The objectivity of mathematics in Cassirer’s symbol-theoretical approach

Continental Philosophy Review 57 (3):517-536 (2024)
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Abstract

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.

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Ernst Cassirer's transcendental account of mathematical reasoning.Francesca Biagioli - 2020 - Studies in History and Philosophy of Science Part A 79 (C):30-40.
Idealization in Cassirer's philosophy of mathematics.Thomas Mormann - 2008 - Philosophia Mathematica 16 (2):151 - 181.

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