more from Palle Yourgrau

### Single Idea 17817

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

Full Idea

The Frege-Maddy definition of number (as the 'property' of being-three) explains why the definitions of Von Neumann, Zermelo and others work, by giving the 'principle of collection' that ties together all threes.

Gist of Idea

Defining 'three' as the principle of collection or property of threes explains set theory definitions

Source

Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'A Fregean')

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.356

A Reaction

[compressed two or three sentences] I am strongly in favour of the best definition being the one which explains the target, rather than just pinning it down. I take this to be Aristotle's view.