Marburg Neo-Kantianism has attracted substantial interest among contemporary philosophers drawn by its founding idea that the success of advanced theoretical science is a given fact and it is the task of philosophical inquiry to ground the objectivity of scientific achievement in its a priori sources (Cohen and Natorp 1906, p. i). The Marburg thinkers realized that recent advances and developments in the mathematical sciences had changed the character of Kant’s transcendental project, demanding new methods and approaches to establish the objectivity (...) of the latest insights into physical reality. Hermann Cohen, one of the founders of the Marburg School, attempted to base the objectivity of science on the concepts of .. (shrink)

This paper offers an introduction to Hermann Cohen’s Das Princip der Infinitesimal-Methode, and recounts the history of its controversial reception by Cohen’s early sympathizers, who would become the so-called ‘Marburg school’ of Neo-Kantianism, as well as the reactions it provoked outside this group. By dissecting the ambiguous attitudes of the best-known representatives of the school, as well as those of several minor figures, this paper shows that Das Princip der Infinitesimal-Methode is a unicum in the history of philosophy: it represents (...) a strange case of an unsuccessful book’s enduring influence. The “puzzle of Cohen’s Infinitesimalmethode,” as we will call it, can be solved by looking beyond the scholarly results of the book, and instead focusing on the style of philosophy it exemplified. Moreover, the paper shows that Cohen never supported, but instead explicitly opposed, the doctrine of the centrality of the ‘concept of function’, with which Marburg Neo-Kantianism is usually associated. (shrink)

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our (...) main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position towards the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals, nor whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity, and to exploit it in making sense of infinitesimals and related concepts. (shrink)