more from Penelope Maddy

Single Idea 18177

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

Full Idea

In the ZFC cumulative hierarchy, Frege's candidates for numbers do not exist. For example, new three-element sets are formed at every stage, so there is no stage at which the set of all three-element sets could he formed.

Gist of Idea

In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets


Penelope Maddy (Naturalism in Mathematics [1997], I.2)

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.23

A Reaction

Ah. This is a very important fact indeed if you are trying to understand contemporary discussions in philosophy of mathematics.