Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions

History and Philosophy of Logic 36 (1):39-61 (2015)
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Abstract

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential..

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Author Profiles

John Corcoran
PhD: Johns Hopkins University; Last affiliation: University at Buffalo
Hassan Masoud
University of Alberta

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Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.

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