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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 Ref
'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.
| 17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
| 17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
| 17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
| 17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
| 17822 | Nothing is 'intrinsically' numbered [Yourgrau] |