“Critical philosophy begins at the very point where logistic leaves off”: Cassirer's Response to Frege and Russell

Abstract

This paper concerns the reception of the new logic and logicism of Frege and Russell among the German Neo-Kantian philosophers of the Marburg school. Paul Natorp and Ernst Cassirer both object to Frege’s and Russell’s conception of the ground, nature, and demarcation of logic. This objection depends on the distinctive Marburg school philosophy of logic, arst articulated by Hermann Cohen: that “formal” logic (in Kant’s sense) depends on a logical investigation of the principles that make mathematical natural science possible. Nevertheless, Cassirer thought that the new logic had profound philosophical implications. First, the new logic provides a technical vindication of some Neo-Kantian theses concerning space and time and mathematical proofs. Second, Cassirer thinks that the new logic allows for a conception of mathematics as the study of relational structures. This conception, in concert with a Kantian notion of objectivity and objecthood, makes possible a justiacation of modern mathematics. According to Michael Friedman, Ernst Cassirer’s “outstanding contribution [to Neo-Kantianism] was to articulate, for the arst time, a clear and coherent conception of formal logic within the context of the Marburg School” (Friedman 2000, p. 30). In his paper “Kant und die moderne Mathematik” (1907), Cassirer argued not only that the new relational logic of Frege 1 and Russell was a major breakthrough with profound