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'Difference and Repetition', 'Response to David Armstrong' and 'Science without Numbers'
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11 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8958

In Field's version of science, spacetime points replace real numbers [Field,H, by Szabó]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18221

'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
8757

The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H]

6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
18212

Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
10261

The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro]

9623

Field needs a semantical notion of secondorder consequence, and that needs sets [Brown,JR on Field,H]

18218

Hilbert explains geometry, by nonnumerical facts about space [Field,H]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
18215

It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H]

6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
18210

Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H]

18214

Mathematics is only empirical as regards which theory is useful [Field,H]

18216

Abstractions can form useful counterparts to concrete statements [Field,H]
