La théorie des nombres chez Herbrand et Lautman

Philosophiques 37 (1):149-161 (2010)
Authors
Yvon Gauthier
Université de Montréal
Abstract
Dans cet article, je compare les vues de Lautman et Herbrand sur la théorie des nombres et la philosophie de l’arithmétique. Je montre que, bien que Lautman eût avoué avoir été marqué par l’influence de Herbrand, les postures fondationnelles des deux amis divergent considérablement. Alors que Lautman versait dans un réalisme platonicien, Herbrand est resté fidèle au finitisme hilbertien. Il est vrai que Lautman était philosophe et que Herbrand était avant tout arithméticien et logicien, mais il demeure que l’oeuvre de Herbrand a une portée philosophique mieux accordée à la logique et aux mathématiques contemporaines.In this paper, I am contrasting Lautman’s and Herbrand’s views on number theory and philosophy of arithmetic. It is argued that despite the fact that Lautman had acknowledged Herbrand’s major influence on his own work, their foundational stances diverge profoundly. Lautman defended a variety of Platonism and Herbrand advocated a personal version of Hilbertian finitism. Of course, Lautman was a philosopher while Herbrand dealt mainly with number theory and logic. It remains though that Herbrand’s work is more in tune with contemporary logic and mathematics from a philosophical perspective
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DOI 10.7202/039716ar
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