Symmetric relations, symmetric theories, and Pythagrapheanism

Philosophy and Phenomenological Research (3):583-612 (2022)
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Abstract

It is a metaphysical orthodoxy that interesting non-symmetric relations cannot be reduced to symmetric ones. This orthodoxy is wrong. I show this by exploring the expressive power of symmetric theories, i.e. theories which use only symmetric predicates. Such theories are powerful enough to raise the possibility of Pythagrapheanism, i.e. the possibility that the world is just a vast, unlabelled, undirected graph.

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Tim Button
University College London

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