Supertasks and arithmetical truth

Philosophical Studies:1-8 (forthcoming)
Authors
Daniel Waxman
Lingnan University
Jared Warren
Stanford University
Abstract
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.
Keywords arithmetical truth  mathematical determinacy  supertasks
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DOI 10.1007/s11098-019-01252-w
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Models and Reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
How We Learn Mathematical Language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.

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