Single Idea 3331

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

Full Idea

There is a suspicion that Frege's definition of 5 (as the set of all sets with 5 members) may be infected with circularity, …and how can we be sure on a priori grounds that 4 and 5 are not both empty sets, and hence identical?

Gist of Idea

If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content

Source

comment on Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.14

Book Reference

Benardete,José A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.104