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'On What Grounds What', 'Review of Husserl's 'Phil of Arithmetic'' and 'History of Ancient Art'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
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17446
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Counting rests on one-one correspondence, of numerals to objects [Frege]
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9582
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Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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9586
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In a number-statement, something is predicated of a concept [Frege]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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9580
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Our concepts recognise existing relations, they don't change them [Frege]
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9589
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Numbers are not real like the sea, but (crucially) they are still objective [Frege]
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13741
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If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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9577
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The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege]
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