Meinwald, Constance. 1992. "Good-bye to the Third Man." In The Cambridge Companion to Plato , edited by Kraut, Richard, 365–396. Cambridge: Cambridge University Press

"I believe that Plato composed the first part of the Parmenides in order to exhibit where his middle-period description of Forms needed development. Our view of Plato's ability to sustain that development

need no longer derive from scrutiny of this passage alone.

Nor need we rely solely on complicated conjectures involving the evidence of other dialogues. The Parmenides as a whole gives the best possible evidence for Plato's response to the problems it introduces.

If I am right or even on the right track, the dialogue shows that his response was successful. As the late period began, the theory of Forms was in new leaf." (p. 391)
———. 2022. "Another Good-bye to the Third Man " In The Cambridge Companion to Plato. Second Edition , edited by Ebrey, David and Kraut, Richard, 399–432. Cambridge: Cambridge University Press

"We have seen that the Parmenides is the first dialogue in which we can securely ground an unproblematic interpretation of the sentences at issue in Plato’s own text. Helping us with this is what Plato was doing in suggesting acceptance of massed results apparently in pervasive, systematic contradiction with each other (i.e., the results of paired sections of Parmenides’ dialectical exercise). In this work, for the first time, Plato is showing over and over that sentences of the type “S is P” have two systematically different readings. These were marked by the two “in-relation-to” qualifications in Parmenides’ prescription for exercise, and his thirty-page demonstration constitutes a treasure-chest of evidence to guide our interpretation of them." (p- 426)
Mignucci, Mario. 1990. "Plato's « Third man » argument in the Parmenides ." Archiv für Geschichte der Philosophie no. 72:143–181

"Although the problems raised by the first part of the Parmenides are perhaps less desperately difficult than those of the second part, they are still very hard for any reader of the dialogue. Among them the question of the so-called "Third Man Argument" (henceforward 'TMA') presented in Prm . 132A1 — B2 enjoys the unenviable privilege of having been the object of a large number of different interpretations and discussions. As soon as one begins to read the relevant literature on the subject one gets the impression that everything (and the opposite of everything) has been said, so that it might appear useless and perhaps conceited to claim to offer a new interpretation of the argument. To avoid this charge, I must declare that I do not intend to propose a new interpretation of the TMA. My purpose is less ambitious, and it consists in checking and discussing the structure of Plato's argument in order to compare it with what is believed by some scholars to be a variant of the TMA proposed in Prm. 132C12-133A7. Let us call this second argument the 'Resemblance Argument' and use 'RA' to refer to it. I leave to more gifted people the task of evaluating the philosophical relevance of Plato's views." (p. 143)
Mohr, Richard D. 1986. "Forms as Individuals: Unity, Being and Cognition in Plato's Ideal Theory." Illinois Classical Studies no. 11:113–128

"That the Ideas are fundamentally individuals rather than things qualified spares Plato's two-tiered ontology from entailing the vicious logical regress of the Third Man Argument (TMA).(13) The unique-world argument helps pinpoint where Plato supposes the TMA goes awry when directed at his theory of Ideas. The TMA assumes that (a) any Form along with its instances can be taken as members of a set of which all the members severally but in common possess the attribute which makes the instances instances of the Form. The TMA further assumes that (b) since in accordance with good Platonic principles all attributions of properties to things are made by reference to some Form beyond the set of things which consists of members with a common property, there must be another Form over and above the first. Given (a) and (b), and if in addition (c) the new Form too is formally identical to the members of the earlier set, then there will be an infinite regress of Forms. The regress will be vicious because by virtue of (b) prior members of the regress presuppose (for their identification) posterior members of the sequence, of which there is no last member. Plato would reject (a) and a fortiori reject (c). He accepts (b). In the vocabulary of the recent critical tradition, (a) and (c) presuppose self-predication of Forms, that is, they assume that each Form possesses the same property it defines in other things.

And (b) presupposes the non-identity of Form and instance, that is, it presupposes that a thing which possesses an attribute cannot be numerically identical with the Form by which one claims the thing has the attribute it has.." (pp. 122-123)

(13) For texts see Parmenides 132a l-b2 and 132d 1-l 33a6; Aristotle's On the Forms, in Alexander (of Aphrodisias), In Metaphysica commentaria, ed. M. Hayduck (Commentaria in Aristotelem graeca, I) (Berlin 1891), 84.21-85.11.
Moravcsik, Julius M. 1963. "The 'Third Man' Argument and Plato's Theory of Forms." Phronesis no. 8:50–62

"The 'Third Man'-argument (Parmenides 132ai-b2) is one of the most controversial passages in Plato's dialogues. In recent years a number of new interpretations of this argument have appeared. 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." (p. 50, two notes omitted)

(3) E.g. Vlastos ascribes to Plato two tacit premisses which are patently inconsistent with each other (see ["he Third Man Argument in the Parmenides" Phil. Rev. v. 63, pp. 319-349], pp. 324-325).

(4) Sellars ascribes to Plato the distinction between predicates and predicate-variables (["Vlastos and the Third Man" Phil. Rev. v. 64, pp. 405-438 ] pp. 416-41I7), while Geach locates the trouble in a complex and inconsistent set of propositions with involved quantificational form (["The Third Man Again" Phil. Rev .. v. 65, pp. 72-82] pp. 77-78).
Nabielek, Marcus. 2010. "The Third Man Argument (Parm . 132a1-b2) - A 'purely' metaphysical exercise?" Tópicos no. 38:135–151

Abstract: "All commentators of the ‘Parmenides’ agree that the Third Man argument, 132a-b2, raises a difficulty for Plato’s theory of forms. Many commentators, following Vlastos, hold that the argument’s infinite regress is vicious for epistemic reasons. Rickless contends that the infinite regress is vicious for exclusively metaphysical reasons. This essay intends to show that Rickless’ interpretation is inadequate, as well as to vindicate Vlastos’ interpretation."

References

Rickless, S. C. (1998): ‘How Parmenides saved the theory of forms’. Philosophical Review , 107, 4, 501-54.
Nails, Debra. 1958. "Epitaph for the Third Man." Auslegung. A Journal of Philosophy :6–23

"From the time of Aristotle, controversy surrounding the third man argument has been vast indeed. Each generation has its own group of philosophers/scholars who attempt anew to determine whether the argument is valid, and how its validity may have affected Plato's attitude toward the forms. Those concerned with the argument as presented in the Parmenides usually defend one of two particularly long-lived positions: (1) that the argument is invalid, or (2) that Plato's recognition of the validity of the third man argument led to his dismissal of the theory of forms.1 I hope to demonstrate that neither of these solutions to the problem of the relationship of the third man argument to Plato's philosophy as a whole can prove satisfactory. Further, I shall show that the validity of the argument does not imply Plato's rejection of the theory of forms; Plato certainly does continue to hold such a theory." (p. 6)

(1) "Here I wish to oppose only a particularly strong form of the position: that Plato—after having written a number of dialogues, and after having posited the theory of forms—developed (or, perhaps, had brought to his attention) the argument which has come to be called "the third man"; further, that Plato recognized this argument as fatal to the theory of forms and therefore rejected that theory.
Nerlich, G. C. 1960. "Regress Arguments in Plato." Mind no. 69:88–90

"There are regress arguments in three Platonic dialogues; two in the Parmenides (131e-132b; 132d-133a) and one each in the Republic (597c) and the Timaeus (31a-b). It has been argued, notably by Cornford,(1) that the Parmenides regresses are sophistical arguments against the Forms and deliberately involve a fallacy. "The arguments of the Republic and the Timaeus indicate that Plato was not blind to the fallacy in Parmenides' assumption that largeness is a large thing." A view somewhat similar to this occurs in Cherniss.(2) I wish to argue (a) that the Republic argument contains (whether or not self-consciously) Parmenides' assumption and so the Parmenides regresses are a valid critique of it; (b) that the Timaeus regress can be almost completely assimilated to the Republic argument; (c) that these facts provide support for G. E. L. Owen's(3) thesis that the Timaeus is earlier than the Parmenides. " (p. 88)

(1) F. M. Cornford, Plato and Parmenides , p. 90.

(2) H. Cherniss Aristotle's Criticisms of Plato's Academy , pp. 292-298.

(3) G. E. L. Owen, " The place of the Timaeus in Plato's dialogues ", Classical Quarterly (1954).
Owen, G. E. L. . 1966. "The Platonism of Aristotle." Proceedings of the British Academy no. 51:121–150

Reprinted in Studies in the Philosophy of Thought and Action , ed. P.F. Strawson, Oxford: Oxford University Press, 1968, 147-74; in Articles on Aristotle , ed. J. Barnes, M. Schofield, and R. Sorabji, London: Duckworth, 1979, vol. 1 (1975), 14-34.

Reprinted in G. E. L. Owen, Logic, Science, and Dialectic. Collected Papers in Greek Philosophy , edited by Martha Nussbaum, Ithaca: Cornell University Press 1986, pp. 200-220.

"Aristotle brings a great variety of arguments against the theory of Forms, and the variety reflects the faces and phases of that theory as well as Aristotle’s shifting interest in it. But the objection to which he recurs most often is that which the Academy dubbed ‘the Third Man’. It makes an ambiguous appearance in Plato’s Parmenides, and it was set out schematically in Aristotle’s early essay On Ideas .(9) It is the argument behind Aristotle’s stock complaint that when Plato invented his Forms he made a mistake about predicates: he took any predicate-expression to stand for some individual thing instead of for some sort of thing (e.g. SE 178b36-179a10; Meta . 1038b34-1039a3). Thereby, Aristotle held, he committed two faults: he failed to explain how we use predicates to classify and describe actual individuals, and he cluttered the scene with other individuals which were fictions." (pp. 133-134)

(9) Parm . 131e-2b (the argument in 132c-133a with which later writers conflated it is a different objection); De Ideis fr.4, Ross; Alexander In Meta . 84. 21-85, 12.
Panagiotou, Spiro. 1971. "Vlastos on Parmenides 132A1-B2: Some of His Text and Logic." The Philosophical Quarterly no. 21:255–259

"In his recent paper on the Third Man Argument(1) (henceforth TMA), Professor G. Vlastos proffers some new insights on the text and logic of the memorable Parmenidean argument. One of these new insights-which is crucial to his present formalization of the argument-is about the reference of the expression πόλλ᾽ ἄττα μεγάλα in the first step of the argument (132A2).

Professor Vlastos argues that the reference of this expression should be understood as being of " unrestricted generality ". By this it is meant that πόλλ᾽ ἄττα is intended to cover both sensibles and Forms. In footnote 11 Vlastos confesses that under pressure from Sellars he had come to realize as early as 1963 that we must so understand the reference of πόλλ᾽ ἄττα. In the same footnote Vlastos produces a number of reasons in defence of his view.

In what follows I shall attempt to show that Vlastos' evidence is not good enough. In fact, some features of his evidence can be effectively employed to refute his view. I shall contend that the overwhelming wEighth of textual evidence supports the view that 76oXX-' Croch ere refers exclusively to sensible particulars. The outcome of the present discussion does affect our general understanding of the TMA, but not to any considerable extent.

What it does affect drastically, however, is Vlastos' formalization of the Parmenidean argument. He himself tells us that the "advantage " in understanding πόλλ᾽ ἄττα the way he does is that the text then warrants

his formalization of the first step of the argument (132A1-4) as the " general principle (" 1 ") ".(2) If I can make good my claim that Vlastos has no textual mandate for his interpretation of πόλλ᾽ ἄττα in his formalization of the first step of the argument is unwarranted. Consequently, his entire formalized system, as I shall show in my conclusion, is thrown out of gear." (p. 255)

(1) 1"Plato's "Third Man" Argument (Parm. 132A1-B2): Text and Logic", this journal, October 1969, pp. 289-301. I shall henceforth refer to this paper as " V 1969 ".

(2) Cf. footnote 11 which I quote below.
———. 1974. "A Note on the Translation and Interpretation of Plato Parmenides 132A1-4." Classical Philology no. 69:50–54

"Parmenides is made to introduce his celebrated "Third Man" argument (Parm . 132A1-B2) as follows:

οἶμαί σε ἐκ τοῦ τοιοῦδε ἓν ἕκαστον εἶδος οἴεσθαι εἶναι: ὅταν πόλλ᾽ ἄττα μεγάλα σοι δόξῃ εἶναι, μία τις ἴσως δοκεῖ ἰδέα ἡ αὐτὴ εἶναι ἐπὶ πάντα ἰδόντι, ὅθεν ἓν τὸ μέγα ἡγῇ εἶναι.

There has been a certain amount of controversy, among translators and commentators, over the exact sense of these lines. Looking over the various versions produced in the last hundred years or so, one may divide the disputants into three main groups, the division being made on the basis of their treatment of the ubiquitous infinitive εἶναι. For the sake of convenience, I shall designate the four occurrences of this infinitive by Roman numerals: I designate as I the εἶναι. of 132A1, as II that of 132A2, and so on. Now, one group (e.g., Burges and Fowler)(1) has I, II, and IV function in a copulative, III in an existential, capacity. Another group (e.g., Taylor and Cornford)(2) has I and III in the existential, II and IV in the copulative, mode.

Finally, the most recent group (so far represented only by Professor Vlastos)(3) would cast all four in an existential role." (p. 50)

(...)

"In Section I, I shall briefly comment on each occurrence of εἶναι. I shall deal first with II, III, and IV, then with I. I deal with the εἶναι of 132A1 last for the simple reason that I am unable to see how we can deal with it first.

That is, we can decide on the function of this line only by considering it in relation to the rest of the passage. In Section II, I shall offer my version along with a few words on the philosophic points at issue." (pp. 50-51)
Peacock, Howard. 2017. "The Third Man and the coherence of the « Parmenides » " Oxford Studies in Ancient Philosophy no. 53:113–176

Abstract: "The ‘Third Man’ in the Parmenides is often reconstructed in terms of unstated background commitments of the Theory of Forms; thus it seems to threaten the internal coherence of that theory. However, the regress can be derived solely from premises explicitly stated within the dialogue, and blocked simply by giving up one candidate account of participation, leaving the central commitments of the Theory of Forms intact. Consequently, the problem highlighted by the argument is not an infinite regress of Forms, but merely the lack of an adequate account of participation. This reading facilitates a coherent account of the dialogue as a whole, using the ‘scorecard’ approach outlined by Zeno himself, and developed more recently for contemporary metaphysics by Lewis and Armstrong: Part I acknowledges non-fatal difficulties for the Forms which are then eclipsed by more serious issues for Eleatic monism in Part II."

References

Armstrong, D. M., Universals: An Opinionated Introduction (Boulder, Colorado, 1989).

Lewis, D. K., ‘New Work for a Theory of Universals’, Australasian Journal of Philosophy , 61 (1983), 343-377.

Lewis, D. K., On the Plurality of Worlds (Oxford, 1986).
Peck, Arthur L. 1962. "Plato versus Parmenides." The Philosophical Review no. 71:159–184

"In this article I begin with an examination of Professor Gregory Vlastos' treatment of the Third Man Argument,(1) partly because his article has aroused considerable interest, and partly because it provides a convenient starting point for a more thorough examination of some aspects of the dialogue than I have given them previously.(2)" (p. 159)

(...)

"We may summarize the foregoing by saying that there is nothing in Plato to justify what is called "predication" as described and assumed by Vlastos. Hence there is no justification for distinguishing in the notation between F and F-ness; and we may use one or the other indiscriminately (as Plato uses "large" and "largeness"), though merely for the sake of clarity for the benefit of us modern readers it will be advisable not to use both in the same proposition. I would also suggest that, as an alternative to Vlastos' phrase "If a [i.e., any particular] is F [e.g., large]..." (p. 341, n. 39; cf. also his (A1, p 320), it might be safer, at any rate for us, where it is convenient sometimes to use the following notation: "If there is F (or F-ness) in a...."-" (p. 163)

(1) "The Third Man Argument in the Parmenides ," Philosophical Review, LXIII (154), 319-349.

(2) "Plato's Alleged Self-Criticism in the Parmenides", Proceedings of the Cambridge Philological Society , CLXXXII (N.S. 2, 1952/3), 2I-36; "Plato's Parmenides: Some Suggestions for Its Interpretation," Classical Quarterly, X,LVII (N.S. 3, 1953), 126 ff., XLVIII (N.S. 4, 1954), 31 ff.
Pelletier, Francis Jeffry, and Zalta, Edward N. 2000. "How to Say Goodbye to the Third Man." Noûs no. 34:165–202

"In what follows, we examine the issues that arise in connection with adopting a two-modes-of-predication theory, both to the proper development of the theory of Forms and to the Third Man argument. One of our goals is to show that there is a logically coherent position involving two modes of predication which both (1) allows for a precise statement of the theory of Forms, and (2) removes the threat that the Third Man argument poses. Our interests will not only be textual, for a proper solution of this kind raises serious logical issues that Plato was not in a position to consider. For example, Plato never worried about formulating his theory of Forms so as to remove the threat of Russell’s paradox. But unless the two-modes-of-predication view is reconstructed on rigorous logical grounds, the theory of Forms is vulnerable to a version of Russell’s paradox (as well as other paradoxes). A second goal in the paper is to defend our reconstruction from some of the criticisms leveled against Meinwald’s position. In the course of doing this, it will become apparent that a more rigorous development of the Theory of Forms predicts and resolves some of the valid criticisms directed at Meinwald."(p. 3)

References

Meinwald, C., 1991, Plato’s Parmenides , Oxford: Oxford University Press.

Meinwald, C., 1992, ‘Good-bye to the Third Man’, in The Cambridge Companion to Plato , R. Kraut (ed.), Cambridge: Cambridge University Press, pp. 365-396.
Peterson, Sandra. 1973. "A Reasonable Self-Predication Premise for the Third Man Argument." The Philosophical Review no. 82:451–470

See also: A Correction to "A Reasonable Self-Predication Premise for the Third Man Argument", Philosophical Review , 84, 1975, p. 96.

Reprinted in: Nicholas D. Smith (ed.), Plato. Critical Assessments , New York: Routledge 1998, vol. IV pp. 51-66.

"I propose a way of understanding the self-predication premise of the third man argument which Plato used against himself. The way I propose fulfills some of the desiderata for a good interpretation of Plato: it is not unreasonable by itself; it is formally consistent with the other premises of the third man, singly and jointly;(1) it could have seemed that the argument containing the premise was a serious threat to the theory of forms, as Plato evidently feared (Parmenides I 35A-B). I do not, however, intend to say that therefore my proposal gives what Plato meant. Section VI explains what I do intend." (p. 451)

(1) The desideratum which the feature described in this clause fulfills is that the premises not be obviously formally inconsistent. I omit here the demonstration of the formal consistency of the premises. There is room for argument that some of the premises entail the denial of others, or entail the denial of others in conjunction with some other beliefs Plato had or could or should have had. I am glad there is room for such argument. I do not wish to be constructing an argument Plato could not have evaded. It seems clear to me that at least by the time of the Sophist Plato thought that the third man did not vitiate the theory of forms.
———. 2019. "Plato's Parmenides : a reconsideration of Forms." In The Oxford Handbook of Plato. Second Edition , edited by Fine, Gail, 231–259. New York: Oxford University Press

"The Third Man Argument has captured commentators’ attention. Given one or another valid and interesting formulation of the argument, scholars have then asked whether Plato’s own views of forms as presented in other dialogues can avoid the Third Man objection.(38)

The logically available responses to the argument are to reject one or more of its premises or to accept its conclusion. One might reject non-self-explanation.(39) One might reject self-predication.(40) S. Marc Cohen urges rethinking the one-over-many premise:

What <the Third Man> shows is that to keep uniqueness, the one-over-many principle will have to be abandoned or modified, for it is an application of that principle to the set consisting of large particulars and the Large itself that generates a second form.(41)

Finally, one might respond to the argument by accepting the conclusion that the form of largeness (or any form of F-ness) is not unique.(42)

I revisit the Third Man later in this chapter." (p. 243)

(38) Fine, Ideas , ch. 16: “Is Plato Vulnerable to the Third Man Argument?”

(39) See earlier in this chapter; Fine, Ideas , 231–38.

(40) For references see Meinwald, Plato , 273

(41) Cohen, “Third Man,” 473. Fine, Ideas , 204–11.

(42) Rickless, Forms , 240. See the Appendix of this chapter.

References

Cohen, S. M. “The Logic of the Third Man,” Philosophical Review 80 (1971), 448–75.

Fine, G. On Ideas: Aristotle’s Criticism of Plato’s Theory of Forms (Oxford, 1993).

Meinwald, C. Plato (New York, 2016).

Rickless, S. Plato’s Forms in Transition (Cambridge, 2006).
Pickering, F. R. 1981. "Plato's 'Third Man' Arguments." Mind no. 90:263–269

"Plato presents us with two 'Third Man' arguments in the Parmenides, the

first (the TMA(i)) at 132a 1-b2 and the second (the TMA (2)) at 132 d9-133 a3. Out of the long controversy begun by G. Vlastos and W. Sellars(1) a certain orthodoxy of interpretation has emerged, in that it is generally held that each of the arguments satisfies the following conditions:

(1) it purports to show, by means of the derivation of an infinite regress that certain fundamental tenets of the Theory of Forms make up an inconsistent set;

(2) to this purpose it contains, as stated or unstated assumptions, at least the following three tenets, all of which are fundamental to the Theory: (a) a self-predication principle (SP), to the effect that any Form by participation in which something is F is itself F (where ' F ' is replaceable by any appropriate predicative expression), (b) a so-called non-identity principle (NI), to the effect that nothing is F by participation in itself, (c) a one-over-many principle (OM), relating to the notion that, if any set of things are all F, then it is by participation in one and the same Form that they are all F;(2)

(3) it does not involve any assumptions about the nature of the relationship which Plato calls 'μέθεξις;' ('participation') apart from any which are contained in the three tenets mentioned above." (p. 263)

(...)

"If my interpretation is correct, none of the three fundamental tenets of the Theory of Forms which appear as assumptions in the TMA(2) appears in the same way in the TMA(i). The latter argument cannot, then, resemble the former in having as its purpose the demonstration of their inconsistency when combined in a set.(...)" (p. 268)

(1) G. Vlastos, 'The Third Man Argument in the Parmenides' and W. Sellars, 'Vlastoa and the "Third Man" ', in The Philosophical Review , lxiii (1954)

(2) I ignore as irrelevant to my discussion the large differences of opinion about the exact form which OM should take. The disagreements about the precise nature of the other two principles are relatively insignificant. For further discussion and a full bibliography, see G. Vlastos, Platonic Studies , PP- 335-365-and lxiv (1955) respectively.
Prior, William J. 1979. "Parmenides 132-133a and the Development of Plato's Thought." Phronesis. A Journal for Ancient Philosophy no. 24:230–240

"The crucial question in the issue of Plato's philosophical development is whether he ever abandoned or significantly modified the theory of forms.

Most pertinent to this question is the nature of Plato's response to his own critique of the theory in the Parmenides . Scholarly opinion on this issue is so divided that it may safely be called the most vexed problem in the interpretation of Plato.

In this paper I shall consider only one view of the force of the Parmenides arguments on Plato's development: that of G. E. L. Owen. According to Owen, one of the arguments of the Parmenides , the so-called second version of the Third Man Argument, conclusively refutes the view of the middle dialogues that the forms are paradigms. After the Parmenides , Owen holds, Plato either adopted the view that the forms are immanent universals or gave no interpretation of their nature.(1) Owen uses this conclusion to support his claim that the Timaeus , in which the forms are construed as paradigms, antedates the Parmenides .

I shall attempt to show that the argument of the Parmenides on which Owen relies does not refute the claim that the forms can be understood as paradigms, even though the argument may be formulated so as to be formally valid. In the absence of other textual evidence that Plato modified the theory of forms, then, it cannot be proved that the paradigm version of the theory is the exclusive property of Plato's middle period, or that the Timaeus is therefore a dialogue of that period.(2)" (p. 230)

(1) G. E. L. Owen, "The Place of the Timaeus in Plato's Dialogues," in R. E. Allen. ed., Studies in Plato's Metaphysics (London, 1965), 321 and 321-2, n. 3. Hereafter all references to this article appear in parentheses in the body of the text.

(2) More can be proved about the position of the Timaeus than this negative conclusion suggests. Stylometric evidence places the dialogue late, at least post-Parmenides , and Owen's arguments against this evidence are not sufficient to shake one's confidence in it. But that cannot be proved in this paper.
———. 1983. "Timaeus 48e-52d and the third man argument." Canadian Journal of Philosophy no. Supplementary Volumes, 9 123–147

Abstract: "In this paper I examine a much discussed passage of the Timaeus . This passage contains one of the most important descriptions of Plato's ontology to be found in all the dialogues. The ontological scheme there described differs from that presented in the middle Platonic dialogues in that a third sort of entity, the Receptacle or space, is added to the two classes of things familiar to readers of the Phaedo and Republic : Being (i.e. the Forms) and Becoming (the phenomenal world). The introduction of the Receptacle into Plato's ontology enables Plato to clarify the relation between the orders of Being and Becoming in a way not otherwise possible. When the relation between the Forms and their phenomenal counterparts has been clarified, I shall argue, it becomes clear that the Theory of Forms as presented in the Timaeus is in fact a coherent metaphysical theory, one which is not susceptible to the Third Man Argument. This fact in turn bears (although somewhat indirectly) on the vexed question of the place of the Timaeus in the chronology of Plato's works.

I shall proceed in the following way. First, I shall attempt to place this passage of the dialogue in its proper context. Second, I shall undertake a detailed explication of the passage itself. Third, I shall indicate what the import of the passage is for Plato's ontology. Fourth, I shall attempt to show how Plato's ontology, thus described, makes the Third Man idle. Fifth, I shall address briefly the chronological issue."
———. 1983. "The Concept of Παπάδειγμα in Plato's Theory of Forms." Apeiron no. 17:33–42

"There has been a good deal of discussion of the claim that Platonic Forms are self-predicative, the result of which seems to be that the claim at present must be regarded as not proven.(4) In this paper, I wish to address the other claim, that Plato's assertion that the Forms are paradigms commits him to the view that they are exemplars.

In section I, I shall argue that the well-known weaknesses of this interpretation, and its incompatibility with Plato's own statements about the Forms, should lead us to reject it. In section II, I shall distinguish two senses of "paradeigma," and examine those passages in which the term is used in connection with the Forms, in order to determine which sense fits the text best. In section III, I shall discuss the relative merits of the interpretation given in section II and the exemplar view." (p. 33)

(4) For alternatives to the straightforward account of self-predication associated with the exemplar view, cf. Allen, "Participation and Predication" [1960], pp. 46-47; H.F. Cherniss, "The Relation of the Timaeus to Plato's Later Dialogues", in Allen, SPM [Studies in Plato's Metaphysics ], pp.369-374; Vlastos, "The Unity of the Virtues in the Protagoras" [The Review of Metaphysics , Vol. 25, No. 3 (Mar., 1972), pp. 415-458], pp. 259-264; and Alexander Nehamas, "Self-Predication and Plato's Theory of Forms", American Philosophical Quarterly 16 (1979), pp.93-103.
Rankin, K. W. 1969. "The Duplicity of Plato's Third Man." Mind no. 78:178–197

"No doubt one should insist that every effort be made to interpret past philosophy sympathetically. At the same time part of the reward which the effort brings is an understanding of the historical relativity and philosophical ambivalence of commonsense. Philosophy is an incessant form of conceptual spillikins. What seems detached or connected at one stage in the game may seem the reverse at another. My foremost concern, however, has not been with the foreign- ness of Plato's thought. On the contrary I have tried to show (a) that current understanding of the distinctness of the types of argument exemplified somewhat confusedly by the TMA is still not at all times much securer than his, and (b) how, despite the insecurity of his understanding, the TMA led him towards issues in the theory of predication that are still front-line." (p.197)
Rees, D. A. 1963. "Plato and the Third Man." Proceedings of the Aristotelian Society, Supplementary Volumes no. 37:165–176

Reply to Colin Strang, Plato and the Third Man (1963).

"Me. Strang's paper has a good deal of meat in it, and covers a good deal of ground, but it may for convenience be divided into three main sections: (1) the translation of Parmenides 132a1-b2 and the formalization of its argument; (2) the discussion of the logical implications of that argument; (3) the discussion of the consequences which follow for the historical development of Plato's thought. The issues are complex and controversial in the extreme, and, finding it extremely difficult to make up my mind on some of them, I shall confine myself to raising some points that need to be faced, and trying to give a few leads.

Mr. Strang's formalization is the latest in a series begun by Professor Vlastos in 1954 and continued by Professor Sellars and Mr. Geach. As compared with Vlastos, Sellars and Geach produced versions which, despite their interest and merits in point of logical finesse, kept less closely to the Greek of Plato; but Mr. Strang has remained conscientiously close to the Platonic text. He has ignored what he calls the Second Version (132d1-133a3), which introduces the relation of copy to original, maintaining that this adds nothing fresh. Clearly Plato's thought is continuing to run along the same lines, but a new facet is emphasized,

and I shall recur to it later." (p. 165)
Rickless, Samuel C. 1998. "How Parmenides Saved the Theory of Forms." The Philosophical Review no. 107:501–554

"The Third Man Argument, as we have reconstructed it, is valid (see appendix 2). Whether the argument is sound depends on whether the following statements are true (the numbers next to the statements correspond to the numbers given to them in appendix 2):

(5) For any property F to which there corresponds a Form, there is a plurality of things that are F.

(10) The result of adding an F thing to a plurality of F things is a plurality of F things.

(22) Anything that partakes of many Forms is many.

(25) The property of being one and the property of being many are contraries.

It should be clear that Socrates accepts (5) and takes (10) and (25) to be platitudinous. Moreover, we've just seen that it is reasonable to suppose that Socrates accepts (22). Thus, Socrates cannot reasonably hold that the premises of the Third Man Argument are false, and must therefore accept that the One-over-Many version of MPTF [Middle Period Theory of Forms] is false." (pp. 524-525)
Ross, David. 1951. Plato's Theory of Ideas . Oxford: Clarendon Press

"Alexander in his commentary on the Metaphysics (4) describes two other forms of 'third man, argument, one of which he assigns to 'the sophists', and the other {on the authority of Phanias) to 'Polyxenus the sophist'. Whether either of these forms was earlier than that used in the Parmenides we do not know, nor does it matter. They are entirely different from Plato's form, and in particular they do not lead to an infinite regress ; so far as we know, Plato was the inventor of the 'infinite regress' argument.

Plato nowhere answers Parmenides' argument, but he continued to hold the theory of Ideas, and therefore plainly thought the argument not fatal to the theory. It is in fact fatal, not to the theory of Ideas, but to the language in which Plato has formulated it. The expressions 'share' and 'imitate', against which the arguments are directed, are alike metaphors inadequate to express the relation of particulars to an Idea, because they both treat the Idea as if it were a thing, instead of being a characteristic of things. Plato's use of the phrase 'the x-itself' (αύτο το) is open to the same objection ; for it treats the Idea of x as one x among others, and implies an x-ness common to it with others.

The mistake occurs in its crudest form in Prot . 330 c 2-e 2, where justice is said to be just and piety to be pious." (pp. 87-88)

(4) 84. 7-21.
Runciman, Walter Garrison. 1959. "Plato's Parmenides ." Classical Philology no. 64:89–120

Reprinted in: R. E. Allen (ed.), Studies in Plato's Metaphysics , London: Routledge & Kegan Paul 1965 pp. 149-184.

"The infinite regress (or 'third man') argument deserves separate comment. Analysis of this argument has been much clarified by the comments of Vlastos and his critics. I do not propose to enter the controversy concerning the formal analysis of the argument itself. Whether or not it is refutable by replacing the 'self-predication' and 'non-identity' assumptions by the 'separation assumption in its explicit form', the important fact is that Plato failed to realise that any instance of an attribute must, even if it is a form, have the logical status of a particular. The 'third man' argument exposes an error which, though Plato did not realise it, is fundamentally damaging to the theory of forms." (p. 156)

(...)

"The evidence of relevant ancient literature not only does not reflect any abandonment by Plato of paradeigmatism but offers positive evidence to the contrary; for references see Cherniss, below, Ch. XVII. We must accordingly conclude that Plato found the present passage damaging only to a theory of strictly literal participation, and that he continued to believe in some other indefinable (or at least undefined) relation between particulars and forms. However, that he was aware that problems arise from the consideration of the relations between the forms themselves is shown by Socrates' remarks at 129d–e. Some of these problems he examined in the Sophist; and they are relevant, as we shall see, to the second part of the Parmenides. " (p. 156)

References

Harold Cherniss, Aristotle's Criticism of Plato and the Academy , (Baltimore, 1944).
Scaltsas, Theodore. 1989. "The Logic of the Dilemma of Participation and of the Third Man Argument." Apeiron no. 22:67–90

"There has been much controversy, since Gregory Vlastos' foundational paper (Vlastos, 1954) on the logic of the Third Man Argument (TMA), over the correct or most plausible reconstruction of the steps of this argument. My main concern in the present paper is to offer an account of Plato's conception of the Forms, and the relation of participation, in the effort to identify the roots of the TMA regress. The route to Plato's understanding of the Forms and of participation in the Forms is through the explanatory work to which he puts his Theory of Forms.

I describe the model of explanation which, I argue, Plato is operating on when he undertakes to explain 'why different things are f ' through his Theory. On the basis of this model I derive the logical analysis of the Dilemma of Participation(1) - the argument preceding the TMA in the Parmenides . I further give the premisses of the TMA and offer an explanation, through the model, of why Plato is committed to them." (p. 67)

(1) 130e-131e. Textual references are to Bumet's edition of Plato's texts. The name of this argument is due to R.E. Allen (1983) 113, and so are quoted translations of the Parmenides .(...)
———. 1992. "A Necessary Falsehood in the Third Man Argument: Dedicated to the Memory of Gregory Vlastos." Phronesis no. 37:216–232

"My aim in this paper is to show that the premisses of the Third Man Argument (TMA) are committed to a distinction that falsifies them in every possible world. The distinction is between what makes a thing, and what makes it qualitatively identical to another f thing. I will argue that according to the TMA what makes something f is not sufficient for making it qualitatively identical to another f thing. But this is the denial of a necessary truth, namely, 'being f is sufficient for being f -identical to another f thing¹; (1) hence, the premisses of the TMA cannot be true in any possible world.

Apart from the logical analysis of the TMA, I also develop an interpretation of the Theory of Forms, regarding the nature of the Forms and of the relation of participation. My aim in proposing this interpretation is to show the plausibility of Plato's commitment to each of the premisses of the TMA, which, on alternative interpretations, become implausible, if not bizarre, beliefs to attribute to Plato. The interpretation will also help us gain an intuitive understanding of where and why the explanation offered by the Theory of Forms breaks down." (p. 216, a note omitted)

(1) use f -identical' to mean identical with respect to being f .
Schofield, Malcolm. 1996. "Likeness and Likenesses in the Parmenides ." In Form and Argument in Late Plato , edited by Gill, Christopher and McCabe, Mary Margaret, 49–77. Oxford: Oxford University Press

Reprinted as Chapter 5 in M. Schofield, How Plato Writes: Perspectives and Problems , Cambridge: Cambridge University Press, 2023.

"Ever since Gregory Vlastos's epoch-making article of 1954 Plato's Parmenides has meant-for most scholars and philosophers-just one thing: the Third Man regress argument (TMA).(...) (1)"

(...)

"Every great achievement is won at the expense of something.

As I reflect upon the view of the Parmenides to be offered in the present chapter, I am struck by its emphasis on something almost wholly absent in Vlastos's article and in much of the work it inspired, not just on the Third Man regress but on Platonic argument more generally-for in some quarters the study of Plato became for a good long time the study of his arguments.

What governs the line of thought developed here is reflection on the Parmenides as a Platonic dialogue. I have in mind a whole range of considerations. A Platonic dialogue is a text, often steeped in intertextual resonances, particularly echoes or preechoes of other Platonic dialogues, on which it may be commenting retrospectively or prospectively. A Platonic dialogue is the dramatic representation of a conversation between interlocutors none of whom can be assumed to be merely spokesman for Plato's own views, any more than in any other form of drama. In such a text, unresolved disagreements or puzzles cannot necessarily be assumed to reflect unresolved tensions in Plato's own mind. A Platonic dialogue says as much in the structure of its conversations and in the themes it pursues through a variety of transformations as in its discrete individual arguments. A Platonic dialogue is a game played between Plato and the reader designed to baffle as much as to elicit interpretation, and thereby to provoke us to philosophy on our own account." (p. 51)

(1) G. Vlastos, 'The Third Man Argument in the Parmenides', Philosophical Review , 63 (1954), 319-49.
Schweizer, Peter. 1994. "Self-Predication and the Third Man." Erkenntnis no. 40:21–42

Abstract: "The paper addresses the widely held position that the Third Man regress in the Parmenides is caused at least in part by the self-predicational aspect of Plato's Ideas. I offer a critique of the logic behind this type of interpretation, and argue that if the Ideas are construed as genuinely applying to themselves, then the regress is dissolved. Furthermore, such an interpretation can be made technically precise by modeling Platonic Universals as non-wellfounded sets. This provides a solution to the Third Man regress, and allows a consistent reading of both self-predication and the singularity of the respective Forms."
Sedley, David. 1998. "Platonic Causes." Phronesis no. 43:114–132

Abstract: "This paper examines Plato's ideas on cause-effect relations in the Phaedo . It maintains that he sees causes as things (not events, states of affairs or the like), with any information as to how that thing brings about the effect relegated to a strictly secondary status. This is argued to make good sense, so long as we recognise that aition means the "thing responsible" and exploit legal analogies in order to understand what this amounts to. Furthermore, provided that we do not presuppose that we already know what can and what cannot count as a cause, Plato proves to have an attractive case for his principle that all causation is a matter of like causing like. Once we appreciate this, we are a little closer to understanding his more idiosyncratic principle, which although puzzling is ubiquitous in his writings and often invoked as a premise in key arguments, that opposites cannot cause opposites. The last part of the paper turns to formnal causes, defending Plato's advocacy of them, and examining their role in the Parmenides ' Third Man Argument. The main proposal is that Plato's conception of Forms as causes opens the door to a better version of that argument's "Non-identity" premise than those currently available."
Sellars, Wilfrid. 1955. "Vlastos and the Third Man." The Philosophical Review no. 64:405–437

Reprinted in W. Sellars, Philosophical Perspectives , Springfield Charles C. Thomas 1967, pp. 23-54.

"In his recent article on “The Third Man Argument in the Paramenides,”(1) Professor Vlastos raises anew the classic questions: “Is the Third Man Argument a valid objection to the Theory of Forms?” “Did Plato believe that it was valid?”(2) He reminds us that “one can find acute and learned critics on both sides of both these questions,”(3) and soundly concludes that “if any progress in agreement is to be made at this juncture, it must come from some advance in understanding the logical structure of the argument.”(4)

(...)

There is much in Vlastos’ paper with which I should like to take issue, for in the course of a rich and complex argument he takes a stand, to my mind not always a wise one, on many of the more exciting issues of Plato interpretation. On the present occasion, however, I shall limit myself to criticizing (1) his reconstruction of the Third Man Argument; (2) his conception of the place of what he calls “Self-Predication” (Triangularity is a triangle) in Plato’s later metaphysics, and, consequently, (3) his interpretation of Plato’s frame of mind when composing the first part of the Parmenides." (p. 405)

(1) Philosophical Review , LXIII:319-349, 1954.

(2) Ibid. p-319

(3) Ibid.

(4) Ibid.
———. 1967. "Vlastos and ‘Third Man’: A Rejoinder (1955)." In Philosophical Perspectives , 55–72. Sprinfield: Charles C. Thomas

Professor Vlastos’ reply(1) to my criticism(2) of his interpretation(3) of the Third Man Argument (TMA) in the Parmenides is divided into three parts.

The first part is devoted to a critique, indeed a refutation, of my interpretation of the TMA. “What he presents is a perfectly lucid and cogent deductive argument, and also a reasonably elegant one. The only trouble with it is that it is not Plato’s.”(4)

(...)

"Vlastos devotes the second section of his Reply to a defense of his epistemological interpretation of the regress in the TMA." (p. 63)

(...)

"In the third section of his Reply, Vlastos takes up our differences with respect to the role of Self-Predication in Plato’s thought and its relation to his “Degrees of Reality Theory.” (pp. 66-67)

(...)

"After all, the purpose of my original paper was polemical; and since my own interpretation of the TMA was expounded with an eye to its similarities and contrasts with that of Vlastos, its relationships to the text of the Parmenides stands out less clearly than would have been the case had it been developed as an independent commentary. Fortunately, given the background which has been built up, it will take but a moment (as these things go) to remedy this situation and to demonstrate how neatly the TMA falls into the framework of my reconstruction, hence it is approached without even a polemical nod at the Procrustean “steps” and “hypotheses” into which Vlastos so blithely cuts it up. Read in this spirit, it becomes obvious not only that a great deal more is going on in the first sentence than is formulated by Vlastos’ (A1)(14) hich, of course, he would admit—but that what is going on is incompatible with the idea that it formulates a proposition p which is both a premise (“hypothesis”) of the TMA and the contradictory of “you will no longer have in every case a single Form"." (p. 5)

(1) Addenda to the Third Man Argument: A reply to Professor Sellars, Philosophical Review , LXIV, 438-448, 1955.

(2) Vlastos and “The Third Man,” Philosophical Review , LXIV, 405-437, 1955.

(3) The Third Man Argument in the Parmenides , Philosophical Review , LXII, 319-349, 1954.

(4) p. 438.

(14) 14The Third Man Argument in the Parmenides, Philosophical Review, p. 320.
Sharma, Ravi. 2005. "What is Aristotle's "Third Man" argument against the Forms?" Oxford Studies in Ancient Philosophy no. 28:123–160

"First, I briefly set out my interpretation of the Third Man and contrast it with what I take to be the more standard one. Then I take up Alexander's account of the argument and point out that although the account can be made to fit either interpretation, some of Alexander's remarks in the surrounding context demonstrate a clear preference for the more standard reading. None the less, I argue, there are good reasons for convicting Alexander of unintentionally distorting Aristotle's meaning. After exploring those reasons, I turn to the Sophistical Refutations and argue that the proper reading of Aristotle's remarks at 178b36-179a10 supports my own account of the Third Man. I close with some suggestions as to why I think Aristotle feels justified in pressing the argument against the Forms." (p. 124)
———. 2007. "The Anatomy of an Illusion: On Plato's Purported Commitment to Self-Predication." Apeiron no. 40:159–198

"In what follows, I want to expand on that judgment by looking at the way Vlastos discusses the import of his "self-predication" and "non-identity" assumptions. I shall begin with the former and concentrate

most of my attention on it. In the first section, I examine the ontological background of Vlastos' talk of self-predication. In so doing, I defend a radical position — namely, that such talk actually represents a misuse of the underlying conception of analysis, a confused application of its motivating principles. In the second section, I go on to discuss the way in which Vlastos proposes to analyze the regress argument of Parmenides 132A-B. Concentrating on the "non-identity" assumption, I contend that Vlastos' insistence on the need for it is a sign of his confusion regarding the conception of analysis on which he relies. Properly explicated, the talk of non-identity merely supplies a roundabout way of exploring the unwelcome implications of self-predication. The argument of the second section thus serves to extend and reinforce that of the first. Next, in the third section, I underscore the need for rejecting the self-predication thesis by pointing out its inability to explain an important Platonic text — Phaedo 100C — and I address a possible objection to my position, one that is in fact raised by Vlastos. Then, in the fourth section, I venture what I think is a more adequate interpretation of the Phaedo passage, and in so doing I propose a different account of Plato's ontological route to the Forms. I close by turning briefly to Plato's epistemology in order to comment on the relationship between the ontological and epistemological roles that are ascribed to the Forms." (pp. 160-161)
Sharvy, Richard. 1986. "Plato's Causal Logic and the Third Man Argument." Noûs no. 20:507–530

Erratum to Plato's Causal Logic and the Third Man Argument Noûs , Sep., 1987, Vol. 21, No. 3 (Sep., 1987), p. 455: "'this' on the last line of p. 527 should read 'his'.

"My principal thesis in this paper is that what drives the Third Man Argument in Plato's Parmenides is a small set of simple and straightforward inference rules of causal logic. This will yield formulations of the TMA which are faithful to Plato, and which place the TMA squarely within the category of Causal Regress Arguments in general. Some ways in which my account differs from most recent ones are these: I stress the causal role played by the Forms in the Theory of Forms; I take the Self-Predication principle to be subordinate to that causal role rather than as an independent doctrine; and I de-emphasize the "uniqueness" requirement that there be exactly one Form by which e.g. large things are large. And although most recent commentators have seen the TMA as depending on one or more "suppressed premises," on my account the Third Man Argument does not depend on any suppressed premises at all." (p. 507)
Shiner, Roger A. 1970. "Self-predication and the third man argument." Journal of the History of Philosophy no. 8:371–396.
Slowik, Edward. 1997. "Plato’s ‘Mirror-Image’ Theory of Particulars." Cogito no. 11:199–205.
Smith, T. G. 1969. "The Theory of Forms, Relations and Infinite Regress." Dialogue. Canadian Philosophical Review no. 8:116–123

"Several difficulties that accompany Plato's theory of Forms have received considerable attention in the philosophical literature in the past half century. A great deal of discussion and controversy surrounds the dialogue Parmenides and the group of considerations commonly called the "Third Man Argument".

Our purpose here is to strike out in one direction suggested by this passage (Parmenides 132 a-b, 132 d), but it can in no way be thought of as an exegesis nor a logical elucidation of the "Third Man Argument" itself. While what we shall say here has an obvious affinity and connection with the Parmenides passage, the two principal questions that concern us here are of a more general nature than the specific points in the Parmenides . The first is whether Plato's theory of Forms involves a regress which is ruinous to the theory. The second is, if a self-destructive regress is a necessary consequence of the theory, what elements of Plato's

theory make the regress inescapable." (p. 116, a note omitted)
Spellman, Lynne. 1983. "Patterns and Copies: The Second Version of the Third Man." Pacific Philosophical Quarterly no. 64:165–175

Abstract: "There are many reconstructions of the Third Man Argument and many assessments of its import. Some have thought that the argument destroys Forms as paradigms; others have said that Parmenides' argument fails because it uses premises which Plato did not hold. In this paper I want to consider primarily the second version of the argument (Parm . 132d-133a). In this version Socrates says that Forms are patterns (paradeigmata ) and that phenomenal particulars are images and likenesses of these patterns. To this Parmenides replies that if various things are made in the image of some form, then that Form cannot fail to be like its images, a clairn which produces the unwanted resull thal there must be yet another Form, namely, that Form in which the Form and its images share. In several now classic papers it has heen claimed that likeness need not be a symmetrical relationship and therefore that this version of the argument, - henceforth the TMA(2}, is unsound. It is my intention to set forth the daims of R. E. Allen, P. T. Geach , and R. S. Bluck and to argue, in response, that in all ways relevant to the TMA(2), likeness is symmetrical. I will conclude that, unless both Parmenides and recent writers have misinterpreted Socrates' proposal (a possibility which l raise in section six), it must be conceded that Parmenides' objection is correct."
Strang, Colin. 1963. "Plato and the Third Man." Proceedings of the Aristotelian Society, Supplementary Volumes no. 37:147–164

With a reply by D. A. Rees (1963).

Reprinted in Gail Fine (ed.), Plato. 1, Metaphysics and Epistemology , New York: Ocford University Press 1999, pp. 184-200.

"I take my formalisation of the TMA to represent what Plato intended. It seems obvious to me that it relies on the Self-Predication Assumption (SP) and the Non-Identity Assumption (NI), and that Plato knew perfectly well that it did. To the objection that if this is so it is odd that scholars have only recently spotted these assumptions the reply is that until recently Plato has greatly excelled his commentators in logical acumen.(1) And it would take someone his equal in logical acumen to convince me that the TMA is invalid. It has been said that the TMA is " a record of honest preplexity " (Vlastos, ["The Third Man Argument in the Parmenides ", Philosophical Review , LXIII, July 1954], p. 343). I cannot see that Plato was at all perplexed, unless it was over the decision as to which of the premisses was to be jettisoned; and I doubt whether he remained perplexed for very long even about this." (pp. 150-151)

(1) In any case, Aristotle spotted them; Alexander In Met , 84, 27 ff., following the Peri Ideon , reads "If the man which is predicated is other than the men of which it is predicated . . . . and if man is predicated both of the particulars and of the idea, there will be a third man over and above the particulars and the idea."
Taylor, Alfred Edward. 1916. "Parmenides, Zeno, and Socrates." Proceedings of the Aristotelian Society, Supplementary Volumes no. 1915-16:234–289

Reprinted in A. E. Taylor, Philosophical Studies , London: Macmillan 1934, pp. 28-90.

"Allusions to Professor Burnet’s views, unless otherwise stated, are to the analysis of the Parmenides in his volume, Greek Philosophy: Thales to Plato (1928)." (p. 28 of the reprint)

"I cannot, of course, undertake to deal here with so wide a subject as the purpose and argument of the Parmenides considered as a whole. All that I intend is to offer a slight contribution to the history of early Greek logical theory by attempting to throw some light on one or two lines of reasoning which are made prominent in the dialogue, and I shall select for special consideration two topics, the use made by Parmenides of the appeal to an infinite regress, and his attempted Refutation of Idealism. Before I can deal with either point in detail it will be necessary to say something in general about the dramatic setting which Plato has provided for the discussion, a subject on which the commentators, so far as I am acquainted with them, have been unduly silent." (p. 29 of the reprint)

(,,,)

"We have, therefore, to bear in mind that the object of the argumentation is not to throw a doubt on the existence of Forms, but to urge the need for a plain and explicit account of the relation which Socrates commonly called that of participation , by which a thing is connected with what he calls the Form of that thing.

As Professor Burnet says, expressing the point with perfect exactness in the terminology of a later generation, it is not the existence of the intelligible but the existence of the sensible which is, according to Parmenides and Zeno, the crux in Socrates’ theory." (p. 42 of the reprint)
Teloh, Henry, and Louzecky, David James. 1972. "Plato's Third Man Argument." Phronesis no. 17:80–94

"Gregory Vlastos claims that Plato's Third Man Argument (TMA), Parmenides 132 a 1-b 2, is inconsistent. Wilfred Sellars counterclaims that the TMA is consistent.(1) Plato's argument cannot bear both interpretations.

We will show that Vlastos is mistaken in thinking that the TMA is inconsistent. Moreover both Vlastos and Sellars are mistaken in supplying suppressed premises which they claim are necessary for the generation of the second and succeeding steps of the argument. In contrast to both Vlastos and Sellars we show that all of the steps of the TMA can be derived from a single assumption. This characterization of the argument better represents the text. Finally we offer a diagnosis of the problems which the TMA presents for a Theory of Forms." (p. 80)

(1) Vlastos, "The Third Man Argument in the Parmenides", Philos. Rev ., LXIII (1954), 319-349; Sellars, "Vlastos and 'The Third Man"', Philos. Rev ., LXIV (1955), 405-437; Vlastos, Reply to Sellars, Ibid ., 438-448. Vlastos' article is reprinted with some minor changes and an addendum in Studies in Plato's Metaphysics , ed. R. E. Allen (London, 1965), pp. 231-263; quotations and page references are from this reprinting.
Thein, Karel. 2005. "The second 'Third man Argument'. What difference does the likeness make?" In Plato's Parmenides. Proceedings of the Fourth Symposium Platonicum Pragense , edited by Havlícek, Ales and Karfík, Filip, 75–87. Prague: Oikoymenh.
Turnbull, Robert G. 1989. "The 'Third Man Argument' and the text of Parmenides ." In Essays in Ancient Philosophy, III: Plato , edited by Anton, John P. and Preus, Anthony, 203–225. Albany: State University of New York Press

"Gregory Vlastos’ 1954 article(1) on the so-called Third Man Argument (henceforth, TMA) of Plato’s Parmenides gave astonishing prominence to a short stretch of the text of that dialogue, namely, 132A1-B2, and elicited an equally astonishing outpouring of sophisticated argument concerning self-predication and related issues.(2) It is my intention in this paper to place that bit of text in context in the dialogue, attempting to show (a) that, thoughthere are similarities, it cannot easily be identified with anything Aristotle would have recognized as the TMA, and (b) that most of the Vlastos-inspired controversy is irrelevant to the interpretation of that text and its context. It is not my intention therefore to enter the controversy but rather simply to establish the irrelevance claim. On the way to establishing it, it will be helpful to pause briefly to inspect an implied argument at 130C which, when made fully explicit, is remarkably close to a TMA which Alexander attributes to Polyxenus(3) and which has the minor virtue of involving the (possible) form Man, not Large. Part I will set the stage for the argument at 132A1-B2.

Part II will attempt careful statement of that argument, implicitly and explicitly criticizing the statement(s) of it by Vlastos and some of his critics.

Part III will deal briefly with Aristotle’s most extended statement of the TMA in Sophistical Refutations (4) in the interest of distinguishing it from that of Parmenides 132. In Part IV, the conclusion, I shall attempt brief and schematic summation of the first three parts." (p. 203)

(1) Gregory Vlastos, “The Third Man Argument in the Parmenides,” Philosophical Review 63 (1954):319—49.

(2) See Vlastos, Platonic Studies (Princeton: University Press, 1973), 361-62, for a partial but useful listing.

(3) lexander of Aphrodisias, Commentary on Aristotle’s Metaphysics , 62, 29-33. Translated and quoted in the “Digression” on Part I, below.

(4) Sophistical Refutations 178b37-179all. Translated and quoted at the beginning of Part III of this paper.
Vandoulakis, Ioannis M. 2007. On the Peripatetic versions of the third man paradox. In Conference: Философия математики: актуальные проблемы (Philosophy of mathematics: Current problems, Proceedings of International Scientific Congress, Moscow 14-16/6/2007, Faculty of Philosophy of the Moscow M.V. Lomonosov University . Moscow

Available on Academia.edu

"In Plato’s Parmenides 132a-133b, the famous ‘Third Man Paradox’ is stated, which has attracted the attention of historians of logic, because of the self-reference that is involved. In our paper, we examine the testimonies about the Third Man Paradox survived in the works of Peripatetic commentators, in the light of our interpretation of the Paradox [Vandoulakis 1991, 1995; Bashmakova, Vandoulakis 1994]. Although the vocabulary used in these versions is different, they do not affect its logical structure, but rather reveal different understandings by Plato and the Peripatetic authors.

No proper exposition of Plato’s Third Large Paradox appears in the surviving texts of Aristotle.

There are only scattered references in the text to an argument that Aristotle calls the “Third Man” (Metaphysics 84.23-85.3, 93.1-7, 990b 17=1079a 13, 1039a 2, 1059b 8; Sophistic Refutations 178b 36),

which is commonly considered essentially the same argument. Nevertheless, nowhere, Aristotle enters into detailed analysis of the Third Man argument.

The Peripatetic commentaries of the Third Man Paradox focus primarily on the statement of the argument and the premises on which it is grounded, rather than on its solution by means of the concept of similarity, as Plato does. We are going to examine three version of the Third Man found in Alexander’s Commentary to Aristotle’s Metaphysics . One of them is ascribed directly to Aristotle; another to Eudemus and the third one is considered the same with the first(1)."

(1) On the various cross-references between these three versions see [Cherniss Aristotle's Criticism of Plato and the Academy 1944, n. 210 and App. 4, 500-501].

References

Bashmakova, Izabella G., Vandoulakis, Ioannis M. 1994. “On the Justification of the Method of Historical Interpretation” K. Gavroglu, J. Christianidis, E. Nicolaidis (Eds). Trends in the Historiography of Science . Dordrecht/ Boston/ London: Kluwer Academic Publisher.

Vandoulakis, Ioannis M. 1991. “Plato’s Semantics of the Theory of Forms and the Third Man Paradox”, Voprosy Istorii Estestvoznanija i Tekhniki , 2, 92-93 [in Russian].

Vandoulakis, Ioannis M. 1995. “Plato’s Anticipation of the Simple Theory of Types.” Istoriko-Matematicheskie Issledovaniya 35, 181-201 [in Russian].
———. 2009. "Plato's "Third Man" Paradox: Its Logic and History." Archives Internationales d'Histoire des Sciences no. 59:3–51

"We divide the Platonic text into three parts, presenting apparent thematic coherence:

a) Formulation of the Third Man Paradox (132a-132b). The central issue of this part is a step-like generation of Forms that can continue ad infinitum .

b) Discussion of the paradoxical situation ( 132b-c ), by passing to the use of terminology echoing Eleatic philosophy. The concept of" thought" (νόημα) and the underlying semantics of Eleatic origin are central in this passage.

c) Solution of the paradox (132d-133a). In our view, this part contains not only a resemblance regress, as most interpretators consider, but also the solution of the paradox by the introduction of a sound definition of the concept of "similarity" (ὁμοιότης).

(...)

In our paper, we also examine other testimonies about the Third Man Paradox found in the works of commentators in order to illuminate the logical structure of the argument. Although the vocabulary used in these versions is different, they do not affect its logical structure, but rather reveal different understandings by the ancient authors. These testimonies are divided into two main categories : those met in Neo-Platonic authors, notably in Proclus' Commentary on Plato's Parmenides , and the versions of the Third Man Paradox found in texts of the Peripatetic tradition (Eudemus, Aristotle, Alexander). From our discussion, it becomes clear that the approaches to the paradox by the various scholars of antiquity are different, depending also on their participation in the one or the other campus of philosophical thought. We are going to show that the Peripatetic authors are aware of the source of the paradox. However, the first scholar of antiquity who explicitly ascribes a solution to Plato seems to be Proclus." (p. 4)
———. 2023. "Self-reference and type distinctions in Greek philosophy and mathematics." In Historia Logicae and its Modern Interpretation , edited by Lemanski, Jens and Ingolf, Max, 3–36. London: College Publications

Abstract: "In this paper, we examine a fundamental problem that appears in Greek philosophy: the paradoxes of self-reference of the type of “Third Man” that appears first in Plato’s 'Parmenides', and is further discussed in Aristotle and the Peripatetic commentators and Proclus. We show that the various versions are analysed using different language, reflecting different understandings by Plato and the Platonists, such as Proclus, on the one hand, and the Peripatetics (Aristotle, Alexander, Eudemus), on the other hand. We show that the Peripatetic commentators do not focus on Plato’s solution but primarily on the formulation of the “Third Man” paradox. On the contrary, Proclus seems to be convinced that Plato suggests a sound solution to the paradox by defining the predicate of similarity (homogeneity) that demarcates two types of homogeneous entities – the eide and the participants in them in a way that their confusion would be inadmissible. We claim that Plato’s solution follows a sound line of reasoning that is formalisable in a language of Frege-Russell type; hence there exists a model in which Plato’s reasoning is valid. Furthermore, we notice that Plato’s definition of the second-order predicate of similarity is attained by resorting to first-order entities. In this sense, Plato’s definition is comparable to Eudoxus’ definition of ratio, which is also attained by resorting to first-order objects. Consequently, Plato seems to follow a logical practice established by the mathematicians of the 5th century, notably Eudoxus, in his solution to the paradox."
Vezjak, Boris. 2017. "Aristotle against Plato: Variants of the third man argument and the self-predication of ideas." Filozofski vestnik no. 38:23–46

Abstract: "Gregory Vlastos famously reconstructed the "tritos anthropos" argument by claiming that the third man regress becomes fatal by affirming at least two contradictory logical features of Plato's theory of ideas at the same time, namely by assuming the principles of self-predication and non-identity. I interpret the third man argument in terms of these two principles by considering two variants of it in Alexander of Aphrodias: the first version is traditionally ascribed to Aristotle under the name Peri ideon and found in Alexander's commentary on Metaphysics, and the second by Eudemus and also quoted with regard to AriAristotle's criticism of Plato's theory of ideas. Also, a comparison is made between Aristotle's versions of the third man argument and Plato's recognition of the infinite regress in two varieties thereof in his Parmenides (the largeness regress and ideas are paradigms), all resulting in logically endless series of new ideas: no longer will each of them be one, but will rather be infinite in multitude."
Vlastos, Gregory. 1954. "The Third Man Argument in the Parmenides ." The Philosophical Review no. 63:319–349

Reprinted in G. Vlastos, Studies in Greek Philosophy. Volume II: Socrates, Plato and Their Tradition , Edited by Daniel W. Graham, Princeton: Princeton University Press 1995, pp. 166-190.

"Hardly a text in Plato has been discussed as much in the last forty years as the two passages in the Parmenides purporting to prove that the Theory of Forms involves an infinite regress, which came to be dubbed within Plato's lifetime the "Third Man" Argument. A flood of light has been thrown both on the meaning of the text and on its philosophical implications. Yet in spite of this, disagreement continues. Is the Third Man Argument a valid objection to the Theory of Forms? Did Plato believe that it was valid? One can find acute and learned critics on both sides of both of these basic questions. I write as the beneficiary of their controversies, but not in a controversial spirit. If any progress in agreement is to be made at this juncture, it must come from some advance in understanding of the logical structure of the Argument. To this end I shall pursue its analysis further than I think anyone has yet found it profitable to push it. This will be the task of Section I. I shall then consider in Section II what this may teach us about the Theory of Forms and also about the state of mind in which Plato held this theory when he turned against it that battery of objections of which the Third Man Argument is the most interesting and the most instructive." (pp. 166-167, a note omitted)
———. 1955. "Addenda to the Third Man Argument: A Reply to Professor Sellars." Philosophical Review no. 64:438–448

Reply to Sellars (1955).

Reprinted in G. Vlastos, Studies in Greek Philosophy. Volume II: Socrates, Plato and Their Tradition , Edited by Daniel W. Graham, Princeton: Princeton University Press 1995, pp. 194-203.

"Professor Sellars' discussion has helped me to rethink the first version of the Third Man Argument in the Parmenides ((2.166ff.) the "TMA," I shall call it hereafter). I now understand some things about it much better than when I wrote my earlier paper, as will appear in the course of Sections I and II below. But I cannot in good conscience follow up my expression of indebtedness to Sellars on this score by conceding the "confusions" with which he belabors me. To exonerate myself from his charges point by point would not be hard, but it would be a bore for the reader. Though a paper such as this cannot avoid controversy, it can at least direct it to matters of substantial and general interest, as I have tried to do here. I have accordingly devoted the last section of the paper to a critique of that very considerable part of Sellars's interpretation of Plato which is still so widespread that it may fairly be called "orthodox"." (p. 194 of the reprint, a note omitted)
———. 1956. "Postscript to the Third Man: A Reply to Mr. Geach." Philosophical Review no. 65:83–94

Reply to Geach (1956).

Reprinted in G. Vlastos, Studies in Greek Philosophy. Volume II: Socrates, Plato and Their Tradition , Edited by Daniel W. Graham, Princeton: Princeton University Press 1995, pp. 204-214 and in in: Reginald E. Allen (ed.), Studies in Plato’s Metaphysics , London: Rotledge 1965, pp. 279–291.

"I fee extremely fortunate to have the benefit of comments as acute as those with which Mr. Geach now follows up those previously given me by Professor Sellars ("Vlastos and the 'Third Man,'" PR , 64 [1955],

405ff.). [How much]] I have learned {much} from both [ of them will be evident in a revised version of "The Third Man Argument in the Parmenides" which, I trust, will appear shortly. (Note: This promise was never fulfilled. But see Vlastos 1969b in Bibliography to this volume.) Meanwhile,! I should like to return the compliment to Mr. Geach, telling him, in Section I, what I believe is wrong with his analysis of the TMA and, in Section II, what I think both sound and penetrating in his insight into the Platonic Theory." (p. 205 of the reprint)

References

1969b. "Plato's 'Third Man' Argument (Parm. 132A1-B2): Text and Logic." Philosophical Quartely 19:289-301. Reprinted with revisions in Platonic Studies , pp. 342-65.
———. 1965. "Addendum to the Third Man Argument in the Parmenides ." In Studies in Plato's Metaphysics , edited by Allen, Reginald Edgar, 261–263. London: (Routledge & Kegan Paul

Reprinted in G. Vlastos, Studies in Greek Philosophy. Volume II: Socrates, Plato and Their Tradition , Edited by Daniel W. Graham, Princeton: Princeton University Press 1995, pp. 191-193.

"The following analysis of the Third Man Argument avoids a few technical defects in my earlier one." (p 191 of the reprint):
———. 1969. "Plato's “Third Man” Argument (Parm , 132a1-b2): Text and Logic." Philosophical Quarterly no. 19:289–301

Reprinted in G. Vlastos, Platonic Studies , Princeton: Princeton University Press 1973, pp. 342-360.

Appendix I Recent Papers on the TMA 361-364; Appendix II: The First Regress Argument in Parm. 132A-B2: 363-365.

"A cardinal feature of the interpretation I submitted in 1954 was the inconsistency of the premises from which the regress was deduced.

This blemish was smoothed out beautifully in an alternative line of analysis first worked out by Professor Wilfrid Sellars (1955) and retained, with modifications, in a no less felicitous formalization offered later (1963) by Professor Colin Strang. That this makes the TMA a vastly more attractive specimen of philosophical reasoning goes without saying. But is Plato really to get the credit for it, as Sellars so modestly insists? Since Plato's text is all we have of him now, we have to look to that for the answer.

This will be my business in this paper. I shall go about it by laying out, first of all, what I myself get from the text. This is the analysis I offered in 1954, revised in the light of more careful work on the passage and

incorporating things I have learned on the formal side from criticisms that have luckily come my way. This part of the paper, Section I, will be annotated copiously, chiefly on matters dealing with textual points which I had failed to cover in previous papers. I shall then go on in Section II to consider the alternative interpretation, explaining its logical assets and its textual liabilities." (p. 343 of the reprint, notes omitted)
———. 1969. "Self-Predication and Self-Participation in Plato's Later Period." The Philosophical Review no. 78:74–78

Reprinted in: G. Vlastos, Platonic Studies , Princeton: Princeton University Press 1973, pp. 335-341.

"Is there any evidence in the Platonic corpus which would prove that Plato ever consciously rejected the assumption that the Form corresponding to a given character itself has that character ("self-predication,"(1) abbreviated to SP)? Harold Chemiss thought he had found this in Parmenides 157E6-158B2.(2) His interpretation has not been challenged in print to myknowledge, and it is highly persuasive. It has persuaded, among others, Colin Strang, who holds (contrary to Chemiss, but in common with many scholars) that Plato subscribed to SP in the middle dialogues; Strang refers to this text as clear evidence that Plato jettisoned SP in the Parmenides .(3) As I do not believe that the text warrants such a conclusion, I had best explain why." (p. 335 of the reprint)

(1) Cf. UVP [The Unity of the Virtues in the Protagoras], above, n. 97.

(2) At ("The Relation of the TIMAEUS to Plato's Later Dialogues," American Journal of Philology 78 (1957), 225-661957, 258)—a paper which has already become a classic of scholarly controversy.

(3) ([Plato and the Third Man] 1963, 147-64)—a most acute contribution to its topic.
———. 1981. "On a Proposed Redefinition of "Self-Predication" in Plato." Phronesis. A Journal for Ancient Philosophy no. 26:76–79

Reprinted in G. Vlastos, Studies in Greek Philosophy. Volume II: Socrates, Plato and Their Tradition , Edited by Daniel W. Graham, Princeton: Princeton University Press 1995, pp. 215-219.

"In an important paper,(4) remarkable for the boldness of its attack on fundamental problems of Platonic ontology, Professor Alexander Nehamas puts forward a formal redefinition of "self-predication" which is meant to be a fourth way of reading such sentences in Plato, distinct from each of the three I have just set forth. He proposes "the following analysis of self-predication:

The F itself is F = df. The F itself, whatever it turns out to be, is what it is to be F ." (95b)

Dropping unessential wording from the proposed definiens, I abbreviate it to

[A] The F itself is what it is to be F .

The proposal has proved attractive,6 presumably because it appears to offer a via media between the first and the second of the above readings of self-predications in Plato.7 But this appearance is delusive, as I shall try to show. I wish to argue that when the proposed definiens is correctly analyzed it turns out to be a simple identity disguised by periphrastic grammar. If this argument succeeds, it will show that the proposal takes us inadvertently back to the second of the above readings. And I shall argue further that the author, mistaking the disguised identity for predication, is led to ascribe to Plato a metaphysical doctrine which only the strongest version of the first reading could hope to justify." (pp. 215-216 of the reprint, some noters omitted)

(4) "Self-Predication and Plato's Theory of Forms," APQ 16 (1979), 93ff.
Waterlow, Sarah. 1982. "The Third Man's Contribution to Plato's Paradigmatism." Mind no. 91:339–357

"This survey of Plato's various paradigmatisms accords with the result which he himself has compactly delivered in the Parmenides: that none of his earlier pronouncements on the relation of sensibles to Forms can explain participation without undue assimilation. In driving this failure home by means of the Third Man paradox, he clears the way for an advance: to the metaphysics of the Timaeus .

That is the Third Man's contribution to Plato's paradigmatism." (p. 357)
White, F. C. . 1977. "Plato's middle dialogues and the independence of particulars." The Philosophical Quarterly no. 27:193–213

"In this paper I want to discuss a view which looks as if it might easily become entrenched in a growing tradition. It is this. At no time was Plato's theory of Forms open to the kind of attack encountered in the Third Man argument and its related objections; and this becomes obvious as soon as we grasp what is involved in Plato's theory of predication and the central analogy that accompanies it - the analogy of particulars as shadows or reflections. The paper is divided into a number of sections:

I An exposition of the view mentioned above. From now on I shall refer to it as the "Reflection Doctrine".

II A brief summary of the teaching concerning particulars contained in the Phaedo and Republic V.

III Arguments in favour of the Reflection Doctrine.

IV Arguments against the Reflection Doctrine.

V Conclusion." (p. 193)
———. 1979. "Plato on naming-after." The Philosophical Quarterly no. 29:255–259

"In a recent issue of this journal ("Common Properties and Eponymy in Plato", July 1978), T. Bestor went to the trouble of presenting a detailed criticism of a paper of mine (this journal also, July 1977), in which I argued that Plato's theory of eponymous predication could not succeed in freeing him from the trammels of the Third Man. I am grateful for this criticism, and for the wider observations that were made on the way. Nonetheless, I am not persuaded. My comments will fall into two parts. The first will deal with Bestor's own thesis, the second with his criticisms." (p. 255)

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