Single Idea 17814

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

Frege defines the natural number n in terms of the set of n-membered sets.

Gist of Idea

The natural number n is the set of n-membered sets

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Palle Yourgrau - Sets, Aggregates and Numbers 'Two'

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.355


A Reaction

He says this view 'has been treated rudely by history', because Frege's view of sets was naive, and because independence results have undermined set-theoretic platonism.