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Ideas for 'fragments/reports', 'Sources of Knowledge of Mathematics' and 'The Emotions'

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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

9545	Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
	Full Idea: Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'.
	From: report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3
	A reaction: We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject.