Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections

Toby Meadows

Research output: Contribution to journalArticle

4 Citations (Scopus)
7 Downloads (Pure)

Abstract

This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday mathematical practice.
Original languageEnglish
Pages (from-to)191-212
Number of pages22
JournalNotre Dame Journal of Formal Logic
Volume56
Issue number1
DOIs
Publication statusPublished - 2015

Keywords

  • Cantor's theorem
  • set theory
  • the liar paradox
  • truth
  • Tarski
  • Kripkean truth
  • forcing
  • generic elements

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