108 ideas
11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
14452 | All the propositions of logic are completely general [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
14464 | Logic can be known a priori, without study of the actual world [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
7758 | 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan] |
5772 | The idea of a variable is fundamental [Russell] |
18941 | Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
4945 | Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke] |
18942 | Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer] |
7745 | Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell] |
10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
10449 | Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach] |
15159 | The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames] |
2612 | Russell rewrote singular term names as predicates [Russell, by Ayer] |
7757 | "Nobody" is not a singular term, but a quantifier [Russell, by Lycan] |
18943 | Russell implies that all sentences containing empty names are false [Sawyer on Russell] |
7311 | The only genuine proper names are 'this' and 'that' [Russell] |
14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
6411 | Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell] |
10433 | Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury] |
1608 | The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine] |
7754 | Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan] |
21529 | Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey] |
6333 | The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich] |
6412 | Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell] |
7743 | Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh] |
7310 | Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A] |
12006 | Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G] |
4569 | Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE] |
11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
21549 | The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell] |
12796 | Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell] |
7532 | Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk] |
11988 | Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell] |
6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
14439 | A complex number is simply an ordered couple of real numbers [Russell] |
14421 | Discovering that 1 is a number was difficult [Russell] |
14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
14425 | A number is something which characterises collections of the same size [Russell] |
14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
14449 | There is always something psychological about inference [Russell] |
14463 | Existence can only be asserted of something described, not of something named [Russell] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
18775 | Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B] |
7533 | The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk] |
14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
6063 | Russell can't attribute existence to properties [McGinn on Russell] |
18777 | If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
14450 | All forms of implication are expressible as truth-functions [Russell] |
14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
22167 | Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas] |
22117 | Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
4567 | Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE] |
5810 | Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell] |
16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
5774 | Denoting phrases are meaningless, but guarantee meaning for propositions [Russell] |
5775 | In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell] |
16987 | By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke] |
4570 | Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell] |
16349 | Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati] |
7313 | 'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A] |
7767 | The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
21726 | In graspable propositions the constituents are real entities of acquaintance [Russell] |
22118 | Augustine created the modern concept of the will [Augustine, by Matthews] |
4348 | Love, and do what you will [Augustine] |
7821 | Pagans produced three hundred definitions of the highest good [Augustine, by Grayling] |
22119 | Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews] |
5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |
22116 | Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews] |
19338 | Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins] |