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

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, first 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 justification of modern mathematics.