Combining Texts
Ideas for
'The Sign of Four', 'Science without Numbers' and 'Of Organum or Ars Magna of Thinking'
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11 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8958
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In Field's version of science, space-time points replace real numbers [Field,H, by Szabó]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18221
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'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
8757
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The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H]
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6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
18212
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Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
10261
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The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro]
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18218
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Hilbert explains geometry, by non-numerical facts about space [Field,H]
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9623
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Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
18215
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It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H]
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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
18210
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Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H]
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18214
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Mathematics is only empirical as regards which theory is useful [Field,H]
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18216
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Abstractions can form useful counterparts to concrete statements [Field,H]
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