61 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] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 18270 | Choice suggests that intensions are not needed to ensure classes [Coffa] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 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] |
| 18263 | The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition [Coffa] |
| 18272 | Platonism defines the a priori in a way that makes it unknowable [Coffa] |
| 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] |
| 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] |
| 18266 | Mathematics generalises by using variables [Coffa] |
| 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] |
| 18279 | Relativity is as absolutist about space-time as Newton was about space [Coffa] |
| 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] |