Leopold Kronecker's conception of the foundations of mathematics

Boniface, Jacqueline

Philosophia Scientiae, Fonder autrement les mathématiques, Tome 9 (2005) no. S2, pp. 143-156.

On réduit habituellement les idées de Kronecker sur les fondements des mathématiques à quelque boutade ou à quelques principes rétrogrades. Ces idées constituent pourtant une doctrine originale et cohérente, justifiée par des convictions épistémologiques. Cette doctrine apparaît dans un article intitulé ‘Sur le concept de nombre', paru en 1887 dans le Journal de Crelle, et surtout dans le dernier cours professé par Kronecker à Berlin au semestre d'été 1891. Le but de cet article est d'en préciser les principes et les éléments en la comparant aux autres entreprises de fondement, afin d'en souligner l'originalité, et de montrer comment elle a déterminé la pratique mathématique de Kronecker.

Most of the time, Kronecker's views on the foundations of mathematics are reduced to some scattered ideas. However, they constitute an original and coherent doctrine, justified by epistemological convictions. This doctrine appears in the article On the concept of number, published in the Journal of Crelle (1887) and, especially, in the last course taught by Kronecker, which took place in Berlin during the 1891 summer semester. This article would precise the principles and the insights of the Kroneckerian doctrine and then compare it to the other ones in order to underline its originality; and it would highlight how this doctrine determinated Kronecker's mathematical work.

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