Ernst Cassirer’s book Substanzbegriff und Funktionsbegriff is a difficult book for contemporary readers to understand. Its topic, the theory of concept formation, engages with debates and authors that are largely unknown today. And its “historical” style violates the philosophical standards of clarity first propounded by early analytic philosophers. Cassirer, for instance, never says explicitly what he means by “substance-concept” and “function-concept.” In this article, I answer three questions: Why did Cassirer choose to focus on the topic of concept formation? What (...) did Cassirer mean in contrasting “substance-concepts” and “function-concepts”? How does Cassirer’s polemic against traditional theories of concept formation lead to the distinctive philosophy of mathematics that he defends in the book? I argue that Cassirer’s contrast between substance-concepts and function-concepts includes a series of interrelated contrasts—contrasts that touch on issues in logic, metaphysics, epistemology, and the theory of objectivity. Cassirer’s defense of mathematical structuralism flows out of a progressively unfolding and intricate argument that begins with epistemological problems in the theory of concept formation. (shrink)

According to Michael Friedman, Ernst Cassirer’s “outstanding contribution [to Neo-Kantianism] was to articulate, for the first time, a clear and coherent conception of formal logic within the context of the Marburg School” (Friedman 2000, p. 30). In his paper “Kant und die moderne Mathematik” (1907), Cassirer argued not only that the new relational logic of Frege1 and Russell was a major breakthrough with profound philosophical implications, but also that the logicist thesis itself was a “fact” of modern mathematics. Cassirer summarizes (...) his evaluation of Russell’s work: Here logic and mathematics have been fused into a true, henceforth indissoluble unity; and from this inner connection there arises for each... (shrink)

The neo-Kantian Hermann Cohen is famously anti-empiricist in that he denies that sensations can make a definable contribution to knowledge. However, in the second edition of Kant’s Theory of Experience (1885), Cohen considers a proposition that contrasts with both his other work and that of his followers: a Kantian who studies scientific claims to truth—and the grounds on which they are made—cannot limit himself to studying mathematics and logical principles, but needs to also investigate underlying presuppositions about the empirical element (...) of science. Due to his subjectivist approach, Cohen argues, Kant not only failed to explain how scientific observation and experiments are possible, but also misconceived the role of the ideas, particularly the idea of a system of nature. (shrink)

Such are those thick & gloomie shadows dampe Oft seene in charnel vaults, & sepulchers, Lingering, & sitting by a new made grave, As loath to leave the bodie that it lov'd, & link’t it selfe by carnall sensualtie To a degenerate, & degraded state.