Combining Philosophers
Ideas for Baron,S/Miller,K, A.George / D.J.Velleman and Judith (Jarvis) Thomson
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10 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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10089
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Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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10131
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If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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10092
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In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman]
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10094
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The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman]
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10095
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Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman]
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17901
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Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman]
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6. Mathematics / C. Sources of Mathematics / 8. Finitism
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10114
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Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman]
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10134
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Much infinite mathematics can still be justified finitely [George/Velleman]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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10123
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The intuitionists are the idealists of mathematics [George/Velleman]
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10124
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Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman]
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