46 ideas
| 7910 | Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha] |
| 5278 | Philosophy is no more than abstractions concerning observations of human historical development [Marx/Engels] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 5287 | Philosophical problems are resolved into empirical facts [Marx/Engels] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 23872 | 'Society determines consciousness' is contradictory; society only exists in minds [Weil on Marx/Engels] |
| 5277 | Life is not determined by consciousness, but consciousness by life [Marx/Engels] |
| 5280 | Language co-exists with consciousness, and makes it social [Marx/Engels] |
| 5276 | The nature of an individual coincides with what they produce and how they produce it [Marx/Engels] |
| 5281 | Consciousness is a social product [Marx/Engels] |
| 5289 | When aristocracy or the bourgeoisie dominate, certain values dominate with them [Marx/Engels] |
| 5274 | Young Hegelians proposed changing our present consciousness for liberating critical consciousness [Marx/Engels] |
| 21992 | Producing their own subsistence distinguishes men from animals [Marx/Engels] |
| 5275 | Men distinguish themselves from animals when they begin to produce their means of subsistence [Marx/Engels] |
| 5292 | Individuals are mutually hostile unless they group together in competition with other groups [Marx/Engels] |
| 5293 | Only in community are people able to cultivate their gifts, and therefore be free [Marx/Engels] |
| 5273 | Young Hegelians think consciousness is chains for men, where old Hegelians think it the bond of society [Marx/Engels] |
| 5283 | In communist society we are not trapped in one activity, but can act freely [Marx/Engels] |
| 5282 | If the common interest imposes on the individual, his actions become alienated and enslaving [Marx/Engels] |
| 5288 | The class controlling material production also controls mental production [Marx/Engels] |
| 5290 | The revolutionary class is opposed to 'class', and represents all of society [Marx/Engels] |
| 5294 | To assert themselves as individuals, the proletarians must overthrow the State [Marx/Engels] |
| 5285 | Slavery cannot be abolished without the steam-engine [Marx/Engels] |
| 5284 | Communism abolishes private property and dissolves the powerful world market [Marx/Engels] |
| 5291 | The law says private property is the result of the general will [Marx/Engels] |
| 5279 | Human history must always be studied in relation to industry and exchange [Marx/Engels] |
| 5286 | Most historians are trapped in the illusions of their own epoch [Marx/Engels] |
| 7909 | The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha] |
| 7908 | At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha] |