Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'Philosophies of Mathematics' and 'The Theory of Logical Types'
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13 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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
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
23457
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Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
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21556
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Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
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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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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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6. Mathematics / C. Sources of Mathematics / 8. Finitism
10134
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Much infinite mathematics can still be justified finitely [George/Velleman]
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10114
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Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21568
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A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
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