49 ideas
| 354 | Wisdom makes virtue and true goodness possible [Plato] |
| 370 | Philosophy is a purification of the soul ready for the afterlife [Plato] |
| 350 | In investigation the body leads us astray, but the soul gets a clear view of the facts [Plato] |
| 362 | The greatest misfortune for a person is to develop a dislike for argument [Plato] |
| 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] |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| 13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| 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] |
| 21347 | If Simmias is taller than Socrates, that isn't a feature that is just in Simmias [Plato] |
| 360 | We must have a prior knowledge of equality, if we see 'equal' things and realise they fall short of it [Plato] |
| 1 | There is only one source for all beauty [Plato] |
| 368 | Other things are named after the Forms because they participate in them [Plato] |
| 16516 | The ship which Theseus took to Crete is now sent to Delos crowned with flowers [Plato] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 357 | People are obviously recollecting when they react to a geometrical diagram [Plato] |
| 359 | If we feel the inadequacy of a resemblance, we must recollect the original [Plato] |
| 9343 | To achieve pure knowledge, we must get rid of the body and contemplate things with the soul [Plato] |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| 15859 | To investigate the causes of things, study what is best for them [Plato] |
| 13154 | Do we think and experience with blood, air or fire, or could it be our brain? [Plato] |
| 364 | One soul can't be more or less of a soul than another [Plato] |
| 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] |
| 361 | It is a mistake to think that the most violent pleasure or pain is therefore the truest reality [Plato] |
| 351 | War aims at the acquisition of wealth, because we are enslaved to the body [Plato] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 13156 | Fancy being unable to distinguish a cause from its necessary background conditions! [Plato] |
| 369 | If the Earth is spherical and in the centre, it is kept in place by universal symmetry, not by force [Plato] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 363 | Whether the soul pre-exists our body depends on whether it contains the ultimate standard of reality [Plato] |