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Single Idea 17815

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory ]

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

The 5 ideas from Palle Yourgrau

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]