A Metasemantic Challenge for Mathematical Determinacy

Jared WARREN, Daniel WAXMAN

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

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
JournalSynthese
DOIs
Publication statusE-pub ahead of print - 22 Nov 2016
Externally publishedYes

Fingerprint

sect
mathematics
Sect
language
Mathematics

Keywords

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

Cite this

@article{7f80631e1af84cceb20d01101fd131b3,
title = "A Metasemantic Challenge for Mathematical Determinacy",
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.",
keywords = "Determinacy, Indeterminacy, Metasemantics, Philosophy of mathematics, · Incompleteness",
author = "Jared WARREN and Daniel WAXMAN",
year = "2016",
month = "11",
day = "22",
doi = "10.1007/s11229-016-1266-y",
language = "English",
journal = "Synthese",
issn = "0039-7857",
publisher = "Springer Netherlands",

}

A Metasemantic Challenge for Mathematical Determinacy. / WARREN, Jared; WAXMAN, Daniel.

In: Synthese, 22.11.2016.

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

TY - JOUR

T1 - A Metasemantic Challenge for Mathematical Determinacy

AU - WARREN, Jared

AU - WAXMAN, Daniel

PY - 2016/11/22

Y1 - 2016/11/22

N2 - 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.

AB - 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.

KW - Determinacy

KW - Indeterminacy

KW - Metasemantics

KW - Philosophy of mathematics

KW - · Incompleteness

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-84996561792&doi=10.1007%2fs11229-016-1266-y&partnerID=40&md5=db1262d2e54cc9a67e612a7d33bae0e1

U2 - 10.1007/s11229-016-1266-y

DO - 10.1007/s11229-016-1266-y

M3 - Journal Article (refereed)

JO - Synthese

JF - Synthese

SN - 0039-7857

ER -