76 ideas
| 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] |
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| 21366 | Metaphysics must understand the world thoroughly, as a principal source of knowledge [Schopenhauer] |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 4168 | Matter and intellect are inseparable correlatives which only exist relatively, and for each other [Schopenhauer] |
| 21492 | Realism is basic to the scientific method [Peirce] |
| 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] |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| 4165 | Descartes found the true beginning of philosophy with the Cogito, in the consciousness of the individual [Schopenhauer] |
| 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] |
| 4164 | Direct feeling of the senses are merely data; perception of the world comes with understanding causes [Schopenhauer] |
| 4163 | All perception is intellectual [Schopenhauer] |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| 4166 | A consciousness without an object is no consciousness [Schopenhauer] |
| 21369 | We have hidden and unadmitted desires and fears, suppressed because of vanity [Schopenhauer] |
| 21367 | I know both aspects of my body, as representation, and as will [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] |
| 4170 | Man's actions are not free, because they follow strictly from impact of motive on character [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] |
| 4173 | If we were essentially intellect rather than will, our moral worth would depend on imagined motives [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] |
| 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] |
| 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] |
| 4184 | Virtue must spring from an intuitive recognition that other people are essentially like us [Schopenhauer] |
| 4179 | The essence of nature is the will to life itself [Schopenhauer] |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |
| 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] |