52 ideas
| 12027 | There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G] |
| 12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
| 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] |
| 12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
| 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] |
| 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] |
| 12023 | Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G] |
| 12017 | In all instances of identity, there must be some facts to ensure the identity [Forbes,G] |
| 12024 | If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G] |
| 11885 | Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P] |
| 12014 | An individual essence is a set of essential properties which only that object can have [Forbes,G] |
| 12015 | Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G] |
| 12013 | Essential properties depend on a category, and perhaps also on particular facts [Forbes,G] |
| 12012 | Essential properties are those without which an object could not exist [Forbes,G] |
| 12022 | Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G] |
| 12025 | Artefacts have fuzzy essences [Forbes,G] |
| 12020 | An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G] |
| 11888 | Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 12003 | De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G] |
| 12028 | De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G] |
| 12008 | Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G] |
| 12009 | The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G] |
| 12007 | Possible worlds are points of logical space, rather like other times than our own [Forbes,G] |
| 12011 | Transworld identity concerns the limits of possibility for ordinary things [Forbes,G] |
| 12016 | The problem of transworld identity can be solved by individual essences [Forbes,G] |
| 12004 | Counterpart theory is not good at handling the logic of identity [Forbes,G] |
| 12021 | Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G] |
| 12029 | We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G] |
| 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] |
| 9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor] |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |