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8 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
8717
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Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
9937
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I do not believe mathematics either has or needs 'foundations' [Putnam]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
9939
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It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9940
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Maybe mathematics is empirical in that we could try to change it [Putnam]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9941
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Science requires more than consistency of mathematics [Putnam]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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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6. Mathematics / C. Sources of Mathematics / 8. Finitism
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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