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Single Idea 8630

[from 'Grundlagen der Arithmetik (Foundations)' by Gottlob Frege, in 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers ]

Full Idea

The individual numbers are best derived from the number one together with increase by one.

Gist of Idea

Individual numbers are best derived from the number one, and increase by one

Source

Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §18)

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.25


A Reaction

Frege rejects the empirical approach partly because of the intractability of zero, but this approach has the same problem. I suggest a combination of empiricism for simple numbers, and pure formalism for extensions into complexity, and zero.