Supertasks and Arithmetical Truth

Philosophical Studies 177 (5):1275-1282 (2020)
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This paper discusses the relevance of supertask computation for the determinacy of arithmetic. Recent work in the philosophy of physics has made plausible the possibility of supertask computers, capable of running through infinitely many individual computations in a finite time. A natural thought is that, if supertask computers are possible, this implies that arithmetical truth is determinate. In this paper we argue, via a careful analysis of putative arguments from supertask computations to determinacy, that this natural thought is mistaken: supertasks are of no help in explaining arithmetical determinacy.



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Author Profiles

Jared Warren
Stanford University
Daniel Waxman
National University of Singapore

Citations of this work

Infinite Reasoning.Jared Warren - 2020 - Philosophy and Phenomenological Research 103 (2):385-407.

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References found in this work

Philosophy of Mathematics and Natural Science.Hermann Weyl - 1949 - Princeton, N.J.: Princeton University Press. Edited by Olaf Helmer-Hirschberg & Frank Wilczek.
Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.

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