110 ideas
21916 | Philosophers can't be religious, and don't need to be; philosophy is perilous but free [Schopenhauer] |
4171 | Philosophy considers only the universal, in nature as everywhere else [Schopenhauer] |
4186 | Everyone is conscious of all philosophical truths, but philosophers bring them to conceptual awareness [Schopenhauer] |
12171 | Absurdity is incongruity between correct and false points of view [Schopenhauer] |
21366 | Metaphysics must understand the world thoroughly, as a principal source of knowledge [Schopenhauer] |
21474 | Metaphysics studies the inexplicable ends of explanation [Schopenhauer] |
21918 | Sufficient Reason can't be proved, because all proof presupposes it [Schopenhauer, by Lewis,PB] |
4187 | 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer] |
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
4168 | Matter and intellect are inseparable correlatives which only exist relatively, and for each other [Schopenhauer] |
21470 | For me the objective thing-in-itself is the will [Schopenhauer] |
21926 | Schopenhauer, unlike other idealists, says reality is irrational [Schopenhauer, by Lewis,PB] |
4167 | The knowing subject and the crude matter of the world are both in themselves unknowable [Schopenhauer] |
21920 | No need for a priori categories, since sufficient reason shows the interrelations [Schopenhauer, by Lewis,PB] |
21362 | Necessity is physical, logical, mathematical or moral [Schopenhauer, by Janaway] |
4192 | All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer] |
4190 | All understanding is an immediate apprehension of the causal relation [Schopenhauer] |
21479 | Knowledge is not power! Ignorant people possess supreme authority [Schopenhauer] |
4165 | Descartes found the true beginning of philosophy with the Cogito, in the consciousness of the individual [Schopenhauer] |
21361 | For Schopenhauer, material things would not exist without the mind [Schopenhauer, by Janaway] |
21923 | Schopenhauer can't use force/energy instead of 'will', because he is not a materialist [Lewis,PB on Schopenhauer] |
4162 | The world only exists in relation to something else, as an idea of the one who conceives it [Schopenhauer] |
21922 | We know reality because we know our own bodies and actions [Schopenhauer] |
21913 | Kant rightly separates appearance and thing-in-itself [Schopenhauer] |
21919 | Object for a subject and representation are the same thing [Schopenhauer] |
21476 | A priori propositions are those we could never be seriously motivated to challenge [Schopenhauer] |
4164 | Direct feeling of the senses are merely data; perception of the world comes with understanding causes [Schopenhauer] |
4163 | All perception is intellectual [Schopenhauer] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
21473 | All knowledge and explanation rests on the inexplicable [Schopenhauer] |
21917 | The four explanations: objects by causes, concepts by ground, maths by spacetime, ethics by motive [Schopenhauer, by Lewis,PB] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
4166 | A consciousness without an object is no consciousness [Schopenhauer] |
21369 | We have hidden and unadmitted desires and fears, suppressed because of vanity [Schopenhauer] |
21478 | Half our thinking is unconscious, and we reach conclusions while unaware of premises [Schopenhauer] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
4191 | What we know in ourselves is not a knower but a will [Schopenhauer] |
21367 | I know both aspects of my body, as representation, and as will [Schopenhauer] |
21368 | The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer] |
4175 | It is as perverse to resent our individuality being replaced by others, as to resent the body renewing itself [Schopenhauer] |
4176 | We all regard ourselves a priori as free, but see from experience that character and motive compel us [Schopenhauer] |
21477 | We don't control our own thinking [Schopenhauer] |
4170 | Man's actions are not free, because they follow strictly from impact of motive on character [Schopenhauer] |
21921 | Concepts are abstracted from perceptions [Schopenhauer, by Lewis,PB] |
21475 | All of our concepts are borrowed from perceptual knowledge [Schopenhauer] |
4169 | Every true act of will is also at once and without exception a movement of the body [Schopenhauer] |
7187 | Schopenhauer was caught in Christian ideals, because he didn't deify his 'will' [Nietzsche on Schopenhauer] |
21365 | Only the will is thing-in-itself, seen both in blind nature and in human action [Schopenhauer] |
21924 | As the subject of willing I am wretched, but absorption in knowledge is bliss [Schopenhauer] |
4173 | If we were essentially intellect rather than will, our moral worth would depend on imagined motives [Schopenhauer] |
21363 | Motivation is causality seen from within [Schopenhauer] |
21372 | Aesthetics concerns how we can take pleasure in an object, with no reference to the will [Schopenhauer] |
21370 | Schopenhauer is a chief proponent of aesthetic experience as 'disinterested' [Schopenhauer, by Janaway] |
4182 | A principal pleasure of the beautiful is that it momentarily silences the will [Schopenhauer] |
21488 | The beautiful is a perception of Plato's Forms, which eliminates the will [Schopenhauer] |
21928 | The Sublime fights for will-less knowing, when faced with a beautiful threat to humanity [Schopenhauer, by Lewis,PB] |
21927 | Schopenhauer emphasises Ideas in art, unlike most romantics [Schopenhauer, by Lewis,PB] |
8116 | The will-less contemplation of art brings a liberation from selfhood [Schopenhauer, by Gardner] |
4174 | Man is more beautiful than anything else, and the loftiest purpose of art is to reveal his nature [Schopenhauer] |
21380 | The only aim of our existence is to grasp that non-existence would be better [Schopenhauer] |
21374 | We should no more expect ethical theory to produce good people than aesthetics to produce artists [Schopenhauer] |
21378 | We clearly feel responsible for our deeds, because we are quite certain that we did them [Schopenhauer] |
21375 | Reason can be vicious, and great crimes have to be rational [Schopenhauer] |
21915 | To deduce morality from reason is blasphemy, because it is holy, and far above reason [Schopenhauer] |
21483 | Man is essentially a dreadful wild animal [Schopenhauer] |
21379 | Man's three basic ethical incentives are egoism, malice and compassion [Schopenhauer] |
4181 | Every good is essentially relative, for it has its essential nature only in its relation to a desiring will [Schopenhauer] |
5649 | Will casts aside each of its temporary fulfilments, so human life has no ultimate aim [Schopenhauer, by Scruton] |
4177 | Most people would probably choose non-existence at the end of their life, rather than relive the whole thing [Schopenhauer] |
4185 | Altruistic people make less distinction than usual between themselves and others [Schopenhauer] |
4183 | Only self-love can motivate morality, but that also makes it worthless [Schopenhauer] |
4172 | Happiness is the swift movement from desire to satisfaction, and then again on to desire [Schopenhauer] |
21371 | We can never attain happiness while our will is pursuing desires [Schopenhauer] |
21466 | Pleasure is weaker, and pain stronger, than we expect [Schopenhauer] |
4184 | Virtue must spring from an intuitive recognition that other people are essentially like us [Schopenhauer] |
21484 | A man's character can be learned from a single characteristic action [Schopenhauer] |
21482 | The five Chinese virtues: pity, justice, politeness, wisdom, honesty [Schopenhauer] |
21481 | Buddhists wisely start with the cardinal vices [Schopenhauer] |
21480 | Boredom is only felt by those clever enough to need activity [Schopenhauer] |
21469 | Human life is a mistake, shown by boredom, which is direct awareness of the fact [Schopenhauer] |
21485 | The state only exists to defend citizens, from exterior threats, and from one another [Schopenhauer] |
21486 | Poverty and slavery are virtually two words for the same thing [Schopenhauer] |
21487 | The freedom of the press to sell poison outweighs its usefulness [Schopenhauer] |
21471 | If suicide was quick and easy, most people would have done it by now [Schopenhauer] |
21467 | Would humanity still exist if sex wasn't both desired and pleasurable? [Schopenhauer] |
21376 | Philosophy treats animals as exploitable things, ignoring the significance of their lives [Schopenhauer] |
4179 | The essence of nature is the will to life itself [Schopenhauer] |
4189 | Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer] |
4178 | Christianity is a pessimistic religion, in which the world is equated with evil [Schopenhauer] |
4180 | Religion is the mythical clothing of the truth which is inaccessible to the crude human intellect [Schopenhauer] |
21472 | Only religion introduces serious issues to uneducated people [Schopenhauer] |
21468 | The Creator created the possibilities for worlds, so should have made a better one than this possible [Schopenhauer] |