Symmetry and Its Formalisms

Mathematical Aspects

Datos Bibliográficos

ID10705136
AutoresAlexandre Guay (0000-0002-7857-363X, Laboratoire Interdisciplinaire de Recherches "Sociétés, Sensibilités, Soin"), BRIAN HEPBURN
Año2009
Volumen76
Número2
Páginas160-178
Fecha de publicación2009-04-01
Peer ReviewedSí
Open AccessSí
TipoARTICLE
RevistaPhilosophy of Science (JOURNAL)
Identificadores de la revistaISSN: 0031-8248 • E-ISSN: 1539-767X
EditorialCambridge University Press (CUP) (PUBLISHER)
DOI10.1086/600154
OpenAlexW2170506528
IdiomaEN
Citas recibidas4
Referencias citadas4

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