Combining Philosophers

Ideas for Chrysippus, Micklethwait,J/Wooldridge,A and Bertrand Russell

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28 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
14162 Mathematics doesn't care whether its entities exist [Russell]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17628 Arithmetic was probably inferred from relationships between physical objects [Russell]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
5399 Maths is not known by induction, because further instances are not needed to support it [Russell]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
14465 Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
14103 Pure mathematics is the class of propositions of the form 'p implies q' [Russell]
13414 For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf]
6108 Maths can be deduced from logical axioms and the logic of relations [Russell]
6423 We tried to define all of pure maths using logical premisses and concepts [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21555 For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell]
18003 In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor]
10418 Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
10047 Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
23478 Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
23457 Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
21556 Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
21718 Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
21570 Numbers are just verbal conveniences, which can be analysed away [Russell]
6424 Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell]
6425 Formalism can't apply numbers to reality, so it is an evasion [Russell]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
6104 Numbers are classes of classes, and hence fictions of fictions [Russell]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
6426 Intuitionism says propositions are only true or false if there is a method of showing it [Russell]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21559 We need rules for deciding which norms are predicative (unless none of them are) [Russell]
21558 'Predicative' norms are those which define a class [Russell]
18126 A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
18128 Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
18124 Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
21568 A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
14449 There is always something psychological about inference [Russell]