Speaker Series: Cian Dorr (NYU) In Defence of the Contingency of Distinctness

Abstract: A well-known proof, influentially defended by Saul Kripke (‘Identity and Necessity’), establishes the necesssity of identity: for any x and y, if x=y, it is metaphysically necessary that x=y. Many philosophers have found it natural to pair this claim with the necessity of distinctness: for any x and y, if x≠y, it is metaphysically necessary that x≠y.  But there is a dearth of compelling arguments for this claim.  In fact, the literature contains exactly one argument for the necessity of distinctness that is neither fallacious nor question-begging, namely Williamson’s argument (’The Necessity and Determinacy of Distinctness’) which derives the necessity of identity from certain logical principles about the interaction of modality with an ‘actually’ operator.  In this talk, I will defend the contingency of distinctness from Williamson’s argument by appealing to an insight due to Philip Bricker (‘Quantified Modal Logic and the Plural De Re’), according to which the truth-conditions of the natural-language sentences standardly formalized using ‘actually’ operators can be captured with wide-scope plural quantifiers.  For example, ‘It could have been that every actually rich person was poor’ is equivalent to ’The rich people are such that it could have been that every one of them was poor’.  I will show how Bricker’s idea can be implemented in the form of a systematic translation from a (higher-order) formal language with an ‘actually’ operator (or certain well-known generalizations thereof) into a language without such an operator.  I will explore how this leads to certain logical anomalies in the language with ‘actually', including a failure of the modalized form of Leibniz’s Law used in Williamson’s argument.

DATE & TIME
March 8th 2024 3:30pm
CONTACT NAME
Beth Grybko
EMAIL:
bellena@philos.umass.edu
PHONE
(413) 545-2330