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Counterfactual Logic and the Necessity of Mathematics.
- Source :
- Journal of Philosophical Logic; 2021, Vol. 50 Issue 1, p97-115, 19p
- Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00223611
- Volume :
- 50
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Philosophical Logic
- Publication Type :
- Academic Journal
- Accession number :
- 148190159
- Full Text :
- https://doi.org/10.1007/s10992-020-09563-8