127 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] |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| 20361 | We need 'unities' for reckoning, but that does not mean they exist [Nietzsche] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| 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] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 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] |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| 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] |
| 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] |
| 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] |
| 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] |