Plato: Third Man Argument

Empleando procedimientos de la lógica simbólica, se intenta contribuir a una mejor comprensión del ejercicio dialéctico llevado a cabo en el Parménides. La interpretación de las formas del ser y el no ser a partir de la oposición entre el objeto de conocimiento y el pensamiento acerca del mismo, abre la puerta a una manera original de enfocar el problema de la verdad en Platón. Puede resultar interesante, asimismo, la solución que se propone a la aporía planteada en Parménides 132b-c, (...) relativa a la confusión del pensamiento o el no ser con otras formas. (shrink)

In the first argument of Metaphysics Μ.2 against the Platonist introduction of separate mathematical objects, Aristotle purports to show that positing separate geometrical objects to explain geometrical facts generates an ‘absurd accumulation’ of geometrical objects. Interpretations of the argument have varied widely. I distinguish between two types of interpretation, corrective and non-corrective interpretations. Here I defend a new, and more systematic, non-corrective interpretation that takes the argument as a serious and very interesting challenge to the Platonist.

Este trabajo pretende ser una referencia útil para los estudiosos de la filosofía de Platón. Aporta un enfoque original a la investigación de los procesos lógicos que condicionan que unas formas participen de otras. Con la introducción del concepto de participación relacional, abre una posible vía de solución a las distintas versiones del argumento del «tercer hombre». Puede resultar de interés asimismo el método de generación de los números a partir de lo par y lo impar, propuesto en la interpretación (...) de Parménides 143e-144a. El escrito tiene continuidad en un segundo artículo acerca del ser y la verdad en Platón. (shrink)

Aquinas consistently criticizes Plato and his followers for their commitment to the existence of separate forms or ideas. There is no whiteness existing by itself apart from any particular white things or any particular person's thoughts about them. The same goes for every natural form, from humanity to heat. And yet Aquinas is happy to appeal to such separate forms as examples to illustrate his own metaphysical views. This seems like a strange and dangerous procedure. If Aquinas considers Platonic forms (...) to be incoherent, then surely their incoherence will infect the notions he uses them to illustrate. But does Aquinas consider Platonic forms to be incoherent? I don't think so. The very fact that he uses them as examples to illustrate his own views suggests otherwise. And at one point Aquinas even grants that God could create a Platonic form such as a separate whiteness. Why, then, does he reject such forms? What has Aquinas got against them? An examination of his main critical discussions of Platonic forms shows that he rejects them not because he thinks they are impossible, but because he thinks they are unnecessary. In other words, Aquinas rejects Platonic forms on grounds of parsimony, since he thinks they cannot explain any of the things that Plato posited them to explain, such as the changes things undergo, the nature and existence of things, and our knowledge of them. Where Plato's separate forms fail, however, Aquinas thinks Aristotle's inherent forms succeed. (shrink)

Y a-t-il des Idées et peut-on démontrer qu’elles existent ? Parmi les protagonistes anciens de la controverse qui a opposé partisans et adversaires des Idées, Aristote mérite une attention toute particulière. De fait, si – au moment où Aristote intervient dans le débat autour de l’hypothèse des Idées – ce débat a déjà une histoire, c’est avec lui que cette histoire atteint une maturité qui est à la fois d’ordre doctrinal et doxographique. De fait, non seulement Aristote est le premier (...) à avoir défini certaines au moins des propriétés de ce qui est et se dit en commun de plusieurs, mais encore a-t-il pris soin d’inscrire ces définitions dans la continuité de l’héritage socratique dont il s’est explicitement revendiqué tout en dénonçant sa dérive aux mains des successeurs de Socrate. L’objectif principal du cycle de conférences a été d’étudier les objections qu’Aristote a formulées à l’encontre des partisans des Idées en prenant comme fil conducteur la notion de substance que sa discussion des Formes platoniciennes tantôt présuppose, tantôt mobilise explicitement. Pour ce faire, nous avons procédé à une lecture détaillée d’un certain nombre de documents, tirés aussi bien de ses écrits d’école que des vestiges de ses traités perdus, où Aristote rejette la notion d’un universel substantiel (autant dire, en l’occurrence, séparé) et s’efforce de mettre à mal les arguments que ses partisans avançaient pour prouver son existence. (shrink)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)

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)

Luc Brisson’s translation and challenging interpretation of the Parmenides stands out as one of the most influential contributions to contemporary exegesis of Plato’s arguably most controversial dialogue. While acknowledging its many virtues, the essay rejects Brisson’s understanding of the text’s focus and purpose. Brisson’s methodological assumptions are especially discussed and proven to be highly questionable on account of a rather straightforward transfer of the doxographical concerns which Plato is supposed to share with contemporary historians of Parmenides’ philosophy.

Philosophica. Revista del Instituto de Filosofía de la Pontificia Universidad Católica de Valparaíso, Chile.

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)

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)

Do Ideas exist and can we prove it ? Do proofs of their existence have all the same value or not ? Aristotle addresses these issues in two famous documents of the controversy that pitted supporters of the theory of Forms against its opponents within Plato’s Academy : his lost work, quoted by Alexander of Aphrodisias by the title of Peri Ideon, and the lengthy thrust against Ideas that can be read, with some minor variations, in books A, chapter 9, (...) and M, chapter 4, of his Metaphysics. As we only have fragments of the first, the second being laconic and little more than a summary, there has been much speculation about the exact number and nature of the arguments for and against the Forms. Since the pioneering works of Léon Robin, Paul Wilpert et Harold Cherniss, one problem in particular has attracted the attention of specialists : what arguments does Aristotle accuse of either producing Ideas on relatives for one or of dragging in the « Third Man » for another ? Why does he consider these arguments to be more rigorous than the others ? If we are not dealing with the same arguments, how can these be more or better argued than those mentioned by Aristotle in the same breath, namely the arguments Plato’s followers took from the sciences, the one over many and the thought about things that have perished ? Through detailed analysis of texts from the Corpus Aristotelicum and Alexander’s commentary on Aristotle’s Metaphysics, Rationes ex machina develops a new interpretation of the controversial file of the akribesteroi tôn logôn as well as a micrological solution to the puzzle that has come to be a sort of compulsory figure of the exegesis of the Aristotelian criticism of « Plato’s Ideas ». (shrink)

The essay deals with some aspects of Aristotle's second substances and of Aristotle's universals; the ontological status of second substances and of universals opposes the characteristics of the ideas; these characteristics are presented in the arguments of Aristotle's lost work On Ideas. The ontological presuppositions of the third man arguments are taken into examination. Aristotle's construction of a typological ontology is analyzed; the typological ontology builds the only possibility of obtaining a correct ontology. The ontological position of first substances in (...) the Categories as entities which are numerical ones is described; the ontological position of second substances and universals as suches is explained. The differentiation of entities in individuals and universals is then taken into consideration. The implications of the attribute of the being separated and the contradictions which are involved in the attribution of being separated to universals complete the essay. (shrink)

Plato scholars such as Matthias Baltes (1940-2003) and Luc Brisson have defended the thesis that Plato‘s Idea of the Good is on the one hand beyond being (epekeina tês ousias) in dignity and power, but is nevertheless not transcendent over being. The article gives first (I.), an introduction into the status questionis. Second (II.), it delivers the most important arguments for the thesis of Baltes and Brisson. Third (III.), it gives two counterarguments against the thesis. Fourth (IV), it deals with (...) the translation of L. Brisson "Apollon, quelle merveilleuse emphase" of 509c1-2. Fifth (V.), it concludes with some general questions concerning the deflationist interpetation of Plato‘s Republic, 509b9-10. (shrink)

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)

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 (...) pre-suppose 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 formal 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. (shrink)

As a means of overcoming the "Third Man" argument, several commentators have developed an influential theory of the relationship between Platonic Forms and particulars based on Plato's use of "image" analogies. This essay explores the viability of this "image-analogy" hypothesis and, in particular, examines an important, but neglected, argument advanced by R. E. Allen intent on establishing an ontological distinction between an image and its object-source.

As a means of overcoming the "Third Man" argument, several commentators have developed an influential theory of the relationship between Platonic Forms and particulars based on Plato's use of "image" analogies. This essay explores the viability of this "image-analogy" hypothesis and, in particular, examines an important, but neglected, argument advanced by R. E. Allen intent on establishing an ontological distinction between an image and its object-source.

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.

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)

The historian of philosophy often encounters arguments that are enthymematic: they have conclusions that follow from their explicit premises only by the addition of "tacit" or "suppressed" premises. It is a standard practice of interpretation to supply these missing premises, even where the enthymeme is "real," that is, where there is no other context in which the philosopher in question asserts the missing premises. To do so is to follow a principle of charity: other things being equal, one interpretation is (...) better than another just to the extent that the one produces a better argument than the other. We show that this principle leads to paradoxical conclusions, including the following: there is no objectively correct interpretation of any real enthymeme found in the text of a major philosopher; an interpreter will not regard a real enthymeme of a major philosopher as adequately interpreted until he has found a way of reading it that makes it into a good argument; every classical philosopher is infallible and omniscient; major philosophers never disagree. These conclusions are preposterous, but there are indications that they are in fact being reached, as we show by means of a case study of recent scholarship on Plato's Third Man Argument. To avoid the overinterpretation and anachronism that result from the unrestrained use of the principle of charity, one must employ a counterbalancing principle of parsimony: to seek the simplest explanation for the text under discussion. We study the role of the principle of parsimony by means of a mathematical case study, involving the suppressed premises in Euclid's Elements. Here the principle of parsimony plays a larger role than it does in the interpretation of philosophical texts, leading to a sharper distinction between Euclid's geometry and Euclidean geometry than we find between Plato and Platonism. We conclude by comparing two models of interpretation, which we call prospective and retrospective. Although the prospective model of interpretation leads to Platonism rather than to Plato, we argue that it still has a place in Platonic scholarship. (shrink)

In this book, Malcolm presents a new and radical interpretation of Plato's earlier dialogues. He argues that the few cases of self-predication contained therein are acceptable simply as statements concerning universals, and that therefore Plato is not vulnerable in these cases to the Third Man Argument. In considering the middle dialogues, Malcolm takes a conservative stance, rejecting influential current doctrines which portray the Forms as being not self-predicative. He shows that the middle dialogues do indeed take Forms to be both (...) universals and paradigms, and thus to exemplify themselves. The author goes on to consider why Plato should have been unsuccessful in avoiding self-predication. He shows that Plato's concern to explain how the truths of mathematics can indeed be true played an important role in his postulation of the Form as an Ideal Individual. The author concludes with the claim that reflection on the ambiguity of the notion of the "Standard Yard" may help us to appreciate why Plato failed to distinguish Forms as universals from Forms as paradigm cases. (shrink)

In this paper i offer a detailed analysis of the dilemma of participation (parmenides, 130e-131e), in which plato considers the consequences of participation in the whole, and in a part of, a form. This analysis explains, in contrast to existing interpretations of the argument, plato's claim that participation in parts of a form is incompatible with the uniqueness of the form, and his modal claim that becoming equal by possessing part of the equal is absurd. In the second part of (...) the paper, i give the premisses and logical steps of the third man argument in the parmenides, and show the premisses to be committed to absurdity, even without the assumption that there is a unique form per character f. (shrink)

(1) anything that fs does so because it participates in the f itself. (2) it is impossible that: a form phi fs because phi participates in phi. (3) the f itself fs. These are inconsistent all right, but (1) is not a doctrine of the theory of forms, and (2) is neither reasonable nor held by plato! but the tma does not involve any of these three. Rather, the tma is aimed at (4) anything that fs does so (a) because (...) it participates in the f itself and (b) because the f itself fs. And the tma uses only simple inference rules of the logic of 'because'–no suppressed premises. I also discuss causal regress arguments generally. (shrink)

Generations of scholars have worked to clarify the structure and content of the TMA, one of the most famous arguments in the history of philosophy. Though progress has been made, I show that a premise crucial to the argument has yet to be stated openly. This premise holds the way out of the predicament that enables Plato to retain intact the foundations of the Theory of Forms.

Studies of Plato’s metaphysics have tended to emphasise either the radical change between the early Theory of Forms and the late doctrines of the Timaeus and the Sophist, or to insist on a unity of approach that is unchanged throughout Plato’s career. The author lays out an alternative approach. Focussing on two metaphysical doctrines of central importance to Plato’s thought – the Theory of Forms and the doctrine of Being and Becoming – he suggests a continuous progress can be traced (...) through Plato’s works. He presents his argument through an examination of the metaphysical sections of six of the dialogues: the Euthyphro, Phaedo, Republic, Parmenides, Timaeus, and Sophist. (shrink)

Scholars often assume that when Plato said that Forms are paradeigmata he meant that they were exemplars of the property they represent. I argue that "paradeigma" is better read as "pattern" than "exemplar." This reading is compatible with Plato's use of the term in all passages except Parm. 132d, where Parmenides misinterprets the term to make the theory of Forms susceptible to the Third Man Argument.

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.

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)

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)

In this paper I argue against the view of G.E.L. Owen that the second version of the Third Man Argument is a sound objection to Plato's conception of Forms as paradigms and that Plato knew it. The argument can be formulated so as to be valid, but Plato need not be committed to one of its premises. Forms are self-predicative, but the ground of self-predication is not the same as that of ordinary predication.

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.

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.