Supertasks and arithmetical truth

Jared WARREN*, Daniel WAXMAN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

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 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.
Original languageEnglish
Pages (from-to)1275-1282
Number of pages8
JournalPhilosophical Studies
Volume177
Issue number5
Early online date18 Feb 2019
DOIs
Publication statusPublished - May 2020

Bibliographical note

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.

Keywords

  • Arithmetical truth
  • Determinacy
  • Supertasks

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