La lecture à portée de main
Suivre
Documents
Mathematical intuition and the cognitive roots of mathematical concepts1 Giuseppe Longo Arnaud Viarouge CNRS et Ecole Normale Superieure Psychology and Human Development Dpt et CREA Ecole Polytechnique Paris Fr Peabody College Vanderbilt University http: www di ens fr users longo Nashville TN USA Abstract The foundation of Mathematics is both a logico formal issue and an epistemological one By the first we mean the explicitation and analysis of formal proof principles which largely a posteriori ground proof on general deduction rules and schemata By the second we mean the investigation of the constitutive genesis of concepts and structures the aim of this paper This genealogy of concepts so dear to Riemann Poincaré and Enriques among others is necessary both in order to enrich the foundational analysis by this too often disregarded aspect the cognitive and historical constitution of mathematical structures and because of the provable incompleteness of proof principles also in the analysis of deduction For the purposes of our investigation we will hint here to the philosophical frame as well as to the some recent advances in Cognition that support our claim the cognitive origin and the constitutive role of mathematical intuition From Logic to Cognition Over the course of the XXth century the relationships between Philosophy and Mathematics have been dominated by Mathematical Logic A most interesting area of Mathematics which from onwards year of one of the major mathematical results of the century Gödelian Incompleteness enjoyed the double status of a discipline that is both technically profound and philosophically fundamental From the foundational point of view Proof Theory constituted its main aspect also on account of other remarkable results Ordinal Analysis after Gentzen Type Theory in the manner of Church Gödel Girard various forms of incompleteness independence in Set Theory and Arithmetics and produced spin offs which are in the course of changing the world: the functions for the computation of proofs ...
Giuseppe Longo
Documents
Rapports de stage
Mathematical intuition and the cognitive roots of mathematical concepts1 Giuseppe Longo Arnaud Viarouge CNRS et Ecole Normale Superieure Psychology and Human Development Dpt et CREA Ecole Polytechnique Paris Fr Peabody College Vanderbilt University http: www di ens fr users longo Nashville TN USA Abstract The foundation of Mathematics is both a logico formal issue and an epistemological one By the first we mean the explicitation and analysis of formal proof principles which largely a posteriori ground proof on general deduction rules and schemata By the second we mean the investigation of the constitutive genesis of concepts and structures the aim of this paper This genealogy of concepts so dear to Riemann Poincaré and Enriques among others is necessary both in order to enrich the foundational analysis by this too often disregarded aspect the cognitive and historical constitution of mathematical structures and because of the provable incompleteness of proof principles also in the analysis of deduction For the purposes of our investigation we will hint here to the philosophical frame as well as to the some recent advances in Cognition that support our claim the cognitive origin and the constitutive role of mathematical intuition From Logic to Cognition Over the course of the XXth century the relationships between Philosophy and Mathematics have been dominated by Mathematical Logic A most interesting area of Mathematics which from onwards year of one of the major mathematical results of the century Gödelian Incompleteness enjoyed the double status of a discipline that is both technically profound and philosophically fundamental From the foundational point of view Proof Theory constituted its main aspect also on account of other remarkable results Ordinal Analysis after Gentzen Type Theory in the manner of Church Gödel Girard various forms of incompleteness independence in Set Theory and Arithmetics and produced spin offs which are in the course of changing the world: the functions for the computation of proofs ...
Giuseppe Longo
18 pages
English
Documents
Reflections on Concrete Incompleteness
Giuseppe Longo
Documents
Etudes supérieures
Reflections on Concrete Incompleteness
Giuseppe Longo
23 pages
English
Documents
Forms of Linguistic Ambiguity: a Case Study of Teaching Persian ...
Admin 2004
Documents
Travaux de classe
Forms of Linguistic Ambiguity: a Case Study of Teaching Persian ...
Admin 2004
4 pages
English
Documents
Social network viSualization
Documents
LIDERAZGO ENTRE IGUALES EN EQUIPOS DEPORTIVOS: UNA REVISIÓN CAMINO A LA INTEGRACIÓN (An Integrated Vision of Peer Leadership in Sports Teams: A Review)
Julio
Documents
Autres
LIDERAZGO ENTRE IGUALES EN EQUIPOS DEPORTIVOS: UNA REVISIÓN CAMINO A LA INTEGRACIÓN (An Integrated Vision of Peer Leadership in Sports Teams: A Review)
Julio
8 pages
Español
Documents
Dybvig, Shan, and Tang Sankar De Does Informal Finance Help ...
Glenn Borchardt
Documents
Cours
Dybvig, Shan, and Tang Sankar De Does Informal Finance Help ...
Glenn Borchardt
4 pages
English
Documents
Expected Coverage of Computer Sciences 313K
Navkala Roy
Documents
Travaux de classe
Expected Coverage of Computer Sciences 313K
Navkala Roy
26 pages
English
Collection
{{collectionTitle}}
Collection
{{collectionTitle}}
Collection
{{collectionTitle}}
{{productCategoryLabel}}
{{productTitle}}
{{productAuthors}}
{{productCategoryLabel}}
{{productThemeLabel}}
{{productTitle}}
{{productAuthors}}
{{productPages}}
{{productLanguageIsoCode}}