Single Idea 10034

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity]

Full Idea

Frege shows that the number of natural numbers is not identical to any natural number. This is because, while no natural number is identical to its successor, the number of natural numbers is.

Gist of Idea

The number of natural numbers is not a natural number

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.41


A Reaction

Frege is notorious for the lack of respect shown in his writings for the great Cantor, and this seems to have blocked him from a more sophisticated account of infinity, but this idea seems a nice one.