The Philosophical Significance of the Paradoxes

December 2023

The Philosophical Significance of the Paradoxes (to appear in the Oxford Handbook of Philosophical Logic)

In this essay, I examine the significance of the semantic, set-theoretic and sorites paradoxes for a number of different philosophical issues concerning logic, including the choice of a logical system, the epistemology of logic, and the boundary–if there is one–between logical and non-logical concepts. Along the way, I consider the difference between revisionary logical proposals motivated by expanding the range of models (e.g. by adopting three-valued valuations), and those motivated by restricting the structure of proofs (e.g. by restricting the application of the structural rules of contraction or cut).

I also argue that whether to conserve or to revise logical principles in the light of the paradoxes is orthogonal to the question of whether to be an exceptionalist or an anti-exceptionalist about logic. All four combinations these positions have been staked out in recent work: anti-exceptionalist conservative (Tim Williamson) and anti-exceptionalist revisionist (Graham Priest), exceptionalist conservative (Per Martin-Löf), exceptionalist revisionist (Uwe Petersen).

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