49 ideas
9355 | One sort of circularity presupposes a premise, the other presupposes a rule being used [Braithwaite, by Devitt] |
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] |
13258 | The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki] |
13288 | Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki] |
14506 | 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki] |
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] |
14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
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] |
13289 | Structures have positions, constituent types and number, and some invariable parts [Koslicki] |
14501 | 'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki] |
14495 | I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki] |
13264 | If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki] |
14497 | The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki] |
13280 | Statue and clay differ in modal and temporal properties, and in constitution [Koslicki] |
14496 | Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki] |
13279 | There are at least six versions of constitution being identity [Koslicki] |
14498 | For three-dimensionalist parthood must be a three-place relation, including times [Koslicki] |
13283 | The parts may be the same type as the whole, like a building made of buildings [Koslicki] |
13266 | Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki] |
14500 | Wholes are entities distinct from their parts, and have different properties [Koslicki] |
13281 | Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki] |
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] |
14504 | The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki] |
13285 | Natural kinds support inductive inferences, from previous samples to the next one [Koslicki] |
13287 | Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki] |
13284 | Should vernacular classifications ever be counted as natural kind terms? [Koslicki] |
13286 | There are apparently no scientific laws concerning biological species [Koslicki] |