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

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

Authors
John Corcoran
State University of New York, Buffalo
Hassan Masoud
University of Alberta
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..
Keywords FIRST-ORDER LOGIC  EXISTENTIAL-IMPORT  UNIVERSALIZED CONDITIONAL  EXISTENTIALIZED CONJUNCTION  EXISTENTIAL-IMPORT EQUIVALENCE  ENTHYMEME  MANY-SORTED LOGIC  PROEXAMPLE  COUNTEREXAMPLE  EXTENSION [TRUTH-SET]
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Reprint years 2015
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DOI 10.1080/01445340.2014.952947
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References found in this work BETA

Philosophy of Logic.W. V. O. Quine - 1970 - Harvard University Press.
Elements of Symbolic Logic.Hans Reichenbach - 1947 - London: Dover Publications.

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Citations of this work BETA

Existential-Import Mathematics.John Corcoran & Hassan Masoud - 2015 - Bulletin of Symbolic Logic 21 (1):1-14.
Existential Import and an Unnecessary Restriction on Predicate Logics.George Boger - 2018 - History and Philosophy of Logic 39 (2):109-134.

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