68 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] |
| 425 | A thing can have opposing tensions but be in harmony, like a lyre [Heraclitus] |
| 416 | Beautiful harmony comes from things that are in opposition to one another [Heraclitus] |
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| 1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 15658 | The hidden harmony is stronger than the visible [Heraclitus] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| 13782 | Everything gives way, and nothing stands fast [Heraclitus] |
| 11853 | A mixed drink separates if it is not stirred [Heraclitus] |
| 16640 | Form is the principle that connects a thing's constitution (rather than being operative) [Hill,N] |
| 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] |
| 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] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 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] |
| 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] |
| 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] |