Supertasks and arithmetical truth
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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 true, this implies that arithmetical truth is determinate (at least for e.g. sentences saying that every number has a certain decidable property). 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.
KeywordsArithmetical truth Determinacy Supertasks
Thanks to Sharon Berry, Hartry Field, Tomi Francis, Casper Storm Hansen, Beau Madison Mount, James Studd, Jack Woods, and two (possibly identical) referees for this journal.
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