83 ideas
| 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] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 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] |
| 18658 | The 'Kantian' self steps back from commitment to its social situation [Kymlicka] |
| 18650 | Teleological theories give the good priority over concern for people [Kymlicka] |
| 18664 | Maybe the particularist moral thought of women is better than the impartial public thinking of men [Kymlicka] |
| 18624 | Utilitarianism is not a decision-procedure; choice of the best procedure is an open question [Kymlicka] |
| 18626 | One view says start with equality, and infer equal weight to interests, and hence maximum utility [Kymlicka] |
| 18627 | A second view says start with maximising the good, implying aggregation, and hence equality [Kymlicka] |
| 18625 | To maximise utility should we double the population, even if life somewhat deteriorates? [Kymlicka] |
| 18638 | The difference principles says we must subsidise the costs of other people's choices [Kymlicka] |
| 23418 | Liberal state legitimacy is based on a belief in justice, not in some conception of the good life [Kymlicka] |
| 18635 | Social contract theories are usually rejected because there never was such a contract [Kymlicka] |
| 23369 | Some liberals thinks checks and balances are enough, without virtuous citizens [Kymlicka] |
| 23370 | Good citizens need civic virtues of loyalty, independence, diligence, respect, etc. [Kymlicka] |
| 23373 | Liberals accept that people need society, but Aristotelians must show that they need political activity [Kymlicka] |
| 23375 | Minimal liberal citizenship needs common civility, as well as mere non-interference [Kymlicka] |
| 23376 | Modern non-discrimination obliges modern citizens to treat each other as equals [Kymlicka] |
| 23377 | The right wing sees citizenship in terms of responsibility to earn a living, rather than rights [Kymlicka] |
| 23414 | Liberals say state intervention in culture restricts people's autonomy [Kymlicka] |
| 18630 | Utilitarianism is no longer a distinctive political position [Kymlicka] |
| 18623 | The quest of the general good is partly undermined by people's past entitlements [Kymlicka] |
| 18628 | We shouldn't endorse preferences which reject equality, and show prejudice and selfishness [Kymlicka] |
| 18629 | Using utilitarian principles to make decisions encourages cold detachment from people [Kymlicka] |
| 18637 | Utilitarianism is irrational if it tells you to trade in your rights and resources just for benefits [Kymlicka] |
| 23371 | Modern democratic theory focuses on talk, not votes, because we need consensus or compromise [Kymlicka] |
| 23390 | In a liberal democracy all subjects of authority have a right to determine the authority [Kymlicka] |
| 18663 | Modern liberalism has added personal privacy to our personal social lives [Kymlicka] |
| 23374 | We have become attached to private life because that has become greatly enriched [Kymlicka] |
| 18632 | Liberalism tends to give priority to basic liberties [Kymlicka] |
| 22818 | Liberals are not too individualistic, because people recognise and value social relations [Kymlicka] |
| 23410 | Modern liberals see a community as simply a society which respects freedom and equality [Kymlicka] |
| 23387 | Liberals must avoid an official culture, as well as an official religion [Kymlicka] |
| 23388 | Liberals need more than freedom; they must build a nation, through a language and institutions [Kymlicka] |
| 23380 | Some individuals can gain citizenship as part of a group, rather than as mere individuals [Kymlicka] |
| 23381 | The status hierarchy is independent of the economic hierarchy [Kymlicka] |
| 23383 | Some multiculturalists defended the rights of cohesive minorities against liberal individualism [Kymlicka] |
| 23384 | 'Culturalist' liberals say that even liberal individuals may need minority rights [Kymlicka] |
| 23385 | Multiculturalism may entail men dominating women in minority groups [Kymlicka] |
| 23386 | Liberals must prefer minority right which are freedoms, not restrictions [Kymlicka] |
| 23389 | Why shouldn't national minorities have their own right to nation-build? [Kymlicka] |
| 23391 | Multiculturalism is liberal if it challenges inequality, conservative if it emphasises common good [Kymlicka] |
| 18656 | Marxists say liberalism is unjust, because it allows exploitation in the sale of labour [Kymlicka] |
| 23409 | Community can focus on class or citizenship or ethnicity or culture [Kymlicka] |
| 18659 | The 'Kantian' view of the self misses the way it is embedded or situated in society [Kymlicka] |
| 18660 | Communitarians say we should pay more attention to our history [Kymlicka] |
| 23419 | Communitarianism struggles with excluded marginalised groups [Kymlicka] |
| 18657 | Communitarian states only encourage fairly orthodox ideas of the good life [Kymlicka] |
| 23413 | Feminism has shown that social roles are far from fixed (as communitarians tend to see them) [Kymlicka] |
| 23415 | Participation aids the quest for the good life, but why should that be a state activity? [Kymlicka] |
| 18649 | If everyone owned himself, that would prevent slavery [Kymlicka] |
| 18640 | Libertarians like the free market, but they also think that the free market is just [Kymlicka] |
| 18651 | The most valuable liberties to us need not be the ones with the most freedom [Kymlicka] |
| 18661 | Ancient freedom was free participation in politics, not private independence of life [Kymlicka] |
| 18633 | Equal opportunities seems fair, because your fate is from your choices, not your circumstances [Kymlicka] |
| 18634 | Equal opportunity arbitrarily worries about social circumstances, but ignores talents [Kymlicka] |
| 18654 | Marxists say justice is unneeded in the truly good community [Kymlicka] |
| 18652 | The Lockean view of freedom depends on whether you had a right to what is restricted [Kymlicka] |
| 23379 | Rights are a part of nation-building, to build a common national identity and culture [Kymlicka] |
| 23382 | Rights derived from group membership are opposed to the idea of state citizenship [Kymlicka] |
| 18655 | Justice corrects social faults, but also expresses respect to individuals as ends [Kymlicka] |
| 23411 | Communitarians see justice as primarily a community matter, rather than a principle [Kymlicka] |
| 23412 | Justice resolves conflicts, but may also provoke them [Kymlicka] |
| 23378 | The welfare state helps to integrate the working classes into a national culture [Kymlicka] |