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  1. Parmenides' Theistic Metaphysics.Jeremy C. DeLong - 2016 - Dissertation, University of Kansas
    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 (...)
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  • Category theory and set theory as theories about complementary types of universals.David P. Ellerman - 2017 - Logic and Logical Philosophy 26 (2):1-18.
    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, (...)
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  • On the self-predicative universals of category theory.David Ellerman - manuscript
    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 (...)
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  • How to say goodbye to the third man.Francis Jeffry Pelletier & Edward N. Zalta - 2000 - Noûs 34 (2):165–202.
    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 (...)
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  • Beginning the 'Longer Way'.Mitchell Miller - 2007 - In G. R. F. Ferrari (ed.), The Cambridge Companion to Plato’s R Epublic. New York: Cambridge University Press. pp. 310--344.
    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 (...)
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  • Owen, Aristotle, and the Third Man.Gail Fine - 1982 - Phronesis 27 (1):13-33.
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  • Socratic Heterodoxy? Ontological Commitment in the Hippias Major.Sean Driscoll - 2024 - Phronesis 69 (1):1-30.
    The question of ontological commitment in Plato’s Hippias Major has been important in disputes over the dialogue’s place in the corpus, its meaning, and its authenticity. But this question seems to have been settled—the Hippias Major is not committed to the ‘forms.’ Such an ontological conclusion has been vigorously defended, but its defenses rest on a problematic meta-ontological framework. This paper suggests a more adequate framework and brings more evidence to the evaluation of the question of ontological commitment in the (...)
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  • (1 other version)Aristotle’s objection against Forms in Metaphysics M.9.Edgar González-Varela - 2020 - Archai: Revista de Estudos Sobre as Origens Do Pensamento Ocidental 30:03030-03030.
    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 (...)
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  • The Logic of the Dilemma of Participation and of the Third Man Argument.Theodore Scaltsas - 1989 - Apeiron 22 (4):67 - 90.
    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 (...)
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  • Is There Something in Common? Forms and the Theory of Word Meaning.Timothy Pritchard - 2017 - European Journal of Philosophy 25 (4):1675-1694.
    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 (...)
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  • Self-Predication in Plato's Euthyphro?Elliot C. Welch - 2008 - Apeiron 41 (4):193-210.
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  • (1 other version)Der Platonismus, wissenschaftstheoretisch betrachtet.Ulrich Nortmann - 1998 - History of Philosophy & Logical Analysis 1 (1):31-55.
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