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'Precis of 'Limits of Abstraction'', 'On the Foundations of Logic and Arithmetic' and 'The Foundations of Empirical Knowledge'
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4 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 / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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Logic already contains some arithmetic, so the two must be developed together [Hilbert]
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