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'On What Grounds What', 'Structuralism' and 'Concepts and Counting'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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17462
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A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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17461
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Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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8921
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Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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8922
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Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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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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