Symmetry and its formalisms: Mathematical aspects

Philosophy of Science 76 (2):160-178 (2009)
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: ; or to Brian Hepburn, Department of Philosophy, University of British Columbia, 1866 Main Mall E370, Vancouver, BC, Canada V6T 1Z1; e‐mail:
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1086/600154
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,470
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

80 ( #60,716 of 1,925,542 )

Recent downloads (6 months)

10 ( #88,276 of 1,925,542 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.