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'Lectures 1930-32 (student notes)', 'Sapiens: brief history of humankind' and 'Mathematics without Foundations'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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18738
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We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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18708
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Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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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
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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
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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
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9941
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Science requires more than consistency of mathematics [Putnam]
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