115 ideas
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
| 3807 | Reason is and ought to be the slave of the passions [Hume] |
| 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] |
| 10057 | Logic can only assert hypothetical existence [Russell] |
| 12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
| 14464 | Logic can be known a priori, without study of the actual world [Russell] |
| 14458 | Asking 'Did Homer exist?' is employing an abbreviated description [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] |
| 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] |
| 8649 | Two numbers are equal if all of their units correspond to one another [Hume] |
| 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] |
| 21291 | There is no medium state between existence and non-existence [Hume] |
| 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] |
| 11942 | Power is the possibility of action, as discovered by experience [Hume] |
| 11949 | There may well be powers in things, with which we are quite unacquainted [Hume] |
| 11950 | We have no idea of powers, because we have no impressions of them [Hume] |
| 11941 | The distinction between a power and its exercise is entirely frivolous [Hume] |
| 11098 | Momentary impressions are wrongly identified with one another on the basis of resemblance [Hume, by Quine] |
| 7954 | If we see a resemblance among objects, we apply the same name to them, despite their differences [Hume] |
| 21293 | Individuation is only seeing that a thing is stable and continuous over time [Hume] |
| 12048 | The only meaning we have for substance is a collection of qualities [Hume] |
| 13424 | Aristotelians propose accidents supported by substance, but they don't understand either of them [Hume] |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| 21300 | A change more obviously destroys an identity if it is quick and observed [Hume] |
| 21299 | Changing a part can change the whole, not absolutely, but by its proportion of the whole [Hume] |
| 1330 | If a republic can retain identity through many changes, so can an individual [Hume] |
| 1321 | If identity survives change or interruption, then resemblance, contiguity or causation must unite the parts of it [Hume] |
| 21302 | If a ruined church is rebuilt, its relation to its parish makes it the same church [Hume] |
| 21303 | We accept the identity of a river through change, because it is the river's nature [Hume] |
| 21301 | The purpose of the ship makes it the same one through all variations [Hume] |
| 21290 | Multiple objects cannot convey identity, because we see them as different [Hume] |
| 1207 | Both number and unity are incompatible with the relation of identity [Hume] |
| 21289 | 'An object is the same with itself' is meaningless; it expresses unity, not identity [Hume] |
| 21292 | Saying an object is the same with itself is only meaningful over a period of time [Hume] |
| 9428 | Nothing we clearly imagine is absolutely impossible [Hume] |
| 4766 | Necessity only exists in the mind, and not in objects [Hume] |
| 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] |
| 6526 | Hume says objects are not a construction, but an imaginative leap [Hume, by Robinson,H] |
| 6489 | Associationism results from having to explain intentionality just with sense-data [Robinson,H on Hume] |
| 6182 | Even Hume didn't include mathematics in his empiricism [Hume, by Kant] |
| 12417 | Mathematicians only accept their own proofs when everyone confims them [Hume] |
| 5548 | Hume became a total sceptic, because he believed that reason was a deception [Hume, by Kant] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 7446 | The idea of inductive evidence, around 1660, made Hume's problem possible [Hume, by Hacking] |
| 21806 | Memory, senses and understanding are all founded on the imagination [Hume] |
| 3819 | Hume's 'bundle' won't distinguish one mind with ten experiences from ten minds [Searle on Hume] |
| 1317 | A person is just a fast-moving bundle of perceptions [Hume] |
| 1331 | The parts of a person are always linked together by causation [Hume] |
| 1388 | Hume gives us an interesting sketchy causal theory of personal identity [Perry on Hume] |
| 21297 | A person is simply a bundle of continually fluctuating perceptions [Hume] |
| 1316 | Introspection always discovers perceptions, and never a Self without perceptions [Hume] |
| 1333 | Memory only reveals personal identity, by showing cause and effect [Hume] |
| 1332 | We use memory to infer personal actions we have since forgotten [Hume] |
| 21305 | Memory not only reveals identity, but creates it, by producing resemblances [Hume] |
| 21307 | Who thinks that because you have forgotten an incident you are no longer that person? [Hume] |
| 21306 | Causation unites our perceptions, by producing, destroying and modifying each other [Hume] |
| 21294 | A continuous lifelong self must be justified by a single sustained impression, which we don't have [Hume] |
| 21295 | When I introspect I can only observe my perceptions, and never a self which has them [Hume] |
| 21298 | We pretend our perceptions are continuous, and imagine a self to fill the gaps [Hume] |
| 21304 | Identity in the mind is a fiction, like that fiction that plants and animals stay the same [Hume] |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 20030 | If one event causes another, the two events must be wholly distinct [Hume, by Wilson/Schpall] |
| 6692 | For Hume, practical reason has little force, because we can always modify our desires [Hume, by Graham] |
| 8257 | Reason alone can never be a motive to any action of the will [Hume] |
| 22374 | You can only hold people responsible for actions which arise out of their character [Hume] |
| 22382 | We cannot discover vice by studying a wilful murder; that only arises from our own feelings [Hume] |
| 4008 | Modern science has destroyed the Platonic synthesis of scientific explanation and morality [Hume, by Taylor,C] |
| 8067 | The problem of getting to 'ought' from 'is' would also apply in getting to 'owes' or 'needs' [Anscombe on Hume] |
| 4578 | You can't move from 'is' to 'ought' without giving some explanation or reason for the deduction [Hume] |
| 3650 | Total selfishness is not irrational [Hume] |
| 14301 | We have no good concept of solidity or matter, because accounts of them are all circular [Hume] |
| 8382 | For Hume a constant conjunction is both necessary and sufficient for causation [Hume, by Crane] |
| 19274 | Hume seems to presuppose necessary connections between mental events [Kripke on Hume] |
| 21296 | If all of my perceptions were removed by death, nothing more is needed for total annihilation [Hume] |