88 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] |
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] |
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] |
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] |
4266 | Having beliefs involves recognition, expectation and surprise [Scruton] |
4265 | If an animal has beliefs, that implies not only that it can make mistakes, but that it can learn from them [Scruton] |
4264 | Perception (which involves an assessment) is a higher state than sensation [Scruton] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
4271 | There is consciousness whenever behaviour must be explained in terms of mental activity [Scruton] |
4272 | Our concept of a person is derived from Roman law [Scruton] |
4267 | Conditioning may change behaviour without changing the mind [Scruton] |
4269 | An emotion is a motive which is also a feeling [Scruton] |
4270 | Do we use reason to distinguish people from animals, or use that difference to define reason? [Scruton] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
4284 | All moral life depends ultimately on piety, which is our recognition of our own dependence [Scruton] |
4273 | Kant's Moral Law is the rules rational beings would accept when trying to live by agreement [Scruton] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
4274 | The modern virtues are courage, prudence, wisdom, temperance, justice, charity and loyalty [Scruton] |
4286 | Only just people will drop their own self-interests when faced with an impartial verdict [Scruton] |
4283 | Sympathy can undermine the moral order just as much as crime does [Scruton] |
4290 | That which can only be done by a callous person, ought not to be done [Scruton] |
4285 | As soon as we drop self-interest and judge impartially, we find ourselves agreeing about conflicts [Scruton] |
4287 | Utilitarianism merely guides us (by means of sympathy) when the moral law is silent [Scruton] |
4282 | Morality is not a sort of calculation, it is what sets the limits to when calculation is appropriate [Scruton] |
4281 | Utilitarianism says we can't blame Stalin yet, but such a theory is a sick joke [Scruton] |
4280 | Utilitarianism is wrong precisely because it can't distinguish animals from people [Scruton] |
4296 | Brutal animal sports are banned because they harm the personality of the watcher [Scruton] |
4288 | Many breeds of animals have needs which our own ancestors planted in them [Scruton] |
4293 | Introducing a natural means of controlling animal population may not be very compassionate [Scruton] |
4295 | We favour our own animals over foreign ones because we see them as fellow citizens [Scruton] |
4268 | Animals command our sympathy and moral concern initially because of their intentionality [Scruton] |
4291 | Letting your dog kill wild rats, and keeping rats for your dog to kill, are very different [Scruton] |
4263 | Many of the stranger forms of life (e.g. worms) interest us only as a species, not as individuals [Scruton] |
4276 | An animal has individuality if it is nameable, and advanced animals can respond to their name [Scruton] |
4277 | I may avoid stepping on a spider or flower, but fellow-feeling makes me protect a rabbit [Scruton] |
4278 | Lucky animals are eaten by large predators, the less lucky starve, and worst is death by small predators [Scruton] |
4279 | We can easily remove the risk of suffering from an animal's life, but we shouldn't do it [Scruton] |
4289 | Sheep and cattle live comfortable lives, and die an enviably easy death [Scruton] |
4292 | Concern for one animal may harm the species, if the individual is part of a bigger problem [Scruton] |
4294 | Animals are outside the community of rights, but we still have duties towards them [Scruton] |