Peut-on fonder l'arithmétique sur la logique pure? La controverse entre Natorp et Rickert

Abstract

ABSTRACTIn this article, I try to shed light on the (Fregean) project of a logic of arithmetic—as discussed by Natorp and Rickert—by outlining three main questions. Is the number a logical object? Is arithmetic reducible to logic? Is it possible to deduce the arithmetical operations from purely logical laws? I argue that rigorous distinction between these three questions makes it possible to elucidate many problems affecting the program of a logic of arithmetic. The Neo-Kantian contribution to this program is at the same time considered in a new light.