Plato Journal 18:111-124 (2018)

Authors
Andy German
Ben-Gurion University of the Negev
Abstract
Many have argued that Plato’s intermediates are not independent entities. Rather, they exemplify the incapacity of discursive thought to cognizing Forms. But just what does this incapacity consist in? Any successful answer will require going beyond the intermediates themselves to another aspect of Plato’s mathematical thought - his attribution of a quasi-numerical structure to Forms. For our purposes, the most penetrating account of eidetic numbers is Jacob Klein’s, who saw clearly that eidetic numbers are part of Plato’s inquiry into the ontological basis for all counting: the existence of a plurality of formal elements, distinct yet combinable into internally articulate unities. However, Klein’s study of the Sophist reveals such articulate unities as imperfectly countable and therefore opaque to διάνοια. And only this opacity, I argue, successfully explains the relationship of intermediates to Forms.
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Reprint years 2019
DOI 10.14195/2183-4105_18_9
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References found in this work BETA

.J. Annas (ed.) - 1976
Greek Mathematical Thought and the Origin of Algebra.Jacob Klein, Eva Brann & J. Winfree Smith - 1969 - British Journal for the Philosophy of Science 20 (4):374-375.
Metaphysica.W. D. Aristotle & Ross - 1908 - Clarendon Press.
Aristotle’s Metaphysics: Books M and N.Julia Annas - 1976 - Philosophical Review 87 (3):479-485.

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