85 ideas
22334 | Analysis must include definitions, search for simples, concept analysis, and Kant's analysis [Glock] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
22332 | German and British idealism is not about individual ideas, but the intelligibility of reality [Glock] |
18658 | The 'Kantian' self steps back from commitment to its social situation [Kymlicka] |
22336 | We might say that the family resemblance is just a consequence of meaning-as-use [Glock] |
22335 | The variety of uses of 'game' may be that it has several meanings, and isn't a single concept [Glock] |
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] |