124 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] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 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] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 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] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 20361 | We need 'unities' for reckoning, but that does not mean they exist [Nietzsche] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 4533 | Logic and maths refer to fictitious entities which we have created [Nietzsche] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 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] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 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] |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| 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] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 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] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |