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'fragments/reports', 'Logicism, Some Considerations (PhD)' and 'works'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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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
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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 / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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3331
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If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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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 / 6. Logicism / a. Early logicism
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16880
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Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge]
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8689
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Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend]
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