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Full Idea
Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move.
Gist of Idea
We can't use sets as foundations for mathematics if we must await results from the upper reaches
Source
Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two')
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.356
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] |