Logic Semantics with the Potential Infinite

History and Philosophy of Logic 31 (2):145-159 (2010)
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Abstract

A form of quantification logic referred to by the author in earlier papers as being 'ontologically neutral' still made use of the actual infinite in its semantics. Here it is shown that one can have, if one desires, a formal logic that refers in its semantics only to the potential infinite. Included are two new quantifiers generalizing the sentential connectives, equivalence and non-equivalence. There are thus new avenues opening up for exploration in both quantification logic and semantics of the infinite

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Mathematical Thought from Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Mathematics in Aristotle.Thomas Heath - 1949 - Philosophy 24 (91):348-349.
Ontologically neutral logic.Theodore Hailperin - 1997 - History and Philosophy of Logic 18 (4):185-200.

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