What Frege Meant When He Said: Kant is Right about Geometry

Philosophia Mathematica 14 (1):44-75 (2006)
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Abstract
This paper argues that Frege's notoriously long commitment to Kant's thesis that Euclidean geometry is synthetic _a priori_ is best explained by realizing that Frege uses ‘intuition’ in two senses. Frege sometimes adopts the usage presented in Hermann Helmholtz's sign theory of perception. However, when using ‘intuition’ to denote the source of geometric knowledge, he is appealing to Hermann Cohen's use of Kantian terminology. We will see that Cohen reinterpreted Kantian notions, stripping them of any psychological connotation. Cohen's defense of his modified Kantian thesis on the unique status of the Euclidean axioms presents Frege's own views in a much more favorable light.
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