Combining Philosophers
Ideas for Stilpo, James Robert Brown and Geoffrey Hellman
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11 ideas
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
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9646
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There is no limit to how many ways something can be proved in mathematics [Brown,JR]
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9647
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Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
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9643
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Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
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9644
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When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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8921
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Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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8698
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Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
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9557
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Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
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10263
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Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
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8922
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Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
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9625
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To see a structure in something, we must already have the idea of the structure [Brown,JR]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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9628
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Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
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