72 ideas
| 421 | Men who love wisdom must be inquirers into very many things indeed [Heraclitus] |
| 326 | For relaxation one can consider the world of change, instead of eternal things [Plato] |
| 1491 | Everyone has the potential for self-knowledge and sound thinking [Heraclitus] |
| 315 | Philosophy is the supreme gift of the gods to mortals [Plato] |
| 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] |
| 306 | Nothing can come to be without a cause [Plato] |
| 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] |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| 1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| 324 | Before the existence of the world there must have been being, space and becoming [Plato] |
| 20364 | The apprehensions of reason remain unchanging, but reasonless sensation shows mere becoming [Plato] |
| 15658 | The hidden harmony is stronger than the visible [Heraclitus] |
| 12042 | Plato's Forms were seen as part of physics, rather than of metaphysics [Plato, by Annas] |
| 307 | Something will always be well-made if the maker keeps in mind the eternal underlying pattern [Plato] |
| 318 | In addition to the underlying unchanging model and a changing copy of it, there must also be a foundation of all change [Plato] |
| 321 | For knowledge and true opinion to be different there must be Forms; otherwise we are just stuck with sensations [Plato] |
| 317 | The universe is basically an intelligible and unchanging model, and a visible and changing copy of it [Plato] |
| 13782 | Everything gives way, and nothing stands fast [Heraclitus] |
| 11853 | A mixed drink separates if it is not stirred [Heraclitus] |
| 11091 | You can bathe in the same river twice, but not in the same river stage [Quine on Heraclitus] |
| 427 | It is not possible to step twice into the same river [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] |
| 334 | Only bird-brained people think astronomy is entirely a matter of evidence [Plato] |
| 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] |
| 5962 | Plato says the soul is ordered by number [Plato, by Plutarch] |
| 330 | No one wants to be bad, but bad men result from physical and educational failures, which they do not want or choose [Plato] |
| 316 | Music has harmony like the soul, and serves to reorder disharmony within us [Plato] |
| 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] |
| 332 | One should exercise both the mind and the body, to avoid imbalance [Plato] |
| 328 | Everything that takes place naturally is pleasant [Plato] |
| 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] |
| 322 | Intelligence is the result of rational teaching; true opinion can result from irrational persuasion [Plato] |
| 331 | Bad governments prevent discussion, and discourage the study of virtue [Plato] |
| 310 | The creator of the cosmos had no envy, and so wanted things to be as like himself as possible [Plato] |
| 311 | The cosmos must be unique, because it resembles the creator, who is unique [Plato] |
| 614 | Heraclitus said sometimes everything becomes fire [Heraclitus, by Aristotle] |
| 424 | Reason tells us that all things are one [Heraclitus] |
| 17539 | The sayings of Heraclitus are still correct, if we replace 'fire' with 'energy' [Heraclitus, by Heisenberg] |
| 5096 | Heraclitus says that at some time everything becomes fire [Heraclitus, by Aristotle] |
| 3054 | Heraclitus said fire could be transformed to create the other lower elements [Heraclitus, by Diog. Laertius] |
| 325 | We must consider the four basic shapes as too small to see, only becoming visible in large numbers [Plato] |
| 15660 | Logos is the source of everything, and my theories separate and explain each nature [Heraclitus] |
| 327 | There are two types of cause, the necessary and the divine [Plato] |
| 12269 | All things are in a state of motion [Heraclitus, by Aristotle] |
| 314 | Heavenly movements gave us the idea of time, and caused us to inquire about the heavens [Plato] |
| 312 | Time came into existence with the heavens, so that there will be a time when they can be dissolved [Plato] |
| 309 | Clearly the world is good, so its maker must have been concerned with the eternal, not with change [Plato] |
| 420 | The cosmos is eternal not created, and is an ever-living and changing fire [Heraclitus] |
| 308 | If the cosmos is an object of perception then it must be continually changing [Plato] |
| 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] |