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Single Idea 17855

[from 'Begriffsschrift' by Gottlob Frege, in 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction ]

Full Idea

Frege's account of the ancestral has made it possible, in effect, to define the natural numbers as entities for which induction holds.

Gist of Idea

It may be possible to define induction in terms of the ancestral relation

Source

report of Gottlob Frege (Begriffsschrift [1879]) by Crispin Wright - Frege's Concept of Numbers as Objects 4.xix

Book Reference

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.161


A Reaction

This is the opposite of the approach in the Peano Axioms, where induction is used to define the natural numbers.