38 ideas
21474 | Metaphysics studies the inexplicable ends of explanation [Schopenhauer] |
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
21470 | For me the objective thing-in-itself is the will [Schopenhauer] |
21479 | Knowledge is not power! Ignorant people possess supreme authority [Schopenhauer] |
21476 | A priori propositions are those we could never be seriously motivated to challenge [Schopenhauer] |
21473 | All knowledge and explanation rests on the inexplicable [Schopenhauer] |
21478 | Half our thinking is unconscious, and we reach conclusions while unaware of premises [Schopenhauer] |
21477 | We don't control our own thinking [Schopenhauer] |
21475 | All of our concepts are borrowed from perceptual knowledge [Schopenhauer] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
21372 | Aesthetics concerns how we can take pleasure in an object, with no reference to the will [Schopenhauer] |
21488 | The beautiful is a perception of Plato's Forms, which eliminates the will [Schopenhauer] |
21483 | Man is essentially a dreadful wild animal [Schopenhauer] |
21466 | Pleasure is weaker, and pain stronger, than we expect [Schopenhauer] |
21484 | A man's character can be learned from a single characteristic action [Schopenhauer] |
21481 | Buddhists wisely start with the cardinal vices [Schopenhauer] |
21482 | The five Chinese virtues: pity, justice, politeness, wisdom, honesty [Schopenhauer] |
21469 | Human life is a mistake, shown by boredom, which is direct awareness of the fact [Schopenhauer] |
21480 | Boredom is only felt by those clever enough to need activity [Schopenhauer] |
21485 | The state only exists to defend citizens, from exterior threats, and from one another [Schopenhauer] |
21486 | Poverty and slavery are virtually two words for the same thing [Schopenhauer] |
21487 | The freedom of the press to sell poison outweighs its usefulness [Schopenhauer] |
21471 | If suicide was quick and easy, most people would have done it by now [Schopenhauer] |
21467 | Would humanity still exist if sex wasn't both desired and pleasurable? [Schopenhauer] |
21472 | Only religion introduces serious issues to uneducated people [Schopenhauer] |
21468 | The Creator created the possibilities for worlds, so should have made a better one than this possible [Schopenhauer] |