A formal theory of sortal quantification
Stevenson (Leslie)
Source: Notre Dame J. Formal Logic 16, no. 2 (1975), 185–207
Paper - Abstract

Paper StatisticsBooks / Papers Citing this PaperNotes Citing this PaperDisclaimer


Philosophers Index Abstract

    Using ideas of Geach, Wiggins, and Wallace, three roles of sortal1 terms are formalized: restricting quantifiers as in 'every a is ...', Restricting identity as in 'is the same a as', and in predications of the form '...Is an a'. It is assumed that there are ultimate sorts (subsets of no other sorts), so that each individual is of one and only one ultimate sort, and there is an ultimate sortal2 term for each individual term and each sortal3 term. An axiomatic system is developed, a suitable semantics is defined in terms of a purely set-theoretic notion of sort, and the soundness and completeness of the system is proved by a Henkin method. Unrestricted quantification and unrestricted identity can be defined, and the classical predicate calculus derived, within the system.

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 - August 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