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'(Nonsolipsistic) Conceptual Role Semantics', 'The Theory of Transfinite Numbers' and 'Logicism, Some Considerations (PhD)'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
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Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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An adequate account of a number must relate it to its series [Benacerraf]
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