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Single Idea 9545

[from 'Sources of Knowledge of Mathematics' by Gottlob Frege, in 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique ]

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'.

Gist of Idea

Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical

Source

report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3

Book Reference

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.3


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.