Number as Scheme of Order : Cassirer's Philosophy of Mathematics in the Context of His Philosophy of Culture

Recently, Ernst Cassirer's philosophy of culture as well as his philosophyof mathematics were rediscovered, but until now, there is little interactionbetween the two research strands. In my paper, I show that itis necessary to consider both, i.e., that there is a correlative relation betweenCassirer's philosophy of culture and his philosophy of mathematics.To illustrate this interdependence, I show in a first step that number hasa double function in Cassirer's philosophy of culture. On the one hand,number – understood as the scheme of order par excellence – is of determiningmeaning for mathematics as a pure theory of relations. This centralimportance is not limited to mathematics: number as a scheme of order isalso the determining principle of the whole symbolic form of science.

On the other hand, in the philosophy of symbolic forms, number is presented,along with space and time, as a form of intuition that takes different shapesin different symbolic forms. In a second step, I argue that Cassirer's characterizationof mathematics as a universal symbolic language can be takenseriously: for Cassirer, mathematics is not only a form of theoretical cognitionbut also can be understood as one possible form of meta-symboliccognition, which Cassirer uses to express functional similarities betweensymbolic forms. Therefore, his overall philosophical approach is bettercharacterized as meta-symbolical than meta-physical. [Publisher's text]

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