It is well known that Felix Klein took a decisive step in investigating the invariants of transformation groups. However, less attention has been given to Klein’s considerations on the epistemological implications of his work on geometry. This paper proposes an interpretation of Klein’s view as a form of mathematical structuralism, according to which the study of mathematical structures provides the basis for a better understanding of how mathematical research and practice develop.

The paper surveys the possibility of keeping a neo-Kantian approach in the face of Loop Quantum Gravity. Together with a preliminary analysis of Cassirer’s re-interpretation of Kantian philosophy that allowed him to harmonize the a priori cognitions with the theory of relativity and quantum mechanics, it will focus on the distinction between constitutive and regulativea priori. In this way, the paper will suggest that despite Rovelli’s refutation of Kant’s interpretation of space and time, he seems, at least implicitly, to hold (...) to a couple of neo-Kantian assumptions: the usage of constitutivea priori principlessuch as granularity, indeterminism and partially relation, and the claim for functionalism as a rule in ordering the ‘appearances’. (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 reconstructs the major transformations in the Marburg neo-Kantian account of experience. By focusing on the problem of ‘conceptualism’, it traces connections between four issues that are central to the transcendental projects of the Marburg philosophers: the interpretation of Kant, the critique of experiential givenness, the account of objective cognition in science, and the relation between scientific and pre-scientific experience. My historical narrative identifies two shifts. The first is from Cohen's conceptualist answer to the threat of subjectivism to Cassirer's (...) functionalist answer to empiricism. The second is from Cassirer's conceptualism about scientific experience to his symbolic non-conceptualism about everyday perception. My reconstruction reveals the fate of neo-Kantian conceptualism to be linked to the fate of pre-scientific perception and suggests that the continuing significance of the Marburg philosophers lies in their responses to the coming apart of the manifest and the scientific image. (shrink)

Cassirer’s concept of symbolic forms represents a cultural-philosophical approach in which specific modes of objectification, the symbolic forms themselves, establish an independent truth. This truth does not consist in a purely analytical truth, but in the fact that we live along these symbolic forms in a specific stubbornness. When we use language, we live and experience language in its specific autonomy. The same applies to the other symbolic forms developed by Cassirer. Both before the cultural-philosophical phase of creation and within (...) the philosophy of symbolic forms, Cassirer refers to mathematics several times. An interesting tension arises as to whether Cassirer could have understood mathematics as a symbolic form in its own right. On the one hand, cultural-historical considerations in Cassirer’s work speak in favour of this; on the other hand, Cassirer embeds mathematics as a mere formal science in physics and thus in the philosophical form of science as a whole. The article explores this tension—mathematics as a symbolic form—and shows that only indications within the framework of the historical-hermeneutical treatment would speak in favour of such an interpretation. Furthermore, the article argues that a specific, cultural-historical semiotics can be considered for mathematics in Cassirer’s work. (shrink)

In this paper I focus on Cassirer’s functionalist theory of truth in order to argue that the Positivistic theory of knowledge fails to explain how it is that physics provides us with truth-evaluable and reliably objective descriptions of the world. This argument is based on Cassirer’s idea that what the Positivistic theory of knowledge normally considers as the “factual” of physics is, in fact, unachievable and falsely conceived. I show that Cassirer’s focus on how measurement is made possible, as well (...) as how technological instruments are put to use in physical research, enables him to offer an alternative account of truth, i.e., a functionalist theory of truth, which is philosophically attractive and rationally plausible. (shrink)

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)