Mathematical sciences as symbolic form: the objects and objectivity of science in Ernst Cassirer’s philosophy of science and culture

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.