Resumo O argumento do Terceiro Homem presente no “Parmênides” constitui uma formidável objeção à teoria das Ideias, à qual Platão não apresentou resposta explícita. A despeito disso, cremos ser possível haurir da filosofia platônica uma solução para a referida objeção, solução esta que estaria verossimilmente à disposição do filósofo. Sendo assim, compreende-se que Platão não tenha sido forçado a renunciar à teoria das Ideias, ao menos no que se refere às dificuldades que o Terceiro Homem lhe opõe.The Third Man (...) Argument presented in the “Parmenides” is a formidable objection to the Theory of Forms, one which Plato did not provide an explicit answer to. In spite of that we believe it is possible to draw from Plato’s philosophy a solution to the referred objection, and one which likely would be available to the philosopher. Thus, it becomes clear that Plato was not forced to renounce his Theory of Forms, at least with regard to the difficulties that the Third Man Argument raises to it. (shrink)

This paper is a brief discussion of the famous 'Third Man Argument' as it appears in Plato's dialogue Parmenides . I mention, criticise and refine the most influential analytic approach to the argument; show that the actual conclusion of the argument is different from the one attributed to it by the majority of scholars; and elaborate two responses to the argument, both of which shed interesting light on the Theory of Forms.

In Plato’s Parmenides 132a-133b, the widely known Third Man Paradox is stated, which has special interest for the history of logical reasoning. It is important for philosophers because it is often thought to be a devastating argument to Plato’s theory of Forms. Some philosophers have even viewed Aristotle’s theory of predication and the categories as inspired by reflection on it [Owen 1966]. For the historians of logic it is attractive, because of the phenomenon of self-reference that involves. Bocheński denies (...) any possibility of correct logical reasoning before Aristotle. In particular, he flatly declares of Plato that “correct logic we find none in his work” [1951, 15]. In this line, many papers have been written that call attention to the violation of a metalogical principle – the type rules – because of the Third Man Paradox. The problem of interpretation of the paradox raised many discussions, since the 50’s, and the literature devoted to this topic is today enormous. Nevertheless, many points in Plato’s reasoning remain obscure. Hitherto, it is commonly believed that the paradox was simply stated by Plato in his "Parmenides", but not actually solved. Even more, it is believed that it is hardly possible for Plato to have suggested a solution, because he confused the categories of substance and attribute. B. Russell has also argued that Plato violates in his arguments the restrictions imposed on language by the theory of logical types. This view is encouraged by the linguistic difficulties, which Plato has faced in his attempt to formulate an ontology of abstract entities, i.e. that in Greek language abstract and concrete terms are formally indistinguishable [Kneales 1984]. In this paper, we analyse the logical structure of the argument in an attempt to give a systematic consistent reconstruction of the text appealing to methods and concepts of modern logic and semantics. Already in 1954 G. Vlastos had noted in his seminal paper “The ‘Third Man’ Argument in the Parmenides” that “if any progress … is to be made at this juncture it must come from some advance in understanding the logical structure of the Argument”. Accordingly, our analysis is primarily focused on the line of logical reasoning, rather than the metaphysical underpinnings and philosophical implications of the paradox for Plato’s theory of Forms. 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” 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 con-sider, but also the solution of the paradox by the introduction of a sound definition of the concept of “similarity”. We should note that the name ‘Third Man Paradox’ never occurs in Plato, who, strictly speaking, formulates a ‘Third Large Paradox’. The name ‘Third Man Paradox’ appears in the works of Aristotle and the commentators of the Peripatetic tradition. Later commentators have identified Aristotle’s Third Man with Plato’s Third Large Argument. 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 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. (shrink)

The "third man" argument presented in plato's "parmenides" is valid against any articulated version of the theory of forms. Plato recognized this fact, yet continued to hold the theory because the most fundamental description of what is (the "unwritten theory") cannot be articulated and does not fall victim to the third man.

Latin commentators came across the « Third Man » in Aristotle’s Sophistici elenchi. The way they dealt with the argument is a fair illustration of how they were both faithful to the text and innovative in their understanding of its most challenging issues. Besides providing a detailed survey of all manuscript sources, the introductory essay shows that Latin interpretation originates from a mistake in Boethius’ translation which radically transformed the argument. The edition makes available for the first time a (...) considerable amount of new documentary evidence which made it possible to solve the riddle of the Latin « Third Man ». (shrink)

The main lines of interpretation offered to date of the Third Man Argument in Plato's Parmenides (132a1-b2) are considered and rejected. A new, set-theoretic, reconstruction of the argument is offered. It is concluded that the philosophical point of the argument is different from what it has been generally supposed to be: Plato is pointing out the logical shortcomings in his earlier formulated principle of One-Over-Many.

Discussions of Plato's Third Man Argument (TMA) have tended to obscure its force within the context of "Parmenides". The TMA introduces a demonstration by Parmenides of the logic of dialectic. The argument does not refute the theory of forms: rather it illuminates particular difficulties involved in any attempt to conceive of what forms do. As a form, the large enables us to observe the same attribute in a number of objects. As such it is not an object of cognition. (...) When we try to think of a form, however, we transform it into such an object. That object presupposes another form which enables us to conceive of it. "there will be no end to this emergence of fresh forms," parmenides tells socrates. "if the form is to be like the things which participate in it". What the regress of the tma manifests is that a form of which we conceive can never bebut will always presupposea form "with" which we conceive. (shrink)

Ohne den Verleger Hermann Niemeyer hätte es keine DVjs gegeben. Am Beispiel dieser Zeitschrift untersucht der Beitrag auf der Grundlage unveröffentlichter Korrespondenzen, unter welchen historischen Bedingungen und Konstellationen eine funktionierende Infrastruktur für wissenschaftliches Publizieren im Deutschland der 1920er und 1930er Jahre geschaffen und unterhalten wurde.

This article is concerned with the problem of how to avoid the Third Man Argument which Plato put forward in Parmenides 132a1-b2. According to Gregory Vlastos, this argument is based on two tacit assumptions: the Self-Predication and the Non-Identity Assumption. In recent years there have been a number ofinterpretations which attempted to avoid the Third Man Argument by proving that the Self-Predication Assumption is not an acceptable part of Plato’s theory. However, in this article I will show that (...) the fallacy of the Third Man Argument does not lie in the Self-Predication Assumption, but in the Non-Identity Assumption. That is, we may avoid the Third Man Argument by proving that the Non-Identity Assumption is false. Besides, in this article I will point out that in putting forward the Third Man Argument, Plato does not really intend to raise a criticism of his own theory. Rather, his device of the Third Man Argument in Parmenides 132a1-b2 should be considered as a warning against the materialistic interpretation of the relation between Forms and particulars: if we interpret the conception of“participation” in a materialistic manner, the Theory of Forms will inevitably be caught in the Largeness Regress. (shrink)

Although Marx dubbed landowners one of the ‘three great classes’ of modern society, the most prominent Marxian and socialist thinkers of capitalism and land over the past century – from Lefebvre to Massey to Harvey – have implicitly or explicitly argued that landowners are not capitalism’s ‘third class’, and that the social relations of land are marginal or contingent to the mode of production as a whole. Through assessing the work of Marxist geographers, political economists, value-form theorists, and others (...) who have dismissed the class-status of landowners and blurred the line between ground rent and interest, this article argues that the theory of the landowning class is fundamental to the understanding of the totality of capitalist social relations, as well as to developing more incisive analyses of struggles around housing, land, and movement today. (shrink)

An analysis of the Third Man Argument, especially in light of Constance Meinwald's book Plato's Parmenides. I argue that her solution to the TMA fails. Then I present my own theory as to what Plato's solution was.

Our interpretation of the "parmenides" 132a1 - 132b2 has the following features. (i) it stresses that the third man argument is an infinite regress and (ii) notes its epistemological thrust. (iii) a faithful translation of the last line of the argument reads "and no longer will each of the forms be for you one but each is infinite in multitude." parmenides' point is that each form, which socrates believed to be complete (one), turns out to be an unbounded, incompletable (...) series of subforms useless for comprehending the unity of many particulars. (iv) related problems are seen to occupy plato in the "philebus" and in the "sophist". (shrink)

In a recent article in the Philosophical Review Professor Gregory Vlastos has given an acute analysis of the ‘Third Man’ Argument as it appears in the Parmenides for which all Platonic scholars will be grateful. In view of the importance of the article and the interest that it has aroused, I should like to offer one or two criticisms of his conclusions.

Plato presents us with two versions of the "third man" argument in the "parmenides": they occur in a tightly-knit passage of reasoning containing four arguments against the theory of forms (130e-133a). The orthodox interpretation is that both versions are attempts to show that certain basic tenets of the theory, including a one-over-many principle, form an inconsistent set. The author argues that this interpretation cannot be correct, since it renders incoherent the train of thought in the wider passage and is (...) unable to explain the occurrence of certain perceptual expressions within the first version of the "third man" argument. The author proposes an alternative reading of this version which avoids these difficulties. (shrink)

Considerable effort has gone into clarifying the structure and the content of the Third Man Argument. Nevertheless, the argument is still an enthymeme. A premise crucial to it has yet to be stated openly. This premise holds the way out of the predicament which, happily, enables Plato to retain intact the foundations of the Theory of Forms. The solution proposed allows us in addition to look beyond the TMA and place this ancient argument in the context of an important (...) modern insight. (shrink)

Theories of revolution invoke human agency to commit the violence that revolution entails, yet theorists of revolution often denounce the general theory of human agency called rational choice because it does not explain macrosocial facts like revolution and also leaves out culture. Actually, however, rational choice is the major premise of any cogent explanation of revolution, and it includes culture as a factual premise. Rational-choice theory applied to explaining revolution dates back to Thucydides, whose method of explanation is sound and (...) whose theory of revolution is true. Thucydides explains the macrosocial fact of revolution by way of models whose elements are people doing what they hope will succeed, that is, acting on opinion alias culture. Theorists of revolution who make sense of it all rehearse Thucydides: they analyze the narrative history into strategic actions and reactions, explain these actions and reactions by rational choice, and document the explanation with direct and circumstantial evidence for hope of success, though they seldom own up on theory and method or preach what they practice. (shrink)

The paper explores possible resources available to Plotinus for responding to Plato's famous "Third Man Argument" in the _Parmenides_.

I aim to show how the enigmatic phrase 'Unánime noche' in the famous first sentence of “The Circular Ruins” is inextricably linked to the story’s last words. Toward this purpose, I argue—against plausible foundational interpretations of the story—for a nonfoundational reading of the text and, moreover, that Borges’s use of ‘unánime’ (one soul) can be understood as one character or one form; namely, as an archetype of “Dreamanity” that leads to a vertiginous Third Man regress.

In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a (...) property which x exemplifies or instantiates in the traditional sense. The latter is a special mode of predication which holds when x is a Form and F is a property which is, in some sense, part of the nature of that Form. Meinwald (1991, p. 75, footnote 18) traces the discovery of this distinction in Plato’s work to Frede (1967), who marks the distinction between pros allo and kath’ hauto predications by placing subscripts on the copula ‘is’. (shrink)

Plato himself would be pleased at the recent emergence of a certain highly Platonic variety of platonism concerning mathematics, viz., the structuralism of Michael Resnik and Stewart Shapiro. In fact, this species of platonism is so Platonic that it is susceptible to an objection closely related to one raised against Plato by Parmenides in the dialogue of that name. This is the Third Man Argument against a view about the relation of Forms to particulars. My objection is not a (...) TMA against structuralism; the position avoids that objection, but is vulnerable to a different one precisely at the point where it avoids the TMA. The way structuralism avoids the TMA has in fact been considered, as one of Plato’s options, by at least one commentator on the Parmenides, Colin Strang, who explicitly rejects it on logical grounds. In the course of the discussion, I shall clarify the reason that I believe led Strang to reject this option, and shall modify his own statement of that reason. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Self-Predication and the "Third Man" Argument ROGER A. SHINER 1.1. IN COMMPm'mO on the 'Third Man' Argument (TMA), Proclus z produces the following line of thought. He argues that. if the relation of resemblance between Form and particular were symmetrical, the argument in question would be valid; the relation is not, however, symmetrical. Where a Form and particular are both alike, have the quality of likeness, the (...) likeness of that which is derived is not the same as the likeness of that from which it is derived, just because of the former's derivatory nature. Consequently, ~k tt~v ala01]x~ bttotoi3c0at ~re[vot~ (sc. xo~ ~Semv), abx~ 8~ xo6~ot~ oSr~xt, 'the sensible particulars resemble the Forms, but they are not in the same relation of resemblance to the particulars' (ibid., 913.29-30). That is to say, the bare relation of similarity may be symmetrical, but the relation of a similar copy to a similar original is not; the copy is 'a copy of' the original, but the original/s not 'a copy of' the copy. This way of defending the Theory of Forms against the TMA I shall for purposes of identification call the 'Ontological Defence'. It lays stress on the ontological difference between Form and particular in order to avoid the fatal implication that the relation between them is symmetrical. If we use the language of predication, the point is as follows: the TMA is valid, if the Forms have a given term predicated of them severally in exactly the same sense as it is predicated of their respective dependent particulars. This, however, is not the case, for the quality in virtue of which a given term is predicated of a given Form differs in ontological status from the quality in virtue of which that term is predicated of that Form's dependent particulars. Thus we see that underlying the Ontological x I am grateful for helpful comments on an earlier version of this paper to Professor Gilbert Ryle, Professor John F. Malcolm and two anonymous readers for this Journal. Since this paper went to press, the following relevant articles have appeared: G. Vlastos, "'Self Predication' in Plato's Later Period," Philosophical Review, LXXVIII (1969), 74-78, and "Plato's 'Third Man' Argument (Parm. 132al-b2): Text and Logic," Philosophical Quarterly, XIX (1969), 289-301; K. W. Rankin, "The Duplicity of Plato's Third Man," Mind, LXXVIII (1969), 178-197; T. O. Smith, "'The Theory of Forms, Relations and Infinite Regress," Dialogue, VIII (1969), 116-123. 2 Proelus, In Platonis Parmenidem, ed. V. Cousin, Paris, 1864; 912.27 ft. [3711 372 HISTORY OF PHILOSOPHY Defence is the following assumption--the fact that the Forms are self-predicating only causes problems for the Theory of Forms, if a given Form F and its corresponding particulars, a set of f things, have 'F' predicated of them univocally, are F in precisely the same sense. My thesis in this paper is that this latter assumption is false, it is, rather, quite sufficient for the Self-Predication Assumption (SPA) to be vicious, if 'F' is predicated of both Form and particular not equivocally. This is not the same as 'univocally', and furthermore it is not possible that Plato could have thought of the predication of a term of both Form and particular as equivocal, the only alternative left to him to escape the TMA. The SPA, therefore, is required for the Theory of Forms to make sense, and leads to an ineradicable defect in that Theory. 1.2. One minor terminological point must be noted before we proceed. There are two versions of the TMA in the Parmenides; the first runs from 131eS-132b2, and the second from 132c11-133a7. The second of these explicitly employs the language of copy-resemblance, 7mpdS~tytm ('paradigm'), 6lxoio)tta ('likeness'), ~tKao0~vat ('resemble') as an explication of ~t~0e~tq ('participation'): the first employs the lan~.,uage of cttx6 ~ xai3xa.., eIvat ('that by which things are...'), which, as Plato has already indicated (Phaedo 100d6-8), is deliberatety noncommittal as to the relation between Forms and particulars. I shall refer to the first argument as TMA(1) and the second... (shrink)

This paper is a restatement of my earlier analysis of this argument (1954), Revised in the light of critical comments by other scholars and of closer study of the text. It includes a critical discussion of an alternative formalization of the argument, First offered by wilfrid sellars (1955) and retained (with modifications) by colin strang (1963), Which eliminates successfully the inconsistency of the premises of the argument but has dubious support from plato's text.

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. (shrink)

In this article I argue that "Timaeus" 48e-52d, the passage in which Plato introduces the receptacle into his ontology, Contains the material for a satisfactory response to the third man argument. Plato's use of "this" and "such" to distinguish the receptacle, Becoming, And the forms clarifies the nature of his ontology and indicates that the forms are not, In general, self-predicative. This result removes one argument against regarding the "Timaeus" as a late dialogue.

Few arguments from the past have stirred up as much interest as Aristotle’s “Third man” and not so many texts have received as much attention as its account in chapter 22 of the Sophistici elenchi. And yet, several issues about both remain highly controversial, starting from the very nature of the argument at stake and the exact signification of some of its features. The essay provides a close commentary of the text, dealing with its main difficulties and suggesting an (...) overall interpretation of Aristotle’s discussion of the “Third Man” argument. (shrink)