Synthese 192 (5):1351-1371 (2015)
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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.
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Keywords | Conventionalism Pluralism Inferentialism Arithmetic Philosophy of Mathematics |
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DOI | 10.1007/s11229-014-0626-8 |
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References found in this work BETA
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 23 references / Add more references
Citations of this work BETA
Set-Theoretic Pluralism and the Benacerraf Problem.Justin Clarke-Doane - 2020 - Philosophical Studies 177 (7):2013-2030.
A Metasemantic Challenge for Mathematical Determinacy.Jared Warren & Daniel Waxman - 2020 - Synthese 197 (2):477-495.
Intertranslatability, Theoretical Equivalence, and Perversion.Jack Woods - 2018 - Thought: A Journal of Philosophy 7 (1):58-68.
View all 10 citations / Add more citations
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