A Metasemantic Challenge for Mathematical Determinacy

Jared WARREN, Daniel WAXMAN

Research output: Journal PublicationsJournal Article (refereed)

1 Scopus Citations

Abstract

This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy (Sect. 1) before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics (Sect. 2). From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate (Sect. 3), motivate two important constraints on attempts to meet our challenge (Sect. 4), and then use these constraints to develop an argument against determinacy (Sect. 5) and discuss a particularly popular approach to resolving indeterminacy (Sect. 6), before offering some brief closing reflections (Sect. 7). We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic.
Original languageEnglish
Pages (from-to)477-495
Number of pages19
JournalSynthese
Volume197
Issue number2
Early online date22 Nov 2016
DOIs
Publication statusPublished - Feb 2020
Externally publishedYes

Keywords

  • Determinacy
  • Indeterminacy
  • Metasemantics
  • Philosophy of mathematics
  • · Incompleteness
  • Incompleteness

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