In this paper, I explore how Cassirer’s early and mature epistemology, philosophy of science, and philosophy of culture make up a coherent and comprehensive view of the mathematical sciences that is fruitful for understanding contemporary science. In Cassirer’s first systematic work, Substanzbegriff und Funktionsbegriff, the mathematical sciences are understood through the concept of function. This implies that scientific investigation aims at increased unity in a system of functional concepts, rather than at answering the substance-rooted question of what is. In his (...) mature work, Philosophie der symbolischen Formen, Cassirer expands his inquiry to diverse notions of objects and principles of symbolic forming, recognizing the mathematical sciences as one of many ways of structuring experience, alongside other symbolic forms such as myth and ordinary language. Together, Cassirer’s early and mature works detail the preconditions and idiosyncrasies of the unfolding of scientific objects and situate the mathematical sciences within the totality of human experience. Applying these insights to contemporary interpretations of science suggests connecting common misconceptions of science to challenges in translating objects between symbolic forms. I propose the concepts of domestication and mythification of science as instructive for clearing up such misunderstandings. (shrink)

The question of the applicability of mathematics is an epistemological issue that was explicitly raised by Kant, and which has played different roles in the works of neo-Kantian philosophers, before becoming an essential issue in early analytic philosophy. This paper will first distinguish three main issues that are related to the application of mathematics: indispensability arguments that are aimed at justifying mathematics itself; philosophical justifications of the successful application of mathematics to scientific theories; and discussions on the application of real (...) numbers to the measurement of physical magnitudes. A refinement of this tripartition is suggested and supported by a historical investigation of the differences between Kant’s position on the problem, several neo-Kantian perspectives, early analytic philosophy, and late 19th century mathematicians. Finally, the debate on the cogency of an application constraint in the definition of real numbers is discussed in relation to a contemporary debate in neo-logicism, in order to suggest a comparison not only with Frege’s original positions, but also with the ideas of several neo-Kantian scholars, including Hölder, Cassirer, and Helmholtz. (shrink)

Cassirer’s neo-Kantian epistemology has become a classical reference in contemporary history and philosophy of science. However, the historical aspects of his thought are sometimes seen to be in some tension with his defence of a priori elements of knowledge. This paper reconsiders Cassirer’s strategy to address this tension by positing functional dependencies at the core of the notion of objectivity. This requires the epistemologist to account for the determination of the objects of knowledge within given scientific theories, but also for (...) conceptual changes over time. (shrink)

This paper shows that Cassirer’s philosophy of mathematics underwent a significant transformation by the end of the 1920s. This transformation was due to Cassirer’s reception of the ‘foundational crisis’ within mathematics itself. David Hilbert’s conception of the ‘ideal elements’ of mathematics attracted Cassirer’s particular attention. Indeed, he sought a ‘transcendental deduction’ of these elements. Reflection on this issue is therefore essential to providing an adequate interpretation of the later Cassirer’s enterprise in the philosophy of mathematics.