71 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] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 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] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 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] |
| 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] |
| 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] |
| 20252 | Marriage is too serious to be permitted for people in love! [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] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 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] |