Plato's Ideas are not constituents or partsin any sense (even "adjectival aspects") of changing things-ismore adequately captured by the language of "likeness." It isessential to realize that "the F in the thing" is not a universal, .e.,is not common to the many F things. By failing to appreciate this,Vlastos further confuses an imperceptive discussion of "the Sepa-ration Assumption"57 He speaks (p. 342, n. 40) of "the F of Fparticulars" as a "predicate which attaches to particulars" andfails altogether to see that theF in thething s, in effect, a subordinateand component particular the whole nature of which is to be F.Interestingly enough, this conception of the F in the thing isechoed in Aristotle's Categories (i a24-bg) where, in effect, hedistinguishes between Whitenessand the white in the thing, and tellsus that while that which is individual is never predicated of asubject,it may be present n a subject.To end this discussion of the comparative philosophical advan-tages of these two terminologies, it should be noted that "sharing"has the virtue that it does not imply Self-Predication. "X sharesy with z" does not imply that x resemblesy; though, of course, ifThe Hot Itself is construed as Empedoclean Fire, sharing in TheHot Itself would involve coming to resemble it. It is thereforeinteresting to note that it is "sharing" rather than "likeness" or"imitation" which plays the role of technical term for the relationof things to Ideas.58

nuants." But the powers of Plato's metaphysics-like those of Leibniz centurieslater-were not the austere "if ..., then ..." 's of contemporary philosophy ofscience. They were rather of the nature of desires or yearnings, and werereally a deeper form of process. The Timaeus, in effect, compares the orderlinessof the world process to the life of a man whose appetites are persuaded by hisreason.

57 Ibid., p. 340 ff.58 "It follows that the other things do not partake of Forms by being like

them; we must look for some other means by which they partake.-So itseems." Parmenides I33a, quoted from Cornford's Plato and Parmenides, p. 93.

434

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VLASTOS AND "THE THIRD MAN"XI

What, then, is the upshot of the first part of the Parmenides?The argument can be summed up as follows:(i) Obvious and insuperable difficulties arise if one construes theIdeas as the same sort of things as the "seeds" or "roots" of thePluralists. For then sharing would be a matter of each thinghaving within it either the whole or a part of the Idea.(2) The temptation to construe the Ideas in this manner arises fromsupposing that in order for The Hot Itself to explain the hotness

of hot objects, it must itself be hot, i.e., be the Fire of Empedocles.How, it is thought, can something make things hot, if it isn't hotitself?(3) But this assumption can be shown to involve a regress (the ThirdMan).(4) On the other hand, Ideas are not mere thoughts. They are reali-ties to which the mind is related in thinking, as physical objectsare realities to which the mind is related in sense perception.(5) Shall we say, then, that things are imitations or likenesses of theIdeas ? This would indeed avoid the difficulties arising inconnection with the first approach ([i] above). But it doesn'tavoid the regress (second version of the Third Man).At this stage, we, in our modern sophistication, would likePlato to "come right out" and say something like the following:"The relation between particulars and universals cannot beidentified with any relation which holds among particulars. Thus,any expression, e.g., "sharing" or "likeness," which mentions arelation which holds among particulars, must be at best a meta-phor, the application of which to the relation between particularsand universals is to be justified with reference to certain formalanalogies between the two relations." Yet it is obviously unreal-istic to expect Plato to make any such statement. The decisivereason for this is that while Plato could say of a given propertythat it was "relative" (pros ti)-"with respect to something"-hehad no general term for relations. In other words, he could saythat sharingis pros ti, likeness s pros ti, etc., but such an expressionas "the relation between things and Ideas" falls outside histechnical vocabulary. Thus, when he became aware of the limi-tations and dangers of the terminologies of "sharing" and "like-

435

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THE PHILOSOPHICAL REVIEWness," the limitations of his philosophical language precluded himfrom saying to himself, "let us use the word '...' for the relationbetween things and Ideas," and directed his search toward thediscovery of another word in ordinary usage which might be moresuitable than either "likeness" or "sharing." Thus we find Parme-nides saying at ParmenidesI33a (quoted above, n. 58), "We mustlook for some other means whereby they partake."'9 In otherwords, these limitations led him to look for still another relationword or phrase in ordinary usage which might be an even moresatisfactory metaphor, once its literal implications had beenbrought under strict philosophical control. We can imagine thathe might have hit on some such phrase as "things are the childrenof the Ideas"-a metaphor which is actually to be found in theTimaeus-as the most useful expression for the relation betweenBecoming and Being.

The substance of the above remarks is that it would be a radicalmistake to interpret Plato's search for another means wherebythings partake of the Ideas as a failure to realize that no relationamong things can be identical with the relation between thingsand Ideas. For the fact that a philosopher makes a certain kind ofphilosophical use of those ordinary relation words which heapplies to the Ideas can be good ground for saying that he recogni-zes the uniqueness of the relation between things and Ideas, inspite of the fact that nowhere does he "come right out and saythis." And once this is realized, we are in a position to appreciatethe subtlety and sophistication of Plato's later Theory of Ideas.

XIIThere are many who will feel, as apparently Vlastos does, that

Platonic Ideas without Self-Predication have ceased to be PlatonicIdeas; that without Self-Predication they are of merely logicalinterest and have ceased to define a metaphysics, a way ofconstruing Man-in-the-World. Nothing could be further from thetruth. The heart of the Platonic tradition lies not in a picturesquerealm where Horseness is a horse, Triangularity a triangle and

59 "Mode of partaking" would perhaps be a better rendering of the thoughtthan "means whereby they partake."

436

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VLASTOS AND "THE THIRD MAN"Courage a ... (a what?), but rather in the conception of a domainof eternal (atemporal) objects which the human mind can "appre-hend" or "see," and the interconnections of which, open at leastin part to human inspection, constitute the fundamental principlesof the World of Becoming. That one can speak in a logician'slanguage of universals, particulars, and their mutual relationshipsand yet share this Platonic conception is made manifest byBertrand Russell's "A Free Man's Worship." Platonism, thuswidely conceived, is a metaphysical framework which admits ofdevelopment in many different directions. And the directiontaken by the early Russell (not to mention that taken by San-tayana) has been taken by but few Platonists. The conceptionof the human mind as apprehending "abstract entities" hasusually been construed (and, I think, reasonably so) to support astraightforward mind-body dualism,60 and to fit harmoniouslywith a theistic cosmology. That it is a mistake has not preventedit from being one of the central threads around which havecrystallized the values and attitudes of civilized Western man.

WILFRID SELLARSUniversityof Minnesota

60 For an elaboration of this point, see my essay "Empiricism and AbstractEntities," forthcoming in The Philosophy of Rudolf Carnap, ed. by P. A. Schilppand to be published by The Library of Living Philosophers, Inc.