107 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] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 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] |
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| 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] |
| 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] |
| 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] |
| 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] |