68 ideas
20262 | Don't use wisdom in order to become clever! [Nietzsche] |
20255 | Early 19th century German philosophers enjoyed concepts, rather than scientific explanations [Nietzsche] |
20260 | Carlyle spent his life vainly trying to make reason appear romantic [Nietzsche] |
20256 | What we think is totally dictated by the language available to express it [Nietzsche] |
20265 | The desire for a complete system requires making the weak parts look equal to the rest [Nietzsche] |
20380 | Why should truth be omnipotent? It is enough that it is very powerful [Nietzsche] |
20235 | Like animals, we seek truth because we want safety [Nietzsche] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
8978 | Events are made of other things, and are not fundamental to ontology [Bennett] |
20258 | Most people treat knowledge as a private possession [Nietzsche] |
20250 | We may be unable to remember, but we may never actually forget [Nietzsche] |
20270 | There is no one scientific method; we must try many approaches, and many emotions [Nietzsche] |
20131 | We can cultivate our drives, of anger, pity, curiosity, vanity, like a gardener, with good or bad taste [Nietzsche] |
20242 | Things are the boundaries of humanity, so all things must be known, for self-knowledge [Nietzsche] |
20249 | Our knowledge of the many drives that constitute us is hopelessly incomplete [Nietzsche] |
20231 | People used to think that outcomes were from God, rather than consequences of acts [Nietzsche] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
20266 | It is essential that wise people learn to express their wisdom, possibly even as foolishness [Nietzsche] |
20251 | Actions done for a purpose are least understood, because we complacently think it's obvious [Nietzsche] |
20271 | Beauty in art is the imitation of happiness [Nietzsche] |
20230 | The very idea of a critique of morality is regarded as immoral! [Nietzsche] |
20234 | Morality prevents us from developing better customs [Nietzsche] |
20237 | Moral feelings are entirely different from the moral concepts used to judge actions [Nietzsche] |
20238 | Treating morality as feelings is just obeying your ancestors [Nietzsche] |
20243 | Human beings are not majestic, either through divine origins, or through grand aims [Nietzsche] |
20268 | Most dying people have probably lost more important things than what they are about to lose [Nietzsche] |
20252 | Marriage is too serious to be permitted for people in love! [Nietzsche] |
20236 | Marriage upholds the idea that love, though a passion, can endure [Nietzsche] |
20263 | Fear reveals the natures of other people much more clearly than love does [Nietzsche] |
20233 | Punishment has distorted the pure innocence of the contingency of outcomes [Nietzsche] |
20248 | People do nothing for their real ego, but only for a phantom ego created by other people [Nietzsche] |
20246 | If you feel to others as they feel to themselves, you must hate a self-hater [Nietzsche] |
20272 | Honesty is a new young virtue, and we can promote it, or not [Nietzsche] |
20240 | The Jews treated great anger as holy, and were in awe of those who expressed it [Nietzsche] |
20244 | Christianity replaces rational philosophical virtues with great passions focused on God [Nietzsche] |
20274 | The cardinal virtues want us to be honest, brave, magnanimous and polite [Nietzsche] |
20257 | Cool courage and feverish bravery have one name, but are two very different virtues [Nietzsche] |
20259 | Teach youth to respect people who differ with them, not people who agree with them [Nietzsche] |
20267 | Seeing duty as a burden makes it a bit cruel, and it can thus never become a habit [Nietzsche] |
20275 | Most people think they are already complete, but we can cultivate ourselves [Nietzsche] |
20229 | No authority ever willingly accepts criticism [Nietzsche] |
20254 | People govern for the pleasure of it, or just to avoid being governed [Nietzsche] |
20273 | The French Revolution gave trusting Europe the false delusion of instant recovery [Nietzsche] |
20232 | Get rid of the idea of punishment! It is a noxious weed! [Nietzsche] |
20253 | Modern wars arise from the study of history [Nietzsche] |
20261 | History does not concern what really happened, but supposed events, which have all the influence [Nietzsche] |
10364 | Facts are about the world, not in it, so they can't cause anything [Bennett] |
20241 | Enquirers think finding our origin is salvation, but it turns out to be dull [Nietzsche] |
20245 | Christianity hoped for a short cut to perfection, that skipped the hard labour of morality [Nietzsche] |
20247 | Christianity was successful because of its heathen rituals [Nietzsche] |
20269 | 'I believe because it is absurd' - but how about 'I believe because I am absurd' [Nietzsche] |
20264 | The easy and graceful aspects of a person are called 'soul', and inner awkwardness is called 'soulless' [Nietzsche] |