Existence and Contingency
Williamson (Timothy)
Source: Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 73 (1999), pp. 181-203
Paper - Abstract

Paper StatisticsBooks / Papers Citing this PaperColour-ConventionsDisclaimer


Author’s Abstract

  1. The paper defends the intelligibility of unrestricted quantification. For any natural number n, 'There are at least n individuals' is logically true, when the quantifier is unrestricted.
  2. In response to the objection that such sentences should not count as logically true because existence is contingent, it is argued by consideration of cross-world counting principles that in the relevant sense of 'exist' existence is not contingent.
  3. A tentative extension of the upward Lowenheim-Skolem theorem to proper classes is used to argue that a sound and complete axiomatization of the logic of unrestricted universal quantification results from adding all sentences of the form 'There are at least n individuals' as axioms to a standard axiomatization of the first-order predicate.

Author’s Introduction
  1. Of the many questions on which logic is neutral, one is usually supposed to be this: 'How many individuals are there?'
  2. On the alternative view defended below, truths about the number of individuals are logically true. They are not contingent logical truths, for it is not contingent what individuals there are.

Comment:

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2019
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



© Theo Todman, June 2007 - June 2019. Please address any comments on this page to theo@theotodman.com. File output:
Website Maintenance Dashboard
Return to Top of this Page Return to Theo Todman's Philosophy Page Return to Theo Todman's Home Page