Frege’s Arguments Against Kant’s Notion of Pure Intuition and the Principles of Logic

Norma B. Goethe

In ”Kant, Bolzano and the Emergency of Logicism” Alberto Coffa argues that Bolzano, Frege, Hilbert and Poincaré regardless of their different approaches to scientific knowledge belonged to a broad ”antikantian” movement which includes the rigorization of the calculus, Frege’s work on arithmetic and Hilbert’s and Poincaré ’s conception of geometry. Its goal being the elimination of pure intuition in arithmetic and geometry, this movement opposed Kant’s conception of pure intuition as a necessary element in grounding pure a priori knowledge by ”creating” semantics as an independent discipline. Kant’s ”deduction” of pure intuition depends on two premises: (1) the assumption that there are synthetic a priori judgments and (2) that there is a principle of synthetic judgments involved in the grounding of synthetic judgments . Kant’s inference for the need to appeal to intuition in synthetic judgments was based on the assumption that from concepts alone no knowledge can be gained. To this Frege, in particular, started asking, how much intuition is there in arithmetic? and proceeded to argue against (2) even though he never rejected (1). In his Begriffsschrift Frege puts to the test the project sketched in Grundlagen its goal being to undermine Kant’s view of mathematical knowledge. In this presentation I shall argue that despite Frege’s ”antikantian” goal in the philosophy of mathematics both Kant and Frege share deep insights concerning the view of the nature of logic and the normative character of its principles . The logical principles must not be taken from psychology because like the laws of the state they prescribe how to think correctly and whithout which there is not thought at all. It is true that when concepts are finally wedded to the word a priori necessary knowledge can be explained free from its psychologistic fetters. But seeing what Kant and Frege share will shed some light on ideas we find later on in Wittgenstein.

Address: Facultad de Filosofia y Humanidades, Universidad Nacional de Cordoba, Argentina

E-mail: ngoethe@ffyh.unc.edu.ar