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'Mathematics without Numbers', 'Precis of 'Limits of Abstraction'' and 'Reference and Necessity'
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5 ideas
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
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Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
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Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
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