What is it about?

Ranked first on the “Most-read list” at History and Philosophy of Logic with over 5000 readers, this demanding but self-contained and widely accessible paper refutes over a century of mistakes about existential import. All terminology is not only explained but discussed. Many useful examples presented in usable form. Central to our campaign is the fact that first-order logic has limited existential import: the universalized conditional implies its corresponding existentialized conjunction in some but not all cases. We prove Corcoran's Existential-Import Equivalence: In any first-order logic, for a universalized conditional to imply the corresponding existentialized conjunction it is necessary and sufficient for the existentialization of the antecedent predicate to be tautological.

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Why is it important?

This paper will help logic teachers to confidently and knowledgeably deal with some notorious stumbling blocks.

Perspectives

The first text I used as an undergraduate fumbled with this issue: it made dogmatic pronouncements but never got clear about the basic issue. The professor and the TAs, all brilliant and dedicated, were somehow satisfied to live with the confusion. This paper is a temporary culmination of years of cooking on the back burner. It is definitive but only in a small area. It gives a platform to rest on, a safe and solid base camp for future explorations and expeditions.

JOHN CORCORAN
University at Buffalo - The State University of New York

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This page is a summary of: Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions, History and Philosophy of Logic, September 2014, Taylor & Francis,
DOI: 10.1080/01445340.2014.952947.
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