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 claim that their argument fails to establish this result for two reasons. First, their assumptions force our hand on a controversial debate within counterfactual logic. In particular, they license 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 many reject. Second, the system they develop is provably equivalent to appending Deduction Theorem to a T modal logic. It is unsurprising that the combination of Deduction Theorem with T results in necessitation; indeed, it is precisely for this reason that many logicians reject Deduction Theorem in modal contexts. If Deduction Theorem is unacceptable for modal logic, it cannot be assumed to derive the necessity of mathematics

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

The modal logic of Reverse Mathematics.Carl Mummert, Alaeddine Saadaoui & Sean Sovine - 2015 - Archive for Mathematical Logic 54 (3-4):425-437.
How to reject a counterfactual.Vittorio Morato - 2017 - Logique Et Analyse 239:317-335.
Counterfactuals and updates as inverse modalities.Mark Ryan & Pierre-Yves Schobbens - 1997 - Journal of Logic, Language and Information 6 (2):123-146.
Modal skepticism and counterfactual knowledge.Juhani Yli-Vakkuri - 2013 - Philosophical Studies 162 (3):605-623.
Embedded counterfactuals and possible worlds semantics.Charles B. Cross - 2016 - Philosophical Studies 173 (3):665-673.
Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.
The counterfactual direct argument.Simon Goldstein - 2020 - Linguistics and Philosophy 43 (2):193-232.
Euthanasia and Counterfactual Consent.Deborah Ruth Barnbaum - 1996 - Dissertation, University of Massachusetts Amherst
Walters on Conjunction Conditionalization.Arif Ahmed - 2011 - Proceedings of the Aristotelian Society 111 (1pt1):115-122.
Counterfactual Scheming.Sam Baron - 2020 - Mind 129 (514):535-562.
Aristotle on Modality and Predicative Necessity.Jean-Louis Hudry - 2013 - International Philosophical Quarterly 53 (1):5-21.
A Lewisian Logic of Causal Counterfactuals.Jiji Zhang - 2013 - Minds and Machines 23 (1):77-93.

Analytics

Added to PP
2020-03-05

Downloads
508 (#37,415)

6 months
122 (#33,166)

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

The Philosophy of Philosophy.Timothy Williamson - 2007 - Malden, MA: Wiley-Blackwell.
Naming and necessity.Saul A. Kripke - 2010 - In Darragh Byrne & Max Kölbel (eds.), Arguing about language. New York: Routledge. pp. 431-433.
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 52 references / Add more references