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] |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13711 | System B introduces iterated modalities [Sider] |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| 13714 | We can treat modal worlds as different times [Sider] |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| 20361 | We need 'unities' for reckoning, but that does not mean they exist [Nietzsche] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 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] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| 4484 | Nihilism results from valuing the world by the 'categories of reason', because that is fiction [Nietzsche] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 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] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| 4528 | For me, a priori 'truths' are just provisional assumptions [Nietzsche] |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| 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] |
| 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] |
| 9423 | If simplicity and strength are criteria for laws of nature, that introduces a subjective element [Mumford on Lewis] |
| 9424 | A number of systematizations might tie as the best and most coherent system [Mumford on Lewis] |
| 9409 | Laws are the best axiomatization of the total history of world events or facts [Lewis, by Mumford] |
| 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] |