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

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