The Philosophical Significance of the Paradoxes (to appear in the Oxford Handbook of Philosophical Logic)
In this essay, I examine the significance of a range of paradoxes (such as
semantic, set-theoretic, 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 (say, by moving from two-valued to three-valued valuations), and those motivated by restricting the structure of proofs (say, by restricting the application of the structural rules of contraction or Cut).
I also argue that whether one could take a conservative or revisionary approach to 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, since 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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