83 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] |
| 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] |
| 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] |
| 12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
| 10057 | Logic can only assert hypothetical existence [Russell] |
| 10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
| 14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
| 14457 | Names are really descriptions, except for a few words like 'this' and 'that' [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] |
| 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] |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| 6504 | For physicalists, the only relations are spatial, temporal and causal [Robinson,H] |
| 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] |
| 6520 | If reality just has relational properties, what are its substantial ontological features? [Robinson,H] |
| 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] |
| 6485 | When a red object is viewed, the air in between does not become red [Robinson,H] |
| 6521 | Representative realists believe that laws of phenomena will apply to the physical world [Robinson,H] |
| 6509 | Representative realists believe some properties of sense-data are shared by the objects themselves [Robinson,H] |
| 6522 | Phenomenalism can be theistic (Berkeley), or sceptical (Hume), or analytic (20th century) [Robinson,H] |
| 6502 | Can we reduce perception to acquisition of information, which is reduced to causation or disposition? [Robinson,H] |
| 6513 | Would someone who recovered their sight recognise felt shapes just by looking? [Robinson,H] |
| 6512 | Secondary qualities have one sensory mode, but primary qualities can have more [Robinson,H] |
| 6497 | We say objects possess no intrinsic secondary qualities because physicists don't need them [Robinson,H] |
| 6494 | If objects are not coloured, and neither are sense-contents, we are left saying that nothing is coloured [Robinson,H] |
| 6499 | Shape can be experienced in different ways, but colour and sound only one way [Robinson,H] |
| 6500 | If secondary qualities match senses, would new senses create new qualities? [Robinson,H] |
| 6484 | Most moderate empiricists adopt Locke's representative theory of perception [Robinson,H] |
| 6508 | Sense-data leads to either representative realism or phenomenalism or idealism [Robinson,H] |
| 6480 | Sense-data do not have any intrinsic intentionality [Robinson,H] |
| 6482 | For idealists and phenomenalists sense-data are in objects; representative realists say they resemble objects [Robinson,H] |
| 6505 | Sense-data are rejected because they are a veil between us and reality, leading to scepticism [Robinson,H] |
| 6506 | 'Sense redly' sounds peculiar, but 'senses redly-squarely tablely' sounds far worse [Robinson,H] |
| 6507 | Adverbialism sees the contents of sense-experience as modes, not objects [Robinson,H] |
| 6511 | If there are only 'modes' of sensing, then an object can no more be red or square than it can be proud or lazy. [Robinson,H] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 6515 | An explanation presupposes something that is improbable unless it is explained [Robinson,H] |
| 6517 | If all possibilities are equal, order seems (a priori) to need an explanation - or does it? [Robinson,H] |
| 6481 | If intentional states are intrinsically about other things, what are their own properties? [Robinson,H] |
| 6503 | Physicalism cannot allow internal intentional objects, as brain states can't be 'about' anything [Robinson,H] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| 6519 | Locke's solidity is not matter, because that is impenetrability and hardness combined [Robinson,H] |