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9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms. | |
From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics | |
A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged. |