Ideas from 'Sets, Aggregates and Numbers' by Palle Yourgrau [1985], by Theme Structure

[found in 'Philosophy of Mathematics: anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,0-631-21870-x]].

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6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Nothing is 'intrinsically' numbered
How many? must first partition an aggregate into sets, and then logic fixes its number
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions
6. Mathematics / B. Foundations for Mathematics / 5. Mathematics as Set Theory / b. Mathematics is not set theory
You can ask all sorts of numerical questions about any one given set
We can't use sets as foundations for mathematics if we must await results from the upper reaches