76 ideas
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] |
18986 | Truth is just a name for verification-processes [James] |
18983 | In many cases there is no obvious way in which ideas can agree with their object [James] |
18972 | Ideas are true in so far as they co-ordinate our experiences [James] |
18973 | New opinions count as 'true' if they are assimilated to an individual's current beliefs [James] |
18984 | True ideas are those we can assimilate, validate, corroborate and verify (and false otherwise) [James] |
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] |
14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [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] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
14464 | Logic can be known a priori, without study of the actual world [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] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [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] |
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] |
14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
14422 | Any founded, non-repeating series all reachable in steps will satisfy 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] |
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] |
18987 | A 'thing' is simply carved out of reality for human purposes [James] |
18981 | 'Substance' is just a word for groupings and structures in experience [James] |
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] |
18974 | Truth is a species of good, being whatever proves itself good in the way of belief [James] |
18989 | Pragmatism accepts any hypothesis which has useful consequences [James] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
18971 | Theories are practical tools for progress, not answers to enigmas [James] |
18985 | True thoughts are just valuable instruments of action [James] |
18982 | Pragmatism says all theories are instrumental - that is, mental modes of adaptation to reality [James] |
18975 | We return to experience with concepts, where they show us differences [James] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
22455 | Many ethical theories neglect the power of regretting the ought not acted upon [Williams,B] |
22453 | Moral conflicts have a different feeling and structure from belief conflicts [Williams,B, by Foot] |
18980 | If there is a 'greatest knower', it doesn't follow that they know absolutely everything [James] |
18978 | It is hard to grasp a cosmic mind which produces such a mixture of goods and evils [James] |
18991 | If the God hypothesis works well, then it is true [James] |
18977 | The wonderful design of a woodpecker looks diabolical to its victims [James] |
18979 | Things with parts always have some structure, so they always appear to be designed [James] |
18976 | Private experience is the main evidence for God [James] |
18990 | Nirvana means safety from sense experience, and hindus and buddhists are just afraid of life [James] |