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Zermelo's Analysis of 'General Proposition'

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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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Document Type: Research Article

Affiliations: Department of Mathematics and Computer Science, Manhattan College, Riverdale, NY, USA

Publication date: May 1, 2009

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