Conventionalism, Consistency, and Consistency Sentences

Synthese 192 (5):1351-1371 (2015)
  Copy   BIBTEX

Abstract

Conventionalism about mathematics claims that mathematical truths are true by linguistic convention. This is often spelled out by appealing to facts concerning rules of inference and formal systems, but this leads to a problem: since the incompleteness theorems we’ve known that syntactic notions can be expressed using arithmetical sentences. There is serious prima facie tension here: how can mathematics be a matter of convention and syntax a matter of fact given the arithmetization of syntax? This challenge has been pressed in the literature by Hilary Putnam and Peter Koellner. In this paper I sketch a conventionalist theory of mathematics, show that this conventionalist theory can meet the challenge just raised , and clarify the type of mathematical pluralism endorsed by the conventionalist by introducing the notion of a semantic counterpart. The paper’s aim is an improved understanding of conventionalism, pluralism, and the relationship between them.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,873

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Conventionalism.Yemima Ben-Menahem - 2006 - New York: Cambridge University Press.
Convention: Poincaré and some of his critics.Yemima Ben-Menahem - 2001 - British Journal for the Philosophy of Science 52 (3):471-513.
Wittgenstein and strong mathematical verificationism.Cyrus Panjvani - 2006 - Philosophical Quarterly 56 (224):406–425.
Wittgenstein’s Philosophy of Mathematics.Pieranna Garavaso - 1988 - Southern Journal of Philosophy 26 (2):179-191.
Conventionalism Revisited.Bogdan Ciomaga - 2012 - Sport, Ethics and Philosophy 6 (4):410-422.
Conventionalism and the Origins of the Inertial Frame Concept.Robert DiSalle - 1990 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:139 - 147.
“Personal identity” minus the persons.Kristie Miller - 2013 - Philosophical Studies 166 (S1):91-109.
Conventionalism and realism in Hans Reichenbach's philosophy of geometry.Carsten Klein - 2001 - International Studies in the Philosophy of Science 15 (3):243 – 251.

Analytics

Added to PP
2014-12-20

Downloads
286 (#73,247)

6 months
36 (#102,227)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Jared Warren
Stanford University

References found in this work

Language, truth and logic.Alfred Jules Ayer - 1936 - London,: V. Gollancz.
The logical syntax of language.Rudolf Carnap - 1937 - London,: K. Paul, Trench, Trubner & co.. Edited by Amethe Smeaton.
Logical Pluralism.Jc Beall & Greg Restall - 2005 - Oxford, England: Oxford University Press. Edited by Greg Restall.
Empiricism, Semantics and Ontology.Rudolf Carnap - 1950 - Revue Internationale de Philosophie 4 (11):20-40.
Language, Truth, and Logic.A. J. Ayer - 1936 - Philosophy 23 (85):173-176.

View all 32 references / Add more references