dc.contributor.author | Joray, Pierre | |
dc.date.accessioned | 2016-03-11T22:05:28Z | |
dc.date.available | 2016-03-11T22:05:28Z | |
dc.date.issued | 2013 | |
dc.identifier.uri | http://revueithaque.org/fichiers/cahiers/Lepage_Fradet.pdf | |
dc.identifier.uri | http://hdl.handle.net/1866/13308 | |
dc.publisher | Société Philosophique Ithaque | |
dc.rights | Ce texte est publié sous licence Creative Commons : Attribution – Pas d’utilisation commerciale – Partage dans les mêmes conditions 2.5 Canada. | |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/2.5/ca/legalcode.fr | |
dc.title | A non reductionist logicism with explicit definitions | |
dc.type | Article | |
dc.contributor.affiliation | Université de Montréal. Faculté des arts et des sciences. Département de philosophie | fr |
dcterms.abstract | This paper introduces and examines the logicist construction of Peano Arithmetic that can be performed into Leśniewski’s logical calculus of names called Ontology. Against neo-Fregeans, it is argued that a logicist program cannot be based on implicit definitions of the mathematical concepts. Using only explicit definitions, the construction to be presented here constitutes a real reduction of arithmetic to Leśniewski’s logic with the addition of an axiom of infinity. I argue however that such a program is not reductionist, for it only provides what I will call a picture of arithmetic, that is to say a specific interpretation of arithmetic in which purely logical entities play the role of natural numbers. The reduction does not show that arithmetic is simply a part of logic. The process is not of ontological significance, for numbers are not shown to be logical entities. This neo-logicist program nevertheless shows the existence of a purely analytical route to the knowledge of arithmetical laws. | |
dcterms.language | eng | |
UdeM.VersionRioxx | Version publiée / Version of Record | |
oaire.citationTitle | Les Cahiers d'Ithaque | |
oaire.citationStartPage | 185 | |
oaire.citationEndPage | 201 | |