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International Philosophical Quarterly

Volume 57, Issue 4, December 2017

Duane Armitage
Pages 401-413

Anti-Reductionism and Self-Reference
From Plato to Gödel

This essay examines the peritrope (literally, “turning around [of the tables]”) argument within the history of philosophy and discusses its various permutations, beginning with Plato and eventually mathematized with Gödel, each of which presents a philosophical system that either stands or collapses with this “peritropic” insight. I argue that the peritrope or self-reference argument itself presupposes a certain anti-reductionism, in terms of both anthropology and metaphysics, and is ultimately grounded in Aristotle’s anthropological insight that the human being is the “rational animal” (zoon logon echon). Thus the root of the anti-reductionist, peritropic argument belongs to the self-transcendent nature of rationality itself. After discussing Aristotle’s anthropology in terms of this rational transcendence, I trace the history of the self-reference argument from Plato to Gödel and discuss its various implications as applied to any and every form of reductionism. My hope is that engagement with this most basic and often overlooked philosophic insight can counter certain anti-reductionist trends in modernity.

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