Le pragmatisme peircéen, la théorie des catégories et le programme de Thiel
Abstracts
Category theory is important by its mathematical applications and by the philosophical debates it causes. It is used to express in algebraic topology, to deduce in homological algebra and, as an alternative to the theory of sets, to construct objects in Grothendieck’s conception of algebraic geometry. Category theory is a fundamental discipline in Christian Thiel’s sense, because it is a theory of some typical operations of structural mathematics. This thesis is defended through a particular interpretation of peircean pragmatism; in this perspective, justification of mathematical knowledge is not provided for by the reduction to basic objects but rather by a technical common sense intervening on each level (the theories on the higher level having as their objects the theories of the original objects).
Author’s notes
Une version préliminaire de cet article a été présentée (en anglais) lors du colloque PILM. Je remercie Manuel Rebuschi et les auditeurs de mon intervention (notamment Steve Awodey, F. William Lawvere et Jean Pierre Marquis) ainsi que les membres du comité scientifique dudit colloque pour leurs suggestions et remarques qui m’ont aidé à approfondir l’argumentaire de l’article. Des remerciements particuliers sont à adresser à Gerhard Heinzmann pour l’enseignement de sa philosophie pragmatiste qu’il m’a offert pendant mes années à Nancy.
References
Bibliographical reference
Ralf Krömer, “Le pragmatisme peircéen, la théorie des catégories et le programme de Thiel”, Philosophia Scientiæ, 9-2 | 2005, 79-96.
Electronic reference
Ralf Krömer, “Le pragmatisme peircéen, la théorie des catégories et le programme de Thiel”, Philosophia Scientiæ [Online], 9-2 | 2005, Online since 15 June 2011, connection on 19 March 2024. URL: http://journals.openedition.org/philosophiascientiae/524; DOI: https://doi.org/10.4000/philosophiascientiae.524
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