46 ideas
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
23128 | The opposite of liberalism is dogmatism [Gopnik] |
23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
23136 | Liberal free speech is actually paid speech [Gopnik] |
23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |