129 ideas
| 20383 | The wisest man is full of contradictions, and attuned to other people, with occasional harmony [Nietzsche] |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 4520 | I don't want to persuade anyone to be a philosopher; they should be rare plants [Nietzsche] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 4545 | Could not the objective character of things be merely a difference of degree within the subjective? [Nietzsche] |
| 4530 | Reason is a mere idiosyncrasy of a certain species of animal [Nietzsche] |
| 4523 | What can be 'demonstrated' is of little worth [Nietzsche] |
| 4531 | Our inability to both affirm and deny a single thing is merely an inability, not a 'necessity' [Nietzsche] |
| 4541 | Everything simple is merely imaginary [Nietzsche] |
| 20357 | Truth was given value by morality, but eventually turned against its own source [Nietzsche] |
| 4534 | 'Truth' is the will to be master over the multiplicity of sensations [Nietzsche] |
| 4548 | Only because there is thought is there untruth [Nietzsche] |
| 5652 | True beliefs are those which augment one's power [Nietzsche, by Scruton] |
| 4508 | The truth is what gives us the minimum of spiritual effort, and avoids the exhaustion of lying [Nietzsche] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 4538 | Judgements can't be true and known in isolation; the only surety is in connections and relations [Nietzsche] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 20361 | We need 'unities' for reckoning, but that does not mean they exist [Nietzsche] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 4533 | Logic and maths refer to fictitious entities which we have created [Nietzsche] |
| 20359 | The nature of being, of things, is much easier to understand than is becoming [Nietzsche] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 4525 | There are no facts in themselves, only interpretations [Nietzsche] |
| 4543 | There are no 'facts-in-themselves', since a sense must be projected into them to make them 'facts' [Nietzsche] |
| 4484 | Nihilism results from valuing the world by the 'categories of reason', because that is fiction [Nietzsche] |
| 4546 | We realise that properties are sensations of the feeling subject, not part of the thing [Nietzsche] |
| 4544 | A thing has no properties if it has no effect on other 'things' [Nietzsche] |
| 20362 | We saw unity in things because our ego seemed unified (but now we doubt the ego!) [Nietzsche] |
| 4528 | For me, a priori 'truths' are just provisional assumptions [Nietzsche] |
| 4537 | We can't know whether there is knowledge if we don't know what it is [Nietzsche] |
| 4485 | Every belief is a considering-something-true [Nietzsche] |
| 4487 | A note for asses: What convinces is not necessarily true - it is merely convincing [Nietzsche] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 4539 | The forms of 'knowledge' about logic which precede experience are actually regulations of belief [Nietzsche] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 4529 | All sense perceptions are permeated with value judgements (useful or harmful) [Nietzsche] |
| 4532 | We can have two opposite sensations, like hard and soft, at the same time [Nietzsche] |
| 19518 | Evidentialism says justifications supervene on the available evidence [Conee/Feldman] |
| 4486 | The extreme view is there are only perspectives, no true beliefs, because there is no true world [Nietzsche] |
| 4536 | It is a major blunder to think of consciousness as a unity, and hence as an entity, a thing [Nietzsche] |
| 4551 | Great self-examination is to become conscious of oneself not as an individual, but as mankind [Nietzsche] |
| 4527 | Perhaps we are not single subjects, but a multiplicity of 'cells', interacting to create thought [Nietzsche] |
| 20374 | Consciousness is a terminal phenomenon, and causes nothing [Nietzsche] |
| 23938 | Passions are ranked, as if they are non-rational and animal pleasure seeking [Nietzsche] |
| 23939 | We fail to see that reason is a network of passions, and every passion contains some reason [Nietzsche] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 4554 | The concept of the 'will' is just a false simplification by our understanding [Nietzsche] |
| 4552 | There is no such things a pure 'willing' on its own; the aim must always be part of it [Nietzsche] |
| 19519 | Rational decisions are either taken to be based on evidence, or to be explained causally [Conee/Feldman] |
| 4521 | None of the ancients had the courage to deny morality by denying free will [Nietzsche] |
| 4496 | 'Conscience' is invented to value actions by intention and conformity to 'law', rather than consequences [Nietzsche] |
| 20136 | There is an extended logic to a great man's life, achieved by a sustained will [Nietzsche] |
| 20358 | The highest man can endure and control the greatest combination of powerful drives [Nietzsche] |
| 20369 | The highest man directs the values of the highest natures over millenia [Nietzsche] |
| 4506 | There is a conspiracy (a will to power) to make morality dominate other values, like knowledge and art [Nietzsche] |
| 4514 | The basic tendency of the weak has always been to pull down the strong, using morality [Nietzsche] |
| 20370 | All evaluation is from some perspective, and aims at survival [Nietzsche] |
| 20354 | The ruling drives of our culture all want to be the highest court of our values [Nietzsche] |
| 4505 | How can it be that I should prefer my neighbour to myself, but he should prefer me to himself? [Nietzsche] |
| 4509 | Utilitarians prefer consequences because intentions are unknowable - but so are consequences! [Nietzsche] |
| 4558 | We have no more right to 'happiness' than worms [Nietzsche] |
| 4500 | It is a sign of degeneration when eudaimonistic values begin to prevail [Nietzsche] |
| 4550 | Pleasure and pain are mere epiphenomena, and achievement requires that one desire both [Nietzsche] |
| 4518 | The question about egoism is: what kind of ego? since not all egos are equal [Nietzsche] |
| 4519 | The ego is only a fiction, and doesn't exist at all [Nietzsche] |
| 4517 | Egoism is inescapable, and when it grows weak, the power of love also grows weak [Nietzsche] |
| 4560 | The Golden Rule prohibits harmful actions, with the premise that actions will be requited [Nietzsche] |
| 4555 | The great error is to think that happiness derives from virtue, which in turn derives from free will [Nietzsche] |
| 4494 | Not "return to nature", for there has never yet been a natural humanity [Nietzsche] |
| 4498 | 'Love your enemy' is unnatural, for the natural law says 'love your neighbour and hate your enemy' [Nietzsche] |
| 4493 | Be natural! But how, if one happens to be "unnatural"? [Nietzsche] |
| 4511 | We would avoid a person who always needed reasons for remaining decent [Nietzsche] |
| 4512 | Virtue is pursued from self-interest and prudence, and reduces people to non-entities [Nietzsche] |
| 20372 | The instinct of the herd, the majority, aims for the mean, in the middle [Nietzsche] |
| 4515 | Modesty, industriousness, benevolence and temperance are the virtues of a good slave [Nietzsche] |
| 4516 | Many virtues are merely restraints on the most creative qualities of a human being [Nietzsche] |
| 4510 | A path to power: to introduce a new virtue under the name of an old one [Nietzsche] |
| 4559 | When powerless one desires freedom; if power is too weak, one desires equal power ('justice') [Nietzsche] |
| 4557 | The supposed great lovers of honour (Alexander etc) were actually great despisers of honour [Nietzsche] |
| 4507 | The categorical imperative needs either God behind it, or a metaphysic of the unity of reason [Nietzsche] |
| 4501 | Utilitarianism criticises the origins of morality, but still believes in it as much as Christians [Nietzsche] |
| 4489 | If faith is lost, people seek other authorities, in order to avoid the risk of willing personal goals [Nietzsche] |
| 4513 | Virtuous people are inferior because they are not 'persons', but conform to a fixed pattern [Nietzsche] |
| 4504 | Morality used to be for preservation, but now we can only experiment, giving ourselves moral goals [Nietzsche] |
| 4495 | The high points of culture and civilization do not coincide [Nietzsche] |
| 4491 | In modern society virtue is 'equal rights', but only because everyone is zero, so it is a sum of zeroes [Nietzsche] |
| 4542 | Science has taken the meaning out of causation; cause and effect are two equal sides of an equation [Nietzsche] |
| 4553 | We derive the popular belief in cause and effect from our belief that our free will causes things [Nietzsche] |
| 4535 | A 'species' is a stable phase of evolution, implying the false notion that evolution has a goal [Nietzsche] |
| 4497 | The concept of 'God' represents a turning away from life, and a critique of life [Nietzsche] |
| 4488 | Those who have abandoned God cling that much more firmly to the faith in morality [Nietzsche] |
| 4502 | Morality cannot survive when the God who sanctions it is missing [Nietzsche] |
| 4499 | Primitive Christianity is abolition of the state; it is opposed to defence, justice, patriotism and class [Nietzsche] |