New forms of science and new sciences of form: On the non-mathematical reception of Grassmann’s work

Abstract

In 1907, two important texts on Kant were published, both highlighting typical aspects of a reception of Grassmannian ideas outside mathematics, mathematical logic ormathematical physics. Ernst Cassirer’s article on “Kant und die moderne Mathematik” [Cassirer 1907] deals mainly with the philosophy of mathematics, but his arguments culminate in his monumental Substanzbegriff und Funktionsbegriff from 1910 and range far beyond the realm of traditional mathematics: a general theory of concept formation, a turn towards “order” as the most fundamental concept imaginable, a shift from substances and things towards relations and functions, and the attempt to formulate a general science of forms. In the same year, the philosopher-plus-psychologist Oswald Külpe – pupil of Wilhelm Wundt, professor of philosophy in Würzburg, Bonn and Munich – presents Kant’s philosophy in the form of a popular survey that is motivated by the problem to bring philosophy and science (Wissenschaft) into a productive relationship [Külpe 1908; onKülpe see Ziche 1999; Kusch 1999].