70 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| 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] |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 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] |
| 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] |
| 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] |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |
| 7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |
| 5299 | Religious feeling is social in origin [Marx] |