Combining Philosophers
Ideas for Anon (Dham), Hilary Putnam and Xenophon
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10 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
18959
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Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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Very large sets should be studied in an 'if-then' spirit [Putnam]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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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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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 / 1. Mathematical Platonism / b. Against mathematical platonism
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How can you contemplate Platonic entities without causal transactions with them? [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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9914
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It is unfashionable, but most mathematical intuitions come from nature [Putnam]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
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Science requires more than consistency of mathematics [Putnam]
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18199
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Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
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8857
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We must quantify over numbers for science; but that commits us to their existence [Putnam]
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