130 ideas
| 20383 | The wisest man is full of contradictions, and attuned to other people, with occasional harmony [Nietzsche] |
| 4520 | I don't want to persuade anyone to be a philosopher; they should be rare plants [Nietzsche] |
| 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] |
| 4538 | Judgements can't be true and known in isolation; the only surety is in connections and relations [Nietzsche] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 20361 | We need 'unities' for reckoning, but that does not mean they exist [Nietzsche] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 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] |
| 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] |
| 4539 | The forms of 'knowledge' about logic which precede experience are actually regulations of belief [Nietzsche] |
| 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] |
| 4486 | The extreme view is there are only perspectives, no true beliefs, because there is no true world [Nietzsche] |
| 2534 | Mindless bodies are zombies, bodiless minds are ghosts [Sturgeon] |
| 2537 | Types are properties, and tokens are events. Are they split between mental and physical, or not? [Sturgeon] |
| 4536 | It is a major blunder to think of consciousness as a unity, and hence as an entity, a thing [Nietzsche] |
| 2532 | Intentionality isn't reducible, because of its experiential aspect [Sturgeon] |
| 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] |
| 2533 | Rule-following can't be reduced to the physical [Sturgeon] |
| 2535 | The main argument for physicalism is its simple account of causation [Sturgeon] |
| 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] |
| 2536 | Do facts cause thoughts, or embody them, or what? [Sturgeon] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 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] |
| 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] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 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] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 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] |