Le schématisme transcendantal dans l’arithmétique : la lecture richirienne de Frege

Abstract

Transcendental Schematism in Arithmetic: On Richir’s Reading of Frege

This article shows how the contemporary phenomenologist Marc Richir developed his reflection on the foundation of arithmetic. Despite Frege’s criticism of the Kantian thesis of arithmetic, Richir discovers, in his reading of Frege’s logicist foundation for arithmetic, a key to rediscovering the Kantian conception of the number as a transcendental schema of quantity (quantitas). We begin this presentation by considering the background of the problem through examining the Kantian and Husserlian notions of the number. At the same time, we show the fundamental difference between Husserl’s and Richir’s phenomenologies by referring to the problem of the intuition of the infinite. Secondly, we show the key points of Richir’s reading of Frege’s work, The Foundation of Arithmetic (1884), which are developed in Richir’s article ‘Heredity and Numbers’ (1983). The impossibility of the intuition of the infinite, which is, for Frege, one of the examples that attest to the impossibility of founding the number’s existence on intuition, proves, for Richir, the impossibility of the thoroughgoing determination of the elements of an infinite set. Departing from this premise, Richir discovers, between the lines of Frege, an undeclared phenomenological foundation of arithmetic.

Keywords: thoroughgoing determination, the transcendental ideal, transcendental schema, zero, the infinite