Cassirer’s Reception of Dedekind and the Structuralist Transformation of Mathematics

Ernst Cassirer was a keen observer of development in the mathematical sciences, especially in the 19th and early 20th centuries. In this essay, the focus is on his reception of Dedekind’s contributions to the foundations of mathematics, and with it, on Dedekind’s mathematical structuralism. Cassirer adopts that structuralism early on, defends it against a number of criticisms, and embeds it into a rich historical account of the structuralist transformation of modern mathematical science. He also adds some original elements to our understanding of structuralism, e.g., by relating it to the Kantian notion of the “construction of concepts” in mathematics, by introducing a basic distinction between “substance concepts” and “function concepts”, and by tracing the “unfolding” of structuralist aspects far back in the history of thought. Overall, Cassirer’s approach is guided by the conviction that the metaphysics of modern mathematics should be approached by way of its distinctive methodology.