Conventionalism, consistency, and consistency sentences

Synthese 192 (5):1351-1371 (2015)
Authors
Jared Warren
Stanford University
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.
Keywords Conventionalism  Pluralism  Philosophy of mathemaitcs   Inferentialism  Arithmetic
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11229-014-0626-8
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 35,527
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Logical Pluralism.Jc Beall & Greg Restall - 2005 - Oxford University Press.
Language, Truth and Logic.A. J. Ayer - 1936 - London: V. Gollancz.
Empiricism, Semantics, and Ontology.Rudolf Carnap - 1950 - Revue Internationale de Philosophie 4 (11):20--40.
Counterpart Theory and Quantified Modal Logic.David K. Lewis - 1968 - Journal of Philosophy 65 (5):113-126.

View all 22 references / Add more references

Citations of this work BETA

Intertranslatability, Theoretical Equivalence, and Perversion.Jack Woods - 2018 - Thought: A Journal of Philosophy 7 (1):58-68.
Change of Logic, Change of Meaning.Jared Warren - 2018 - Philosophy and Phenomenological Research 96 (2):421-442.

Add more citations

Similar books and articles

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.
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 index
2014-12-20

Total downloads
98 ( #64,783 of 2,287,733 )

Recent downloads (6 months)
9 ( #51,166 of 2,287,733 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature