Counterfactual Logic and the Necessity of Mathematics

Journal of Philosophical Logic 50 (1):97-115 (2020)
  Copy   BIBTEX

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, 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, 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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,197

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Counterfactual Scheming.Sam Baron - 2020 - Mind 129 (514):535-562.
The counterfactual direct argument.Simon Goldstein - 2020 - Linguistics and Philosophy 43 (2):193-232.
IV-Counterfactual Entailment.David Barnett - 2012 - Proceedings of the Aristotelian Society 112 (1pt1):73-97.
Counterfactual reasoning and knowledge of possibilities.Dominic Gregory - 2017 - Philosophical Studies 174 (4):821-835.
How to reject a counterfactual.Vittorio Morato - 2017 - Logique Et Analyse 239:317-335.
The Counterfactual Analysis of Cause.Igal Kvart - 2001 - Synthese 127 (3):389-427.
Reversing the counterfactual analysis of causation.Alex Broadbent - 2007 - International Journal of Philosophical Studies 15 (2):169 – 189.

Analytics

Added to PP
2020-06-27

Downloads
61 (#265,071)

6 months
10 (#275,239)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Samuel Elgin
University of California, San Diego

Citations of this work

Counterpossibles.Alexander W. Kocurek - 2021 - Philosophy Compass 16 (11):e12787.

Add more citations

References found in this work

Counterfactuals.David K. Lewis - 1973 - Malden, Mass.: Blackwell.
The Philosophy of Philosophy.Timothy Williamson - 2007 - Malden, MA: Wiley-Blackwell.
Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.

View all 38 references / Add more references