56 ideas
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
17879 | Axiomatising set theory makes it all relative [Skolem] |
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] |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
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] |
8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
6504 | For physicalists, the only relations are spatial, temporal and causal [Robinson,H] |
6520 | If reality just has relational properties, what are its substantial ontological features? [Robinson,H] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
6485 | When a red object is viewed, the air in between does not become red [Robinson,H] |
6521 | Representative realists believe that laws of phenomena will apply to the physical world [Robinson,H] |
6509 | Representative realists believe some properties of sense-data are shared by the objects themselves [Robinson,H] |
6522 | Phenomenalism can be theistic (Berkeley), or sceptical (Hume), or analytic (20th century) [Robinson,H] |
6502 | Can we reduce perception to acquisition of information, which is reduced to causation or disposition? [Robinson,H] |
6513 | Would someone who recovered their sight recognise felt shapes just by looking? [Robinson,H] |
6512 | Secondary qualities have one sensory mode, but primary qualities can have more [Robinson,H] |
6497 | We say objects possess no intrinsic secondary qualities because physicists don't need them [Robinson,H] |
6494 | If objects are not coloured, and neither are sense-contents, we are left saying that nothing is coloured [Robinson,H] |
6499 | Shape can be experienced in different ways, but colour and sound only one way [Robinson,H] |
6500 | If secondary qualities match senses, would new senses create new qualities? [Robinson,H] |
6484 | Most moderate empiricists adopt Locke's representative theory of perception [Robinson,H] |
6508 | Sense-data leads to either representative realism or phenomenalism or idealism [Robinson,H] |
6480 | Sense-data do not have any intrinsic intentionality [Robinson,H] |
6482 | For idealists and phenomenalists sense-data are in objects; representative realists say they resemble objects [Robinson,H] |
6505 | Sense-data are rejected because they are a veil between us and reality, leading to scepticism [Robinson,H] |
6506 | 'Sense redly' sounds peculiar, but 'senses redly-squarely tablely' sounds far worse [Robinson,H] |
6507 | Adverbialism sees the contents of sense-experience as modes, not objects [Robinson,H] |
6511 | If there are only 'modes' of sensing, then an object can no more be red or square than it can be proud or lazy. [Robinson,H] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
6515 | An explanation presupposes something that is improbable unless it is explained [Robinson,H] |
6517 | If all possibilities are equal, order seems (a priori) to need an explanation - or does it? [Robinson,H] |
6481 | If intentional states are intrinsically about other things, what are their own properties? [Robinson,H] |
6503 | Physicalism cannot allow internal intentional objects, as brain states can't be 'about' anything [Robinson,H] |
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] |
6519 | Locke's solidity is not matter, because that is impenetrability and hardness combined [Robinson,H] |