52 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] |
1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [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] |
3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
430 | Senses are no use if the soul is corrupt [Heraclitus] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
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] |
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] |