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)

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.

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)

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)

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.

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.

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.