The primary interpretative challenge for understanding Parmenides’ poem revolves around explaining both the meaning of, and the relationship between, its two primary sections: a) the positively endorsed metaphysical arguments which describe some unified, unchanging, motionless, and eternal “reality”, and b) the ensuing cosmology, which incorporates the very principles explicitly denied in Aletheia. I will refer to this problem as the “A-D Paradox.” I advocate resolving this paradoxical relationship by reading Parmenides’ poem as a ring-composition, and incorporating a modified version of (...) Palmer’s modal interpretation of Aletheia. On my interpretation, Parmenides’ thesis in Aletheia is not a counter-intuitive description of how all the world must truly be, but rather a radical rethinking of divine nature. Understanding Aletheia in this way, the ensuing “cosmology” can be straightforwardly rejected as an exposition of how traditional, mythopoetic accounts have misled mortals in their understanding of divinity. Not only does this interpretative view provide a resolution to the A-D Paradox, it offers a more holistic account of the poem by making the opening lines of introduction integral to understanding Parmenides’ message. By setting forth its own unacceptable fiction, paralleling the elements of the Doxa in a ring-composition, the Proem simultaneously establishes the scope of the ensuing inquiry, and its target. Maintaining Parmenides’ historical position as the “father of metaphysics,” the narrative that he advanced a strictly secular account of all reality is challenged. Instead, Parmenides is best understood as further advancing Xenophanes’ criticisms of traditional religion, an intellectual relationship which the ancient testimonia strongly supports. (shrink)

This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus that the paradoxes arose from having (...) one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or always the other). (shrink)

Aristotle formulates in _Metaphysics_ M.9 an aporia about Forms, according to which, those who introduce Forms make them universal substances and, at the same time, separate entities and, hence, particulars. But, he claims, it is not possible that both attributes, being a universal and being a particular, inhere in the same thing. The interpretation that scholars have offered of this objection is external, in that they hold that it derives from Aristotle’s own conception of separation: only what is particular is (...) separate. Here I defend an internal interpretation which claims that the objection derives from an assumption about the explanatory role of Forms that Aristotle attributes to the Platonists. (shrink)

Plato's reflections on Forms have generally been overlooked, in contemporary Philosophy of Language, as a serious resource for illuminating the notion of word meaning. In part, this is due to the influence of Wittgenstein's critical reflections on looking for ‘something in common’ as explanatory for use of a general term. I argue that, far from being undermined, appeal to Forms can both help explain, and provide corrective critical insight into, Wittgenstein's observations. Plato's reflections provide insight into word meaning that is (...) relevant for contemporary research. Relevant considerations include an explanation as to why an item is F; looking to ‘what something is’; the compresence of opposites; whether participation in a Form involves approximation to the Form. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of categories, (...) dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

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 and Becoming. 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 on the vexed question of the place of the Timaeus in the chronology of Plato's works. (shrink)

At 435c-d and 504b ff., Socrates indicates that there is a "longer and fuller way" that one must take in order to get "the best possible view" of the soul and its virtues. But Plato does not have him take this "longer way." Instead Socrates restricts himself to an indirect indication of its goals by his images of sun, line, and cave and to a programmatic outline of its first phase, the five mathematical studies. Doesn't this pointed restraint function as (...) a provocation, moving us to want to begin the "longer way" and to make use of its conceptual resources to rethink Socrates' images? I begin by finding a double movement in the complex trajectory of the five studies: they both guide the soul in the "turn away from what is coming to be ... [to] what is" (518c) and, at the same time, lead the soul back, albeit in the medium of pure intelligibility, to the sensible world; for the pure figures and ratios that they disclose constitute the core structures of sensible things. I then draw on what Socrates says about geometry and harmonics to address three fundamental questions that he leaves open: the nature of the Good in its responsibility for truth and for the being of the forms; the relations of forms, mathematicals, and sensibles as these are disclosed by dialectic; and the bearing of the philosopher's discovery of the Good on his disposition towards his community and the task of ruling. I close by marking six sets of further questions that these reflections bequeath for dialogues to come. (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)

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)