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Symmetry and Its Formalisms: Mathematical Aspects

Published online by Cambridge University Press:  01 January 2022

Alexandre Guay  and
Brian Hepburn
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Abstract

This article explores the relation between the concept of symmetry and its formalisms. The standard view among philosophers and physicists is that symmetry is completely formalized by mathematical groups. For some mathematicians however, the groupoid is a competing and more general formalism. An analysis of symmetry that justifies this extension has not been adequately spelled out. After a brief explication of how groups, equivalence, and symmetries classes are related, we show that, while it's true in some instances that groups are too restrictive, there are other instances for which the standard extension to groupoids is too unrestrictive. The connection between groups and equivalence classes, when generalized to groupoids, suggests a middle ground between the two.

Type
Research Article
Information
Philosophy of Science , Volume 76 , Issue 2 , April 2009 , pp. 160 - 178
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

Previous versions of this article were presented at the University of Pittsburgh and at the École Normale Supérieure (Paris). Thanks to the members of those audiences for their comments and questions and especially to John Earman and Gordon Belot. Guay's work was supported by a postdoctoral grant form the Fonds de Recherche sur la Société et la Culture du Québec (Canada).

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