27 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
22187 | Genetic behaviours that have enhanced human success include aggression, rape and xenophobia [Wilson,EO, by Okasha] |
23874 | Armies and businesses create moralities in which their activity can do no wrong [Marx, by Weil] |
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] |
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] |
18653 | Marx rejected equal rights because they never actually treat people as equals [Marx, by Kymlicka] |
21999 | False consciousness results from concealment by the superstructure [Marx, by Singer] |
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] |