76 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] |
| 23531 | Philosophers should interpret the world, by expressing its possibilities [Berardi] |
| 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] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 23538 | Nothingness only exists in consciousness [Berardi] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 15658 | The hidden harmony is stronger than the visible [Heraclitus] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 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] |
| 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] |
| 23532 | The delusion of free will brings a sense of guilt [Berardi] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 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] |
| 23537 | American white men trusted the philosophy of winning, and then discovered losing [Berardi] |
| 23536 | Community is now a nostalgic memory, which no longer exists [Berardi] |
| 23534 | Communism failed to unite western workers with the oppressed of the south [Berardi] |
| 23533 | The economy has replaced medieval theocracy at the centre of our society [Berardi] |
| 23535 | Western workers turn to nationalism, to avert the effects of globalisation [Berardi] |
| 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] |