55 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] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
22598 | The authentic self exists at the level of class, rather than the individual [Marx, by Dunt] |
20416 | By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp] |
20418 | The horror expressed in some works of art could equallly be expressed by other means [Kemp] |
20417 | Expression can be either necessary for art, or sufficient for art (or even both) [Kemp] |
20419 | We don't already know what to express, and then seek means of expressing it [Kemp] |
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] |
22000 | From each according to his ability, to each according to his need [Marx] |
21999 | False consciousness results from concealment by the superstructure [Marx, by Singer] |
21989 | Man is dominated by money, which is the essence of his alienation [Marx] |
23862 | By saying the material dialectic of history aspires to the best, Marx agreed with capitalism [Weil on Marx] |
23875 | Marx says force is everything, and that the weak will become strong, while remaining the weak [Weil on Marx] |
22970 | Freedom is making the state subordinate to its society [Marx] |
18653 | Marx rejected equal rights because they never actually treat people as equals [Marx, by Kymlicka] |
21995 | Must production determine superstructure, or could it be the other way round? [Singer on Marx] |
20577 | Even decently paid workers still have their produce bought with money stolen from them [Marx] |
21996 | Freedom only comes when labour is no longer necessary [Marx] |
22969 | People who only have their labour power are the slaves of those permitting them to work [Marx] |
20958 | Capitalism changes the world, by socialising the idea of a commodity [Marx, by Bowie] |
23876 | The essence of capitalism is the subordination of people to things [Marx, by Weil] |
20960 | Marx thought capitalism was partly liberating, and could make labour and ownership more humane [Marx, by Bowie] |
21994 | The handmill gives feudalism, the steam mill capitalism [Marx] |
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] |