123 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] |
15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
20361 | We need 'unities' for reckoning, but that does not mean they exist [Nietzsche] |
15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
4533 | Logic and maths refer to fictitious entities which we have created [Nietzsche] |
15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
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] |
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] |
7357 | People who control others with fluent language often end up being hated [Kongzi (Confucius)] |
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] |
7358 | All men prefer outward appearance to true excellence [Kongzi (Confucius)] |
4496 | 'Conscience' is invented to value actions by intention and conformity to 'law', rather than consequences [Nietzsche] |
7362 | Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)] |
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] |
4500 | It is a sign of degeneration when eudaimonistic values begin to prevail [Nietzsche] |
4558 | We have no more right to 'happiness' than worms [Nietzsche] |
4550 | Pleasure and pain are mere epiphenomena, and achievement requires that one desire both [Nietzsche] |
4517 | Egoism is inescapable, and when it grows weak, the power of love also grows weak [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] |
7360 | Do not do to others what you would not desire yourself [Kongzi (Confucius)] |
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] |
7359 | Excess and deficiency are equally at fault [Kongzi (Confucius)] |
7363 | The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)] |
4510 | A path to power: to introduce a new virtue under the name of an old one [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] |
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] |
7361 | Men of the highest calibre avoid political life completely [Kongzi (Confucius)] |
23393 | Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)] |
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] |