74 ideas
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| 1553 | No perceptible object is truly straight or curved [Protagoras] |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 1549 | Everything that exists consists in being perceived [Protagoras] |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| 1545 | Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius] |
| 1547 | Man is the measure of all things - of things that are, and of things that are not [Protagoras] |
| 3305 | There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras] |
| 3313 | If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras] |
| 3317 | You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras] |
| 247 | God is "the measure of all things", more than any man [Plato on Protagoras] |
| 606 | Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras] |
| 612 | Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras] |
| 4363 | The word 'person' is useless in ethics, because what counts as a good or bad self-conscious being? [Hursthouse] |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| 4355 | There may be inverse akrasia, where the agent's action is better than their judgement recommends [Hursthouse] |
| 4325 | Must all actions be caused in part by a desire, or can a belief on its own be sufficient? [Hursthouse] |
| 4351 | It is a fantasy that only through the study of philosophy can one become virtuous [Hursthouse] |
| 4329 | After a moral dilemma is resolved there is still a 'remainder', requiring (say) regret [Hursthouse] |
| 4330 | Deontologists resolve moral dilemmas by saying the rule conflict is merely apparent [Hursthouse] |
| 4341 | Involuntary actions performed in tragic dilemmas are bad because they mar a good life [Hursthouse] |
| 4340 | You are not a dishonest person if a tragic dilemma forces you to do something dishonest [Hursthouse] |
| 6016 | Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD] |
| 4358 | Virtue may be neither sufficient nor necessary for eudaimonia [Hursthouse] |
| 4337 | Teenagers are often quite wise about ideals, but rather stupid about consequences [Hursthouse] |
| 4324 | Animals and plants can 'flourish', but only rational beings can have eudaimonia [Hursthouse] |
| 1580 | For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik] |
| 4359 | When it comes to bringing up children, most of us think that the virtues are the best bet [Hursthouse] |
| 20195 | Eudaimonia first; virtue is a trait which promotes it; right acts are what virtues produce [Hursthouse, by Zagzebski] |
| 4336 | Any strict ranking of virtues or rules gets abandoned when faced with particular cases [Hursthouse] |
| 4334 | Virtue ethics is open to the objection that it fails to show priority among the virtues [Hursthouse] |
| 4361 | Good animals can survive, breed, feel characteristic pleasure and pain, and contribute to the group [Hursthouse] |
| 4349 | Virtuous people may not be fully clear about their reasons for action [Hursthouse] |
| 4352 | Performing an act simply because it is virtuous is sufficient to be 'morally motivated' or 'dutiful' [Hursthouse] |
| 4353 | If moral motivation is an all-or-nothing sense of duty, how can children act morally? [Hursthouse] |
| 205 | Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras] |
| 4346 | The emotions of sympathy, compassion and love are no guarantee of right action or acting well [Hursthouse] |
| 4339 | According to virtue ethics, two agents may respond differently, and yet both be right [Hursthouse] |
| 4354 | Maybe in a deeply poisoned character none of their milder character traits could ever be a virtue [Hursthouse] |
| 4356 | We are puzzled by a person who can show an exceptional virtue and also behave very badly [Hursthouse] |
| 4364 | Being unusually virtuous in some areas may entail being less virtuous in others [Hursthouse] |
| 4327 | Deontologists do consider consequences, because they reveal when a rule might apply [Hursthouse] |
| 4335 | 'Codifiable' morality give rules for decisions which don't require wisdom [Hursthouse] |
| 4328 | Preference utilitarianism aims to be completely value-free, or empirical [Hursthouse] |
| 4338 | Deontologists usually accuse utilitarians of oversimplifying hard cases [Hursthouse] |
| 4343 | We are torn between utilitarian and deontological views of lying, depending on the examples [Hursthouse] |
| 4365 | We are distinct from other animals in behaving rationally - pursuing something as good, for reasons [Hursthouse] |
| 1659 | Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos] |
| 532 | Successful education must go deep into the soul [Protagoras] |
| 1552 | He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily] |
| 4350 | If people are virtuous in obedience to God, would they become wicked if they lost their faith? [Hursthouse] |
| 1551 | He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras] |