Modal Structuralism Simplified

Canadian Journal of Philosophy 48 (2):200-222 (2018)

Abstract

Since Benacerraf’s ‘What Numbers Could Not Be, ’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical possibility operator raises concerns. In this paper, I show that the work of both these elements can be done by a single natural generalization of the logical possibility operator.

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Author's Profile

Sharon Berry
Indiana University, Bloomington

References found in this work

On the Plurality of Worlds.David Lewis - 1986 - Wiley-Blackwell.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Saving Truth From Paradox.Hartry Field - 2008 - Oxford, England: Oxford University Press.
On the Plurality of Worlds.David K. Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.

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