34 ideas
22366 | There is no objectivity in social sciences - only viewpoints for selecting and organising data [Weber] |
22367 | The results of social research can be true, and not just subjectively valid for one person [Weber] |
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] |
21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
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] |
7082 | Nature requires causal explanations, but society requires clarification by reasons and motives [Weber, by Critchley] |
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] |
22155 | We are disenchanted because we rely on science, which ignores values [Weber, by Boulter] |
20725 | The idea of duty in one's calling haunts us, like a lost religion [Weber] |
21132 | Domination is probable obedience by some group of persons [Weber] |
20722 | Acquisition and low consumption lead to saving, investment, and increased wealth [Weber] |
20724 | When asceticism emerged from the monasteries, it helped to drive the modern economy [Weber] |
20717 | Capitalism is not unlimited greed, and may even be opposed to greed [Weber] |
20718 | Modern western capitalism has free labour, business separate from household, and book-keeping [Weber] |
20719 | Punish the heretic, but be indulgent to the sinner [Weber] |