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