Combining Philosophers
Ideas for Lynch,MP/Glasgow,JM, David Hilbert and Jonathan Schaffer
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10 ideas
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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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
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14604
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If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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17697
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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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17698
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Logic already contains some arithmetic, so the two must be developed together [Hilbert]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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10113
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The grounding of mathematics is 'in the beginning was the sign' [Hilbert]
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10115
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Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]
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22293
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Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
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12459
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The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
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6. Mathematics / C. Sources of Mathematics / 8. Finitism
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10116
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Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]
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18112
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Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
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