Mind 126 (502):429-463 (2017)

Authors
Daniel Waxman
National University of Singapore
Abstract
Many philosophers believe that a deflationist theory of truth must conservatively extend any base theory to which it is added. But when applied to arithmetic, it's argued, the imposition of a conservativeness requirement leads to a serious objection to deflationism: for the Gödel sentence for Peano Arithmetic is not a theorem of PA, but becomes one when PA is extended by adding plausible principles governing truth. This paper argues that no such objection succeeds. The issue turns on how we understand the notion of logical consequence implicit in any conservativeness requirement, and whether we possess a categorical conception of the natural numbers. I offer a disjunctive response: if we possess a categorical conception of arithmetic, then deflationists have principled reason to accept a rich notion of logical consequence according to which the Gödel sentence follows from PA. But if we do not, then the reasons for requiring the derivation of the Gödel sentence lapse, and deflationists are free to accept a conservativeness requirement stated proof-theoretically. Either way, deflationism is in the clear.
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DOI 10.1093/mind/fzv182
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References found in this work BETA

Truth.Paul Horwich - 1998 - Clarendon Press.
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Citations of this work BETA

Deflationism and the Function of Truth.Lavinia Picollo & Thomas Schindler - 2018 - Philosophical Perspectives 32 (1):326-351.
Conservative Deflationism?Julien Murzi & Lorenzo Rossi - 2020 - Philosophical Studies 177 (2):535-549.
Deflating the Determination Argument.Jared Henderson - 2017 - Thought: A Journal of Philosophy 6 (2):167-177.
Infinite Reasoning.Jared Warren - forthcoming - Philosophy and Phenomenological Research.

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