58 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] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 22598 | The authentic self exists at the level of class, rather than the individual [Marx, by Dunt] |
| 5298 | The human essence is not found in individuals but in social relations [Marx] |
| 2854 | Prescriptivism says 'ought' without commitment to act is insincere, or weakly used [Hooker,B] |
| 23874 | Armies and businesses create moralities in which their activity can do no wrong [Marx, by Weil] |
| 2856 | Universal moral judgements imply the Golden Rule ('do as you would be done by') [Hooker,B] |
| 20883 | Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B] |
| 20884 | Rule-utilitarians prevent things like torture, even on rare occasions when it seems best [Hooker,B] |
| 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] |
| 22000 | From each according to his ability, to each according to his need [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] |
| 21996 | Freedom only comes when labour is no longer necessary [Marx] |
| 22970 | Freedom is making the state subordinate to its society [Marx] |
| 21994 | The handmill gives feudalism, the steam mill capitalism [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] |
| 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] |
| 20885 | Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B] |
| 20882 | Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B] |
| 7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |
| 5299 | Religious feeling is social in origin [Marx] |