46 ideas
| 20981 | What justifies reliance on reason? Is it just a tool? Why is it better than blind belief? [Sen] |
| 20982 | In politics and ethics, scrutiny from different perspectives is essential for objectivity [Sen] |
| 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] |
| 20990 | Rationality is conformity to reasons that can be sustained even after scrutiny [Sen] |
| 21005 | A human right is not plausible if public scrutiny might reject it [Sen] |
| 20983 | The original position insures that the agreements reached are fair [Sen] |
| 20987 | The veil of ignorance encourages neutral interests, but not a wider view of values [Sen] |
| 20984 | A social contract limits the pursuit of justice to members of a single society [Sen] |
| 20986 | A person's voice may count because of their interests, or because of their good sense [Sen] |
| 21001 | Famines tend to be caused by authoritarian rule [Sen] |
| 21002 | Effective democracy needs tolerant values [Sen] |
| 20999 | Democracy as 'government by discussion' now has wide support [Sen] |
| 20979 | Democracy needs more than some institutions; diverse sections of the people must be heard [Sen] |
| 20993 | Eradicating smallpox does not impoverish nature [Sen] |
| 20995 | Capabilities are part of freedom, involving real opportunities [Sen] |
| 20998 | Freedom can involve capabilities, independence and non-interference [Sen] |
| 20997 | The need for equality among people arises from impartiality and objectivity [Sen] |
| 20996 | All modern theories of justice demand equality of something [Sen] |
| 20988 | Freedom from torture or terrorist attacks is independent of citizenship [Sen] |
| 20980 | You don't need a complete theory of justice to see that slavery is wrong [Sen] |
| 20978 | Practical justice concerns not only ideals, but ways to achieve them [Sen] |
| 20985 | Our institutions should promote justice, rather than embodying it [Sen] |
| 20994 | We must focus on removing manifest injustice, not just try to design a perfect society [Sen] |
| 21000 | If justice needs public reasoning, which needs democracy, then justice and democracy are linked [Sen] |
| 8326 | Science has shown that causal relations are just transfers of energy or momentum [Fair, by Sosa/Tooley] |
| 10379 | Fair shifted his view to talk of counterfactuals about energy flow [Fair, by Schaffer,J] |