Combining Philosophers
Ideas for Anaxarchus, Henri Poincar and JP Burgess / G Rosen
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8 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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10245
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One geometry cannot be more true than another [Poincaré]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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9923
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We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
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15923
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Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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10180
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Mathematicians do not study objects, but relations between objects [Poincaré]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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9925
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Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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9934
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Number words became nouns around the time of Plato [Burgess/Rosen]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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9916
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Convention, yes! Arbitrary, no! [Poincaré, by Putnam]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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18203
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Avoid non-predicative classifications and definitions [Poincaré]
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