Symmetry and Its Formalisms
Mathematical Aspects
Bibliographic Data
| ID | 10705136 |
|---|---|
| Authors | Alexandre Guay (0000-0002-7857-363X, Laboratoire Interdisciplinaire de Recherches "Sociétés, Sensibilités, Soin"), BRIAN HEPBURN |
| Year | 2009 |
| Volume | 76 |
| Issue | 2 |
| Pages | 160-178 |
| Publication date | 2009-04-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0031-8248 • E-ISSN: 1539-767X |
| Publisher | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1086/600154 |
| OpenAlex | W2170506528 |
| Language | EN |
| Citations received | 4 |
| References cited | 4 |
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
Algebra over a field · Epistemology · Equivalence (formal languages) · Equivalence relation · Explication · Extension (predicate logic) · Formalism (music) · Geometry · Homogeneous space · Pure mathematics · Rotation formalisms in three dimensions · Symmetry (geometry) · Symmetry group · Computer Science · Mathematics · Philosophy · Philosophy and History of Science
| Unique citing works | 4 |
|---|---|
| Citations per year | 0,25 |
| Citation span | 2010 - 2022 (13) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 4 |