The 'Third Man' Argument and Plato's Theory of Forms
Author(s): J. M. E. Moravcsik
Source: Phronesis, Vol. 8, No. 1 (1963), pp. 50-62
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of Forms'
The'ThirdMan'Argument
andPlato'sTheory
J. M. E. MORAVCSIK
is oneof themost
'Third Man'-argument (Parmenides132ai-b2)
controversial passages in Plato's dialogues. In recent years a number
of new interpretations of this argument have appeared.z These
interpretations were designed to bring to bear upon the Platonic text
the logical rigour and analytic acumen which are characteristic of contemporary philosophy. Allegedly implicit premisses have been brought
to light with the help of symbolic logic, and attempts have been made to
relate the argument to the problem of change vs. constancy in Plato's
metaphysical position. Though these interpretations contain much that
is stimulating, each of them seems to have the shortcoming of representing Plato as fairly simple-minded philosophically,3 and of locating
the complexity of thought in logical structure.4 Such accounts ascribe
to Plato the kind of argument which is not typical of what we encounter
in the dialogues. For in most of his writings Plato emphasizes philosophical
depth, rather than formal complexity. Thus it is more plausible to suppose
that the passage under consideration is fairly simple in its deductive form,
and that it poses problems with serious metaphysical implications. Such,
at any rate, is the contention of the interpretation presented here.
If correct, this interpretation indicates a need to reexamine the dialogues in ways rarely - if ever - attempted before. For according to the
account presented here, in the middle period dialogues5 we find not
one but five different conceptions of what are known as Plato's Forms,
and part of the difficulty of the 'Third Man'-argument is that it does
T
HE
I I am greatly indebted to Prof. G. Vlastos, Prof. H. Hochberg, and to my colleagues at
the University of Michigan for criticism and advice.
2 G. Vlastos, "The Third Man Argument in the Parmenides"
Phil. Rev. v. 63. pp. 3 19-349,
W. Sellars, "Vlastos and the Third Man" ibid. v. 64 .pp. 405-438, reply by Vlastos,
PP. 439-449, P. Geach, "The Third Man Again" ibid. v. 65. pp. 72-82, reply by Vlastos,
pp. 83-95, R. E. Allen, "Participation and Predication in Plato's Middle Dialogues"
ibid. v. 69 .pp. 147- x 64.
3 E.g. Vlastos ascribes to Plato two tacit premisses which are patently inconsistent with
each other (see op.cit. pp. 324-325).
4 Sellars ascribes to Plato the distinction between predicates and predicate-variables
(op.cit. pp. 416-41I7), while Geach locates the trouble in a complex and inconsistent
set of propositions with involved quantificational form (op. cit. pp. 77-7 8).
5 I am including among these the Timaeus.See G. E. L. Owen, "The Place of the Timaeus
in Plato's Dialogues" ClassicalQuarterlyv. 47. pp. 79-9S.
so
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not affect all of these conceptions in the same way. These different
conceptions have been overlooked because of the traditional emphasis
on the similarities among the various descriptions of the Forms which
Plato provides for us. In order to see Plato's thought in better light, it is
time to concentrate on the differences.
Another distinguishing feature of this interpretation is that it shows
how the notion of self-predication (i.e. the notion that a predicate
should apply with descriptive force to the Form it stands for) which at
first blush appears absurd, can be made intelligible within the context
of Plato's ontology. This should give second thoughts to those who are
all too prone to detect linguistic and logical confusions in the writings
of traditional philosophers. Finally, this interpretation should engender
new interest in the 'Third Man'-argument among philosophers, for it
locates at the heart of the argument metaphysical problems which are
as much alive today as they were 2 300 years ago.
As our point of departure let us take the claim made by Vlastos and
Geach that the "Third Man"-argument remained a source of puzzlement
to Plato; on the one hand he did not accept it as fatal, on the other hand
he could not refute it. Since the Theory of Forms is upheld in such later
dialogues as the Philebus,and at the same time no refutation of the "Third
Man" is ever given, this claim seems eminently acceptable. Thus the
real issue is to locate the causes of this puzzlement. According to Vlastos
the difficulty is that Plato held two principles the inconsistency of which
he failed to recognize.' These principles, the principles of self-predication and of non-identity, are explained as stating that each Form has
the character it stands for, and none of the Forms can be identified with
any of its attributes. A flaw in this interpretation is the vagueness and
ambiguity of these statements. Our first step toward an adequate interpretation is to distinguish various possible interpretations of the principles in question. With regard to self-predication, we must distinguish
between the following two statements.
Si.
S2.
A Form F has 'F' predicated of it in a sense different from and prior to the sense(s)
in which 'F' is predicated of all the entities partaking of this Form.
A Form F has 'F' predicated of it in the same sense in which 'F' is predicated of
particulars2.
See note 3. Geach reproduces the principles as i) F-ness is an F, and 2) No F is identical
with F-ness. Geach himself does not accept these as adequate renderings of what Plato
wished to express.
2 F. M. Cornford also
fails to make this distinction, and thus misses completely the
element which leads to the infinite regress in the argument, as well as its philosophical
implications (see Plato and Parmenidesp. 8 8).
I
Si
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Both of these principles assume that 'F' is not the proper name of F,
but rather that it applies to this Form with descriptive force. They
differ, however, in the kinds of predicative roles which they ascribe
to 'F'. In S2 'F' functions solely as a general predicate, while in Si
when applied to the Form F, 'F' functions like a definite description,
giving a unique characterization of the Form F.' The distinction between
Si and S2 rests on the notion of "difference in sense," which is not to
be confused with "difference in meaning." Words which have different
meanings, like the word 'bank' in English, are ambiguous. There are
other words, however, which do not have several meanings, but have
distinct, though closely related, ranges of application. Such words have
different senses. E.g. the word 'brother,' though not ambiguous, has as
its primary range of applications male siblings, and as its secondary
ranges members of social groups, or friendly persons ("he was a brother
to me"2). We have good evidence to show that Plato - at least in the
later dialogues - was aware of ambiguity, and that at times he was
anxious to call attention to instances of this (e.g. Sophist 2S6ai I-I2).
In view of this, and the fact that Forms and particulars fall into different
categories, it is plausible to suppose that Plato was aware of the notion
of "difference in sense."
With regard to non-identity, we should keep separate the following
two statements.
S3. In any statement of subject-predicate form, the subject- and predicate-expressions
stand for separate entities.
S4. There is a distinct entity corresponding to each sense of any predicate 'F'.
The difference between these two statements can be seen clearly
when one considers propositions like 'Existence exists,' and 'Unchangeability is unchanging.' Unlike most statements involving self-predication, these make sense, and Plato was clearly committed to them.
Such a commitment would lead to difficulties if coupled with the acceptance of S3, but no difficulties arise when S3 is replaced by S4.
Furthermore, reasons which might lead one to accept S4, need not lead
one to the embracing of S3. This latter principle seems quite independent
of any specific metaphysical view.3
I For an elaboration of this point see my paper "Reason and Eros in the Ascent-passage
of the Symposium",minmeographed by the Society for Ancient Greek Philosophy, 1960.
2 For an elaboration of this point, as well as the example, see P. Ziff, SemanticAnalysis
Cornell U. P. Ithaca, N.Y. 1 960, p. i 8o.
3 Such radical principles of non-identity underlie most traditional "realist" accounts
of predication, but for sound criticism of these see D. F. Pears "Universals", reprinted
in Logic and Languagesecond series (ed. A. Flew) pp. S 1-64.
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Having made these distinctions, our second step is to survey what
Plato says about the Forms in the middle period dialogues, and see how
this material is related to SI-S4. It is important to note that in these
dialogues Plato does not simply assume, but rather infers the existence
of the Forms. The task of interpretation is made difficult, however, by
the variety of the arguments which are given for the existence of the
Forms. These correspond to different problems to which the existence
of the Forms is supposed to be the answer, and they represent different
conceptions of these entities.
a) According to one conception Forms are a priori notions - not
dependent on the mind, or anything else, for their existence. We
encounter this view in the Phaedo (e.g. 74a-7gc) and the middle books
of the Republic(e.g. 476-479), where it is argued that some notions are
instantiated always in the presence of their opposites, and thus could
not be derived from sense experience alone. b) Another conception
of the Forms arises when Plato considers the application of terms
corresponding to notions which cannot be derived from sense experience
alone. Plato thinks that we apply these terms in a primary sense to the
corresponding Forms, and to particulars only in a derivative sense (see
Phaedo 02a Io-b3, Timaeus 52a5).' According to this conception the
characterization of the Forms is the paradigm for predication. c) A
third conception emerges in connection with Plato's analysis of sortconcepts. In this context the Forms function as criteria for determining
what belongs to any given kind K, and what will count as a good specimen of K. This conception plays an important role in Plato's account of
creating and producing (Republic596b ff., Timaeus30c ff.). According to
Plato the key to success in these activities is for the agent to keep his
"mental eye" on the Forms. d) We find still another conception of the
Forms in some of Plato's discussions of reference and identification.
At some stages of his development Plato seems to have held the view that
owing to a variety of factors - change, temporality, etc. - particulars
cannot be adequately identified except by relating them to the Forms,
and that these in turn are not dependent on anything outside of themselves for their identity and identifiability (Timaeus49d, sob). Thus in
this context we find the Forms conceived of as providing paradigms of
identification. e) Finally, at various places in the dialogues (e.g. Timaeus
I Translators (e.g. Cornford and Hackforth) use the locution "named after" in their
renderings. This is misleading, because the point is not that our "baptizing" of particulars
needs to be explained, but rather our ability to describe these. It is our description of
particulars that is - according to Plato - posterior to the description of the Forms.
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28a) a dichotomy is drawn between the objects of the senses and the
objects of thought. If we take this dichotomy by itself and identify the
Forms with the latter class, then we have a fifth conception of the Forms,
as concepts (not mind-dependent) of all kinds, a priori or otherwise.
This survey shows that at times Plato thinks of the Forms as a) a priori
notions, at times as b) paradigms of predication, then again as c) criteria
for sort-concepts, also d) paradigms of identifiability, and again simply
as e) concepts of all kinds (in contrast with particulars). That he did
not always hold e) can be seen from Republic 523aio ff. where Plato
contrasts the notions which "lead to thought" and which cannot be
handled adequately by perception alone, with those - like the notion
of a finger - which do not have this role.I The Forms mentioned here
are those for which arguments have been given in the Phaedo and in the
middle books of the Republic with reference to conceptions a) and b)
It might seem, however, difficult to reconcile this passage with Republic
S96a6-7 where we are told that we should posit a Form for every
"plurality which we designate by the same term." But these lines, when
taken in context, need not be read as stating that we are to postulate a
Form for every general term in our language. For the pluralities and
corresponding terms in question seem to be - like "mimesis" - those
which are in need of philosophical investigation. The "customary procedure" to which reference is made in the preceding lines could hardly
be the procedure of postulating a Form for every term in our language;
it is more likely to be the procedure, followed throughout the middle
period dialogues, of postulating Forms for those notions which call for
examination by a philosopher. And this is, of course, a limited class of
notions.
In reviewing these conceptions of what are necessary conditions for
being a Form, we should note various relationships of compatibility
and incompatibility. Conception a) is compatible with b) and d), but it
is incompatible with c) and e), for not all concepts are a priori, nor all are
sort-concepts a priori.2 Conception b) is compatible with a), c), and e),
xIn E23d3-E we are told that it is the mind of the ordinary man which is led to thought
by some notions and not by others. This might lead one to suppose that the contrast
between the two kinds of notions is relative to the ordinary mind, and does not correspond to an ontological division. But earlier, in S23aio-b4, the same contrast is drawn
in terms of what can be judged adequately by perception, and what can not be judged
in this manner. There is no mention of the ordinary man here, and thus the distinction
should be taken as fundamental to Plato's conception of reality at this point.
2 Sort-concepts are not a priori, but neither are they simply "abstracted from sense experience." As one surveys Plato's treatment of the various kinds of concepts, it becomes
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and it seems compatible with d) as well, depending on certain questions
concerning the intepretation of what Plato says about reference. Conception c) is compatible with b) and d), but it is incompatible with a)
and e), for the class of sort-concepts cannot be identified either with
the class of all concepts, or with the class of a priori concepts. To
complete this list of relationships, we should note that d) and e) are
compatible with each other. This examination of the logical relations
between the conceptions gives us a better insight into the complexity
of the considerations which led Plato to postulate Forms. That the
Theory of Forms is not altogether homogeneous is not a novel suggestion.
Vlastos wrote in this spirit when he suggested that Plato wanted his
Forms to be both universals and perfect particulars.' But the result
reached here indicates that the complexity is deeper than this, and that
it cannot be reduced to any simple dichotomy. The most interesting
feature of Plato's Theory of Forms is not simply the multiple metaphysical roles that the Forms are supposed to play, but the multiplicity
of the problems underlying it.
In emphasizing these differences we should not overlook the fact
that throughout these conceptions the Forms retain certain common
characteristics. Plato enumerates these repeatedly (e.g. Symposium 2 I I ab). They include atemporality, independent existence, immateriality,
unchangeability, etc. The point of this paper is not to ignore these,
but to insist that too much stress has been laid on these common denominators, both by Plato and by his readers.
With conceptions a)-e) in mind we can throw light on two related
problems. One of these is the charge of reification which is often brought
against Platonism. Proponents of this charge say that Plato was guilty of
treating universals as if they were particulars. Given, however, the variety
of conceptions a)-e) it is obvious that we cannot issue either a wholesale
conviction or a general acquittal. Furthermore, in dealing with the
problems of reification we must not assume that the universal-particular
and abstract-concrete distinctions are coextensive and exhaustive of
reality. If this were the case, anyone postulating the existence of abstracta which are not universals would be guilty of reification. But
surely entities like "point without extension" are neither concrete nor
universal. Also, entities like battle-plans, recipes, and chemical elements,
cannot be classified as being clearly abstract or concrete. In view of these
apparent that the a priori - a posteriori dichotomy is too crude a tool for explaining how
various concepts are related to sense experience.
I G. VIastos, "Reply to Geach" (see note 2) p. 90.
Ss
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considerations we can see that merely because the Forms were under
any interpretation not concrete, their status as universals or not-universals
was not thereby resolved.
The other problem which we can handle more adequately now is
provided by Parmenides I3ob-d, where the young Socrates is presented
as hesitant concerning the limits of the realm of the Forms. Some
commentators have attributed this hesitation to Socrates' alleged belief
that some entities are more mundane and trivial than others. Cornford
thought that it reflected Plato's shifting interests, from morals and
mathematics to cosmology.' It seems, however, that we have a more
adequate explanation open to us. Plato may be representing Socrates in
this mood to indicate his own hesitation with regard to the possibility
of fitting together all of his commitments and ontological speculations
concerning the Forms.
This last remark raises the question to what extent Plato was aware
of the differences between the five conceptions. The hypothesis that he
was not sufficiently aware of these is strongly supported by the fact
that in the middle period dialogues Plato never discusses more than one
conception at a time, and that he does not say anything about having a
plurality of conceptions. This failure to make the necessary distinctions
is explained partly by Plato's epistemic vocabulary. He frequently uses
"seeing" to describe the knowledge of the Forms (e.g. Republic476aIo,
Symposium 2 ioe4). This tends to obscure the differences, for of course
all of the solutions to the different problems raised involve "seeing something abstract," but these abstracta are not always identical in nature.
We are now in a position to give a general characterization of the
crux of the "Third Man"-argument. This argument marks a period of
critical reflexion and reappraisal in Plato's development. For the first
time Plato wonders how everything that he said about the Forms fits
if any - what he said is damaged by
together, and to what extent
arguments which reveal how difficult it is to describe and to determine
the identity of abstract entities. In order to support this general characterization of the argument by detailed interpretation, we have to restate
the argument and show how it is connected with S-S4, which in turn
need to be related to conceptions a)-e).
The argument itself (i 32a1 ff.) is given in terms of one term which
corresponds to the Form Large. It is obvious, however, that the argument is designed to have a general scope, since the conclusion is stated
I
F. M. Cornford, op. cit. pp. 82-83.
~6
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as applying to all Forms. Thus instead of translating and then generalizing,
we shall turn directly to the construction of the general pattern of the
argument. The logic is relatively simple, and thus Professor Cherniss'
remark that modern interpreters "intended to clarify Plato's text, but
tended to whelm it with the symbols of modern logic"' is justified. The
argument has the following schematic form. ('a' 'b' 'c' stand for particulars, and 'F' 'F'' etc. stand for Forms.)
PI.
We apprehend a, b, c, as F in virtue of the F which is one2.
We apprehend a, b, c, and the F in the same manner in which we apprehend a, b,
and c.
Ci. We apprehend each of a, b, c, and the F as F, and in order to do so we have to
assume the existence of the F'.
P3. We apprehend a, b, c, the F, and the F' in the same manner in which we apprehend
a, b, c, and the F.
C2. We apprehend each of a, b, c, the F, and the F' as F, and in order to do so we have
to assume the existence of the F,', etc. ad inf.
P2.
The two questions facing us are: is the argument valid, and is Plato
committed to the premisses? Answers to both questions depend on
how one interprets P2. The crucial phrase in this statement is: "apprein the same manner." It is usually assumed that this phrase
hend....
means "apprehending a common denominator." But this is not the only
possible reading. Indeed, it is not a very plausible reading, for the manner
of apprehension has to do with form, or structure, and not with content.
Let us consider instead the rendering: "apprehending group A in the
same manner as that in which we apprehend group B" as "if we apprehend
all members of B as F, and such apprehension presupposes the existence
of an entity outside of B, then we apprehend all members of A also as F,
and this apprehension presupposes the existence of an entity outside
of A." Making the proper substitutions we can derive the following
restatement of P2.
P2*. If we apprehend a, b, c, as F, and this presupposes the existence of the F, then we
also apprehend a, b, c, and the F as F, and this presupposes the existence of the Fl
3.
H. F. Cherniss, "The Relation of the Timaeus to Plato's Later Dialogues" American
Journal of Philology v. 78. pp. 225- 266, quote from p. 2S7
2 The text does not have "in virtue of," but from what is said in the passage following
it is clear that nmorethan mere conjunction of appearances is intended. See I 3 2a7-8, a X1,
and bi, where the Large is said to be what all other large entities partake of.
3 Unlike the interpretations of Viastos and Geach, this account does not represent the
tacit premiss as inconsistent with the others.
I
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Note that P2, Ci, etc. do not assert that we apprehend each entity
in the classes in question as F in virtue of the same Form. These statements
assert merely that in order to apprehend each of these entities as F,
we have to assume that there exists an entity outside of the class in
question.
Substituting P2* (as well as P3*) for P2 (P3) we see that the argument
is valid. Our next task is to see whether Plato was committed to P2*.
(We need not waste time on Pi which obviously expresses Plato's view).
The answer to this question can be found by seeing which of S1-S4 entail
P2. It is important to see that the entailment will not hold with any of
S1-S4 taken individually. This needs emphasis because many commentators have seen in S2 the key to the argument. But though S2 may be
absurd, it does not lead by itself to an infinite regress. Since 52 is one
way of committing the sin of reification, this is additional evidence to
show that the "Third Man" does not depend for its success on treating
the Forms as particulars.
Turning to the consideration of possible conjunctions, we see that
Si and S4, as well as S2 and S3, entail P2, but that S2 with S4 does not
yield this premiss. Our next step is to determine which of these
statements Plato might have held. As between S3 and S4, Plato could
not have held the former while he was committed to statements like
"Existence exists.' Furthermore, a glance at a)-e) should convince us
that nothing in Plato's ontology commits one to S3. S4, on the other
hand, has no grave consequences of the kind mentioned above in connection with 53, and Plato was most likely committed to it if he held
that to grasp a sense is to have intuitive acquaintance with an abstract
entity. Thus between these two statements, 54 is by far the more likely
candidate. This counts also against S2, since as we saw, the regress
could not get started with S2 and S4.
In comparing Si and S2 we should note that none of the passages
which contain self-predication (e.g. Protagoras 3 3Oc, Symposium 2 IOC f.)
lends support to either of these statements in favor of the other.
Furthermore, any commitment to self-predication which we can derive
from a)-e) can be read via Si as well as via S2.1 This means that both
I G. E. L. Owen has argued that the self-predicative statements which we find in the
dialogues do not have sense unless the predicate applies without difference of meaning
to Form and particular alike. (See "A Proof in Peri Ideon"Journalof Hellenic Studies v. 77.
p. ioS.) One can agree with this while still insisting that the statements in question
make at least as good sense - if not better - when the predicate is applied in different
senses to Fornmand particular.
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versions have a certain degree of initial plausibility. But as we saw above,
the choice between S3 and S4 already speaks against 52, and further
considerations can be adduced to show the implausibility of ascribing
S2 to Plato. First of all, S2 is absurd. For though it makes sense to say
that Existence exists, it does not make sense to say that the Form Large is
large in the same sense in which an elephant is. Given that we can conceive
of self-predication in more intelligible ways - i.e. via SI - why ascribe
something absurd to Plato? Secondly, there is no evidence to show that
the Early Academy thought of Plato as committed to S2. Lastly, there are
two infinite regresses in the Parmenides,and the second of these (I 32dII 3 3a3) clearly does turn on the symmetrical relationship implied by S2.
If one of the regresses turns on S2, why should Plato construct another
one, turning on the same premiss? If the first regress - the one which
we are considering in this paper - is not to be superfluous, it has to
turn on S I, rather than on S2.
With regard to Si we have seen already that it avoids all of the difficulties of S2. Furthermore, there is good reason why Plato would have
embraced this principle, explicitly or otherwise. Si provides for the
Forms what Plato could not find in any adequate fashion for particulars;
i.e. criteria of identity. If we take the Theory of Forms in the middle
dialogues as including Si, we can see why Plato thinks of Forms as more
intelligible entities than particulars. For according to this interpretation
he could think of the Forms as uniquely identifiable, self-sufficient
entities, and thus superior to particulars. Without Si it is difficult to see
what would lead Plato to think that the separate identity of each Form
can be clearly established. Thus we see that self-predication need not be
nonsense, and that motivation for its acceptance need not be religious,
or a matter of linguistic confusion, but rather a serious concern with the
problem of identity and identification. Of course, while seeing the
plausibility of ascribing Si rather than S2 to Plato, we need not commit
ourselves to saying that Plato has explicitly recognized the difference
between SI and S2, and that he expressly chose the former. We need to
maintain only that Si provides a more faithful reconstruction of Plato's
thought than S2, though it remains implicit in all of the middle period
dialogues.
In short, it is most plausible to interpret Plato as holding SI and S4,
and this conjunction does entail P21. Thus the crux of the argument is SI,
I Si involves "focal meaning," as Owen uses this term. (See G. E. L. Owen, "Logic and
Metaphysics in Some Earlier Works of Aristotle," VII. in Aristotle and Plato in the Midfourth Century,ed. by 1. During and G. E. L. Owen, G6teborg, 1960.) The interpretation
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and the reason Plato does not simply abandon this principle as the result
of this argument is that not all of conceptions a)-e) are equally committed
to Si. Conceptions a) and e) do not entail Si; the claims that there are
a priori notions, and that concepts are to be distinguished fronmparticulars
are independent of any problem of self-predication. On the other hand,
given that S2 is ruled out, b) and d) do entail Si; without Si it is difficult to see what principle in Plato's metaphysics would enable hinmto
look at the Forms as either paradigms of predication or of identifiability.
Finally, with regard to c) the evidence is not sufficient to support a firm
verdict, but it seems that what Plato says about creation, etc. can be
best understood if one ascribes Si to him. This survey shows that there
is no simple answer to the question: was Plato committed to Si ? Thus
there is likewise no simple answer to the question: is the 'Third-Man'argument fatal to the Theory of Forms? Inasmuch as Plato did not
distinguish clearly among the various conceptions of the Forms, his
puzzlement and silence concerning a possible reply to the 'Third Man' is
natural.
It remains for us to assess the damage which this argument causes to
the conceptions of the Forms affected by it. This damage is sumnmedup
by Plato as showing that whereas we regarded each Form as one, they
now turn out to be infinite. The force of this point should be understood
by relating it to the question of identity. When Plato says that each
Form is one, he means to say that each Form has its own identity, and
that the criterion of identity available for Forms meets the most exacting
standard of reason. Thus to show that each Form is not one is to cast
doubt upon the identity of the Forms, and the criterion available. The
real damaging force of the 'Third Man'-argument is that the very theorem - Si - which seemed to provide an ideal criterion for the identit)'
of Forms, will lead to the destruction of the identity of the Forms when
conjoined with certain other assumptions.
Much of what this interpretation ascribes to Plato cannot be found
explicitly in the dialogues. Indirect support for these ascriptions is
provided by some of the developments in the later dialogues. Thus a
brief sketch of these is in order. These developments show that even
though Plato did not formulate clearly the consequences of the "Third
Man"-argument, he saw the direction in which changes had to be made.
Two of the conceptions of the Forms, a) and e) survive in the later
presented in this paper shows that invoking the notion of focal meaning does not help
to evade the "Third Man"-argurment. This is relevant to the problemi of interpreting
Aristotle's reactions to Plato's Theory of Forms.
6o
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dialogues, and we saw that these were the ones which are not affected
by the regress-argument. Self-predication in the sense of S2 occurs in
the late dialogues, but only where this makes good sense. Self-predication
in the sense of Si cannot be found in the dialogues after the Parmenides.
Accordingly, new criteria of identity are sought, and in the Sophist
detailed proofs of non-identity are presented which do not rely on
self-predication. Conception b) disappears, partly as a result of the
demonstration that the Forms themselves have opposites predicated of
them. ' The referential status of particulars is reconsidered, partly
perhaps as the result of the clarification of temporality achieved in the
second half of the Parmenides- thus d) is also abandoned. Finally, in the
place of c) we have the method of division and the complex valuational
scheme of the Philebus.Thus those conceptions which are affected by the
regress seem to be absent - at least partly - in the later dialogues.
In conclusion, let us concentrate on the two philosophical issues
which form the nucleus around which the argument is built. These are:
the problem of identity of Forms (universals), and the problem of how
to explain predication. As we saw, the "Third Man"-argument attacks
that principle in Plato's metaphysics which provided a criterion of
identity for Forms. It is widely believed by philosophers that the subsequent modifications which transformed Plato's Theory of Forms into
what is known as the theory of universals, were beneficial, and helped
to make the notion of a universal a more intelligible one. This belief is
mistaken. Plato's answer to the problem of identity of abstract entities
may have been mistaken, but at least it was an honest attempt at an
answer. The subsequent history of theories of universals shows that this
crucial question has been swept under the rug, and no alternative answer
attempted. Instead, we find heavy emphasis placed on the alleged uniqueness of universals. But the more unique and undescribable universals
tend to be, the less likely it is that their postulation can be of any
explanatory value. The universals of the modern "realists" are beyond
vulnerability indeed, but this is because they are also beyond having
illuminating power for purposes of explanation. Thus Plato's failure
left us with a gap still to be filled.
With regard to the explanation of predication, the argument which
we have been examining raises the question whether it makes sense to
I For this and other points of development in the Sophist, see my "Being and Meaning in
the Sophist,' to appear in Acta PhilosophicaFennica, Fasc. XIV, Helsinki, 1962, pp. 2 3-78.
6i
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explicatie predication as relating two entities of different kinds. The
success of the 'Third Man'-argument renders the prospects of such
explications dim. But the question which still haunts us, and which is
the true heritage of the 'Third Man'-argument is: if predication is not
the relating of entities of different types, what is it?
Universityof Michigan
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