Hermann Cohen’s Philosophy of Mathematics, or What is Wrong with the Marburg Method

Abstract

Neo-Kantianism in general and the Marburg school are becoming an increas­ingly popular subject of research both in the Russian and global academic com­munity. Thanks to the meticulous archival work of H. Holzhey, K.Ch. Köhnke, U. Sieg and other scientists, rich historical and philosophical dimension of this phenomenon has been discovered. As a result, neo-Kantianism is no longer read strictly through the prism of an (unsuccessful) attempt to scientize philosophy in the image of natural scientific knowledge. At the same time, it seems interest­ing to analyze this attempt from the point of view of its internal content. The ob­ject of this study is mainly H. Cohen’s “Das Princip der Infinitesimal-Methode und seine Geschichte”, conjugated with the historical and theoretical context of psychological discussions. The term “Cohen’s method” in its early temporal localization of the beginning of the 1880’s, we expand to the “Marburg method”. It is based on a functional interpretation of the process of cognition using the ex­ample of infinitesimal calculus. Despite the declared opposition to the psycho­logical programs of philosophy, we believe that Cohen could not achieve this task at theoretical level. The intuitive definition of mathematical entities in gen­eral and the usage of a psychophysical mathematical model is an unsuccessful way of countering psychological programs of philosophy. At the same time, we believe that despite the outward exoticism of the philosopher’s conclusions, the desire to “dereify” and “denaturalize” the concept of reality finds full expression in his model, which is extremely important for the formation of the Marburg Neo-Kantianism. Reconstruction and comprehension of what we conditionally call "the philosophy of mathematics of Hermann Cohen" allows us to better un­derstand the essence of the theoretical superstructure that he created over the form of mathematical derivation.