47 ideas
5750 | Consistency is modal, saying propositions are consistent if they could be true together [Melia] |
4037 | Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver] |
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
5737 | Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia] |
5744 | First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia] |
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] |
5740 | Second-order logic needs second-order variables and quantification into predicate position [Melia] |
5741 | If every model that makes premises true also makes conclusion true, the argument is valid [Melia] |
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] |
5735 | Maybe names and predicates can capture any fact [Melia] |
5736 | No sort of plain language or levels of logic can express modal facts properly [Melia] |
4027 | Properties are respects in which particular objects may be alike or differ [Mellor/Oliver] |
4029 | Nominalists ask why we should postulate properties at all [Mellor/Oliver] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia] |
5738 | We may be sure that P is necessary, but is it necessarily necessary? [Melia] |
5732 | 'De re' modality is about things themselves, 'de dicto' modality is about propositions [Melia] |
5739 | Sometimes we want to specify in what ways a thing is possible [Melia] |
5734 | Possible worlds make it possible to define necessity and counterfactuals without new primitives [Melia] |
5742 | In possible worlds semantics the modal operators are treated as quantifiers [Melia] |
5743 | If possible worlds semantics is not realist about possible worlds, logic becomes merely formal [Melia] |
5749 | Possible worlds could be real as mathematics, propositions, properties, or like books [Melia] |
5751 | The truth of propositions at possible worlds are implied by the world, just as in books [Melia] |
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] |
4039 | Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver] |
5748 | We accept unverifiable propositions because of simplicity, utility, explanation and plausibility [Melia] |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |