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'fragments/reports', 'Logicism, Some Considerations (PhD)' and 'The Philosophy of Logic'
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7 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 / i. Cardinal infinity
18200
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Very large sets should be studied in an 'if-then' spirit [Putnam]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
13415
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An adequate account of a number must relate it to its series [Benacerraf]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
18199
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Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
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8857
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We must quantify over numbers for science; but that commits us to their existence [Putnam]
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