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Zermelo’s Analysis of ‘General Proposition’
Author: R. Gregory Taylor
Affiliation: Department of Mathematics and Computer Science, Manhattan College, Riverdale, NY, USA
DOI: 10.1080/01445340802367434
Publication Frequency: 4 issues per year
Published in: journal History and Philosophy of Logic, Volume 30, Issue 2 May 2009 , pages 141 – 155
Subjects: Computational Logic; History & Philosophy of Mathematics; History of Science & Technology; Mathematical Logic; Philosophy of Logic; Philosophy of Mathematics;
Formats available: HTML (English) : PDF (English)
Abstract
On Zermelo’s view, any mathematical theory presupposes a non-empty domain, the elements of which enjoy equal status; furthermore, mathematical axioms must be chosen from among those propositions that reflect the equal status of domain elements. As for which propositions manage to do this, Zermelo’s answer is, those that are ‘symmetric’, meaning ‘invariant under domain permutations’. We argue that symmetry constitutes Zermelo’s conceptual analysis of ‘general proposition’. Further, although others are commonly associated with the extension of Klein’s Erlanger Programme to logic, Zermelo’s name has a place in that story.
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Taylor, R. Gregory (MCfac)
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