Combining Philosophers

Ideas for Rescher,N/Oppenheim,P, Plotinus and Hartry Field

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13 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9226 If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8958 In Field's version of science, space-time 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]
18218 Hilbert explains geometry, by non-numerical facts about space [Field,H]
9623 Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on 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
18214 Mathematics is only empirical as regards which theory is useful [Field,H]
18216 Abstractions can form useful counterparts to concrete statements [Field,H]
8714 Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H]
18210 Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H]