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GENERALITY AND EXISTENCE: QUANTIFICATIONAL LOGIC IN HISTORICAL PERSPECTIVE

Published online by Cambridge University Press:  30 December 2014

JAN VON PLATO
JAN VON PLATO*
Affiliation:
UNIVERSITY OF HELSINKI, FINLAND, 00014 HELSINKI, FINLANDE-mail: jan.vonplato@helsinki.fi
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Abstract

Frege explained the notion of generality by stating that each its instance is a fact, and added only later the crucial observation that a generality can be inferred from an arbitrary instance. The reception of Frege’s quantifiers was a fifty-year struggle over a conceptual priority: truth or provability. With the former as the basic notion, generality had to be faced as an infinite collection of facts, whereas with the latter, generality was based on a uniformity with a finitary sense: the provability of an arbitrary instance.

Keywords

quantifierspredicate logicFregeRussellSkolemHilbertBernaysBrouwerHeytingGentzenWittgensteinGoodstein
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 20 , Issue 4 , December 2014 , pp. 417 - 448
Copyright
Copyright © The Association for Symbolic Logic 2014 

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