Combining Texts
Ideas for
'Abstract Objects: a Case Study', 'The Philosophy of Logic' and 'Axiomatic Thought'
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8 ideas
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 / 2. Proof in Mathematics
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To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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Number theory just needs calculation laws and rules for integers [Hilbert]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
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Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
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We must quantify over numbers for science; but that commits us to their existence [Putnam]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
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Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
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