53 ideas
| 5300 | Philosophers have interpreted the world, but the point is to change it [Marx] |
| 5297 | Whether human thinking can be 'true' must be decided in practice, not theory [Marx] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 22598 | The authentic self exists at the level of class, rather than the individual [Marx, by Dunt] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 5298 | The human essence is not found in individuals but in social relations [Marx] |
| 23874 | Armies and businesses create moralities in which their activity can do no wrong [Marx, by Weil] |
| 22001 | The real will of the cooperative will replace the 'will of the people' [Marx] |
| 21991 | The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer] |
| 21990 | Theory is as much a part of a revolution as material force is [Marx] |
| 22971 | In moving from capitalism to communism a revolutionary dictatorship of the proletariat is needed [Marx] |
| 18662 | Liberal freedom is the right to be separate, and ignores the union of man with man [Marx] |
| 23372 | Liberals want the right to be separate, rather than for people to be united [Marx] |
| 20576 | Early Marx anticipates communitarian objections to liberalism [Marx, by Oksala] |
| 21989 | Man is dominated by money, which is the essence of his alienation [Marx] |
| 21996 | Freedom only comes when labour is no longer necessary [Marx] |
| 23862 | By saying the material dialectic of history aspires to the best, Marx agreed with capitalism [Weil on Marx] |
| 21999 | False consciousness results from concealment by the superstructure [Marx, by Singer] |
| 23875 | Marx says force is everything, and that the weak will become strong, while remaining the weak [Weil on Marx] |
| 21995 | Must production determine superstructure, or could it be the other way round? [Singer on Marx] |
| 18653 | Marx rejected equal rights because they never actually treat people as equals [Marx, by Kymlicka] |
| 20577 | Even decently paid workers still have their produce bought with money stolen from them [Marx] |
| 22969 | People who only have their labour power are the slaves of those permitting them to work [Marx] |
| 22000 | From each according to his ability, to each according to his need [Marx] |
| 22970 | Freedom is making the state subordinate to its society [Marx] |
| 21994 | The handmill gives feudalism, the steam mill capitalism [Marx] |
| 23876 | The essence of capitalism is the subordination of people to things [Marx, by Weil] |
| 20958 | Capitalism changes the world, by socialising the idea of a commodity [Marx, by Bowie] |
| 20960 | Marx thought capitalism was partly liberating, and could make labour and ownership more humane [Marx, by Bowie] |
| 22972 | Bourgeois 'freedom of conscience' just tolerates all sorts of religious intolerance [Marx] |
| 20519 | Marxists say liberal rights are confrontational, and liberal equality is a sham [Marx, by Wolff,J] |
| 7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |
| 5299 | Religious feeling is social in origin [Marx] |