more from Penelope Maddy

Single Idea 18175

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity]

Full Idea

By the mid 1890s Cantor was aware that there could be no set of all sets, as its cardinal number would have to be the largest cardinal number, while his own theorem shows that for any cardinal there is a larger.

Gist of Idea

For any cardinal there is always a larger one (so there is no set of all sets)


Penelope Maddy (Naturalism in Mathematics [1997], I.1)

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.17

A Reaction

There is always a larger cardinal because of the power set axiom. Some people regard that with suspicion.