Supertasks and arithmetical truth
Philosophical Studies:1-8 (forthcoming)
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| 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.
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| Keywords | arithmetical truth mathematical determinacy supertasks |
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| DOI | 10.1007/s11098-019-01252-w |
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References found in this work BETA
Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.
Forever is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes.John Earman & John D. Norton - 1993 - Philosophy of Science 60 (1):22-42.
A Metasemantic Challenge for Mathematical Determinacy.Jared Warren & Daniel Waxman - forthcoming - Synthese:1-19.
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