56 ideas
13736 | Quinean metaphysics just lists the beings, which is a domain with no internal structure [Schaffer,J on Quine] |
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
3302 | Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Quine, by Benardete,JA] |
10211 | Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro] |
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] |
3336 | Two things can never entail three things [Quine, by Benardete,JA] |
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] |
8453 | If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine] |
10311 | No sense can be made of quantification into opaque contexts [Quine, by Hale] |
10538 | Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett] |
10793 | Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)] |
10245 | One geometry cannot be more true than another [Poincaré] |
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] |
10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
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] |
8466 | For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein] |
8467 | Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein] |
8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
10667 | A logically perfect language could express all truths, so all truths must be logically expressible [Quine, by Hossack] |
16021 | Quine says we can expand predicates easily (ideology), but not names (ontology) [Quine, by Noonan] |
3325 | For Quine everything exists theoretically, as reference, predication and quantification [Quine, by Benardete,JA] |
8534 | Quine says the predicate of a true statement has no ontological implications [Quine, by Armstrong] |
10295 | Quine suggests that properties can be replaced with extensional entities like sets [Quine, by Shapiro] |
3322 | Quine says that if second-order logic is to quantify over properties, that can be done in first-order predicate logic [Quine, by Benardete,JA] |
6078 | Quine brought classes into semantics to get rid of properties [Quine, by McGinn] |
8479 | Don't analyse 'red is a colour' as involving properties. Say 'all red things are coloured things' [Quine, by Orenstein] |
3751 | Universals are acceptable if they are needed to make an accepted theory true [Quine, by Jacquette] |
7970 | Quine is committed to sets, but is more a Class Nominalist than a Platonist [Quine, by Macdonald,C] |
15783 | Definite descriptions can't unambiguously pick out an object which doesn't exist [Lycan on Quine] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
15782 | Quine wants identity and individuation-conditions for possibilia [Quine, by Lycan] |
2796 | For Quine the only way to know a necessity is empirically [Quine, by Dancy,J] |
8450 | Quine's empiricism is based on whole theoretical systems, not on single mental events [Quine, by Orenstein] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
3868 | To proclaim cultural relativism is to thereby rise above it [Quine, by Newton-Smith] |
4713 | For Quine, theories are instruments used to make predictions about observations [Quine, by O'Grady] |
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] |
4712 | Quine says there is no matter of fact about reference - it is 'inscrutable' [Quine, by O'Grady] |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
7330 | The principle of charity only applies to the logical constants [Quine, by Miller,A] |
17862 | Essence gives an illusion of understanding [Quine, by Almog] |