Abstract

The paper discusses neo-Kantian commentaries on Russell's views on logic and the philosophy of mathematics at the beginning of the twentieth century. Although Russell and the neo-Kantians had similar philosophical interests at this time, their views were usually incompatible. First, I examine the differences between Russell's A Critical Exposition of the Philosophy of Leibniz and Cassirer's Leibniz' System in seinen wissenschaftlichen Grundlagen. Second, I discuss the critiques of the logicist programme presented by the neo-Kantians Paul Natorp, Ernst Cassirer and Jonas Cohn. They argued that Russell's attempt to deduce the number concept from the class concept is a petitio principii. Russell replied that the sense in which every object is ‘one’ must be distinguished from the sense in which ‘one’ is a number. I claim that Russell was wrong in dismissing the neo-Kantian argument as an elementary error. Neo-Kantians understood the logicist definition of number in terms of the neo-Kantian movement to which they belonged; that is to say, although the notion ‘a class with one object’ does not presuppose the number ‘one’ if one accepts the logicist definition of number, it will presuppose it if one advocates a neo-Kantian theory of number.