Russell’s Principles of Mathematics and the Revolution in Marburg Neo-Kantianism

Bertrand Russell’s Principles of Mathematics offered a sustained criticism of Hermann Cohen’s foundations of neo-Kantianism, evoking a radical re-thinking of the basis of Marburg thought by Cohen’s student, Ernst Cassirer. Russell’s criticisms were directed at the understanding of the concepts of the differential calculus, which grounded the objectivity of scientific thought in Cohen’s effort to resurrect the Kantian transcendental project. On the basis of Russell’s criticisms, Cassirer abandoned Cohen’s foundations and instead drew on the general relational form, borrowed from Russell’s work in mathematical logic, to serve as the a priori source of objectivity. However, Cassirer’s reliance on Russell’s thought was limited, for he rejected Russell’s Logicism, the principal philosophical thesis of his Principles. Instead, Cassirer specified that the serial relation, as defined by the Formalist mathematicians, was the source of objectivity of the advanced mathematical sciences. The result was a structuralist epistemology, which was not only founded on distinctively Marburg premises, but deepened and enriched its traditional doctrines, like the genetic conception of knowledge.