Неевклидова геометрия в „Критика на чистия разум“?
Non-Euclidean Geometry in The Critique of Pure Reason?

Symbolic Construction beyond the Dictate of Pure Intuition

Summary/Abstract: The paper discusses a traditionally construed as problematic aspect of Kant's philosophy of mathematics: the place and importance of non-Euclidean geometry in the structure of mathematics. Kant's conception of pure intuition in mathematics is usually considered incompatible with the existence of mathematics, leaving no place for the latter. In this paper I argue that we can find a place for them, provided we know where to look. Of key importance in this respect is the concept of symbolic construction, which Kant employs in his discussion of algebra. The concept makes it possible to sidestep the limitations related to the requirement of constructibility in pure intuition. The development of Hilbert's formalism in the philosophy of mathematics can be seen as a continuation of this move that makes manifest its full potential, which was not, and even could not, be realized by Kant.

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