Herbrand semantics, the potential infinite, and ontology-free logic

History and Philosophy of Logic 13 (1):69-90 (1992)
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Abstract

This paper investigates the ontological presuppositions of quantifier logic. It is seen that the actual infinite, although present in the usual completeness proofs, is not needed for a proper semantic foundation. Additionally, quantifier logic can be given an adequate formulation in which neither the notion of individual nor that of a predicate appears

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10.1080/01445349208837195

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Citations of this work

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Structure and meaning.Jaroslav Peregrin - 1997 - Semiotica 113 (1-2):71-88.
Aggregate theory versus set theory.Hartley Slater - 2003 - Erkenntnis 59 (2):189 - 202.
Logic Semantics with the Potential Infinite.Theodore Hailperin - 2010 - History and Philosophy of Logic 31 (2):145-159.

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References found in this work

From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
Introduction to mathematical logic.Elliott Mendelson - 1964 - Princeton, N.J.,: Van Nostrand.

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