58 ideas
| 5278 | Philosophy is no more than abstractions concerning observations of human historical development [Marx/Engels] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 5287 | Philosophical problems are resolved into empirical facts [Marx/Engels] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 2526 | Philosophers regularly confuse failures of imagination with insights into necessity [Dennett] |
| 2523 | That every mammal has a mother is a secure reality, but without foundations [Dennett] |
| 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] |
| 2528 | Does consciousness need the concept of consciousness? [Dennett] |
| 2525 | Maybe language is crucial to consciousness [Dennett] |
| 2527 | Unconscious intentionality is the foundation of the mind [Dennett] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 2530 | Could a robot be made conscious just by software? [Dennett] |
| 2524 | A language of thought doesn't explain content [Dennett] |
| 2529 | Maybe there can be non-conscious concepts (e.g. in bees) [Dennett] |
| 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] |