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).
Keywords universals  set theoretic antinomies  Plato's Theory of Forms  category theory
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The Development of Logic.William Calvert Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
The Oxford Companion to Philosophy.Ted Honderich (ed.) - 1995 - Oxford University Press.
Platonic Studies.Gregory Vlastos - 1973 - [Princeton, N.J.]Princeton University Press.

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