Counterfactual Logic and the Necessity of Mathematics

Abstract

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from ‘If A were true, then C would be true’ to ‘If A and B were true, then C would be true’), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics.

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Correspondence to Samuel Z. Elgin.

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Elgin, S.Z. Counterfactual Logic and the Necessity of Mathematics. J Philos Logic (2020). https://doi.org/10.1007/s10992-020-09563-8

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Keywords

  • Necessity of mathematics
  • Counterfactual conditionals
  • Modality