Symmetry and its formalisms: Mathematical aspects

Philosophy of Science 76 (2):160-178 (2009)
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 un restrictive. The connection between groups and equivalence classes, when generalized to groupoids, suggests a middle ground between the two. *Received July 2007. †To contact the authors, please write to: Alexandre Guay, UFR Sciences et Techniques, Université de Bourgogne, 9 Avenue Alain Savary, 21078 Dijon Cedex, France; e‐mail: alexandre.guay@gmail.com ; or to Brian Hepburn, Department of Philosophy, University of British Columbia, 1866 Main Mall E370, Vancouver, BC, Canada V6T 1Z1; e‐mail: brh15@interchange.ubc.ca.
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