64 ideas
421 | Men who love wisdom must be inquirers into very many things indeed [Heraclitus] |
1491 | Everyone has the potential for self-knowledge and sound thinking [Heraclitus] |
5863 | Reason is eternal, but men are foolish [Heraclitus] |
414 | Logos is common to all, but most people live as if they have a private understanding [Heraclitus] |
416 | Beautiful harmony comes from things that are in opposition to one another [Heraclitus] |
425 | A thing can have opposing tensions but be in harmony, like a lyre [Heraclitus] |
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] |
1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
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] |
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] |
15658 | The hidden harmony is stronger than the visible [Heraclitus] |
13782 | Everything gives way, and nothing stands fast [Heraclitus] |
11853 | A mixed drink separates if it is not stirred [Heraclitus] |
427 | It is not possible to step twice into the same river [Heraclitus] |
11091 | You can bathe in the same river twice, but not in the same river stage [Quine on Heraclitus] |
2064 | If flux is continuous, then lack of change can't be a property, so everything changes in every possible way [Plato on Heraclitus] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
430 | Senses are no use if the soul is corrupt [Heraclitus] |
1500 | When we sleep, reason closes down as the senses do [Heraclitus, by Sext.Empiricus] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
417 | Donkeys prefer chaff to gold [Heraclitus] |
426 | Sea water is life-giving for fish, but not for people [Heraclitus] |
431 | Health, feeding and rest are only made good by disease, hunger and weariness [Heraclitus] |
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] |
429 | To God (though not to humans) all things are beautiful and good and just [Heraclitus] |
12294 | Good and evil are the same thing [Heraclitus, by Aristotle] |
419 | If one does not hope, one will not find the unhoped-for, since nothing leads to it [Heraclitus] |
415 | If happiness is bodily pleasure, then oxen are happy when they have vetch to eat [Heraclitus] |
5155 | It is hard to fight against emotion, but harder still to fight against pleasure [Heraclitus] |
433 | For man character is destiny [Heraclitus] |
422 | The people should fight for the law as if for their city-wall [Heraclitus] |
614 | Heraclitus said sometimes everything becomes fire [Heraclitus, by Aristotle] |
424 | Reason tells us that all things are one [Heraclitus] |
5096 | Heraclitus says that at some time everything becomes fire [Heraclitus, by Aristotle] |
17539 | The sayings of Heraclitus are still correct, if we replace 'fire' with 'energy' [Heraclitus, by Heisenberg] |
3054 | Heraclitus said fire could be transformed to create the other lower elements [Heraclitus, by Diog. Laertius] |
15660 | Logos is the source of everything, and my theories separate and explain each nature [Heraclitus] |
12269 | All things are in a state of motion [Heraclitus, by Aristotle] |
20646 | Helmholtz used 'energy' to mathematically link heat, light, electricity and magnetism [Helmholtz, by Watson] |
20973 | All forces conserve the sum of kinetic and potential energy [Helmholtz, by Papineau] |
420 | The cosmos is eternal not created, and is an ever-living and changing fire [Heraclitus] |
1499 | Heraclitus says intelligence draws on divine reason [Heraclitus, by Sext.Empiricus] |
15659 | Purifying yourself with blood is as crazy as using mud to wash off mud [Heraclitus] |
1501 | In their ignorance people pray to statues, which is like talking to a house [Heraclitus] |