51 ideas
| 1564 | True and false statements can use exactly the same words [Anon (Diss)] |
| 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] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [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] |
| 1561 | Anything can be acceptable in some circumstances and unacceptable in others [Anon (Diss)] |
| 1559 | Thracians think tattooing adds to a girl's beauty, but elsewhere it is a punishment [Anon (Diss)] |
| 1560 | Lydians prostitute their daughters to raise a dowery, but no Greek would marry such a girl [Anon (Diss)] |
| 1567 | How could someone who knows everything fail to act correctly? [Anon (Diss)] |
| 1563 | Every apparent crime can be right in certain circumstances [Anon (Diss), by PG] |
| 1562 | It is right to lie to someone, to get them to take medicine they are reluctant to take [Anon (Diss)] |
| 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] |
| 23371 | Modern democratic theory focuses on talk, not votes, because we need consensus or compromise [Kymlicka] |
| 1566 | The first priority in elections is to vote for people who support democracy [Anon (Diss)] |
| 23390 | In a liberal democracy all subjects of authority have a right to determine the authority [Kymlicka] |
| 23374 | We have become attached to private life because that has become greatly enriched [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] |
| 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] |
| 23378 | The welfare state helps to integrate the working classes into a national culture [Kymlicka] |
| 1565 | We learn language, and we don't know who teaches us it [Anon (Diss)] |