56 ideas
| 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] |
| 16235 | Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley] |
| 14753 | The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider] |
| 16072 | 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman] |
| 14751 | Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider] |
| 16071 | Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman] |
| 16234 | Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley] |
| 13278 | Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki] |
| 14750 | Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider] |
| 23590 | Criminal responsibility can be fully assigned to each member of a group [Walzer] |
| 23578 | Double Effect needs a double intention - to achieve the good, and minimise the evil [Walzer] |
| 23564 | Deep ethical theory is very controversial, but we have to live with higher ethical practice [Walzer] |
| 20595 | You can't distribute goods from behind a veil, because their social meaning is unclear [Walzer, by Tuckness/Wolf] |
| 20592 | Complex equality restricts equalities from spilling over, like money influencing politics and law [Walzer, by Tuckness/Wolf] |
| 20549 | Equality is complex, with different spheres of equality where different principles apply [Walzer, by Swift] |
| 23568 | If whole states possess rights, there can be social relations between states [Walzer] |
| 23581 | The aim of reprisals is to enforce the rules of war [Walzer] |
| 23567 | Even non-violent intrusive acts between states count as aggression, if they justify resistance [Walzer] |
| 23570 | The only good reason for fighting is in defence of rights [Walzer] |
| 23571 | States can rightly pre-empt real and serious threats [Walzer] |
| 23582 | Reprisal is defensible, as an alternative to war [Walzer] |
| 23580 | States need not endure attacks passively, and successful reprisals are legitimate [Walzer] |
| 23588 | With nuclear weapons we have a permanent supreme emergency (which is unstable) [Walzer] |
| 23572 | Just wars are self-defence, or a rightful intercession in another's troubles [Walzer] |
| 23587 | Nuclear bombs are not for normal war; they undermine the 'just war', with a new morality [Walzer] |
| 23577 | Napoleon said 'I don't care about the deaths of a million men' [Walzer] |
| 23593 | Jus ad bellum and Jus in bello are independent; unjust wars can be fought in a just way [Walzer] |
| 23573 | For moral reasons, a just war must be a limited war [Walzer] |
| 23589 | Kidnapped sailors and volunteers have different obligations to the passengers [Walzer] |
| 23614 | Even aggressor soldiers are not criminals, so they have equal rights with their opponents [Walzer] |
| 23574 | The duties and moral status of loyal and obedient soldiers is the same in defence and aggression [Walzer] |
| 23575 | We can't blame soldiers for anything they do which clearly promotes victory [Walzer] |
| 23584 | Rejecting Combatant Equality allows just soldiers to be harsher, even to the extreme [Walzer] |
| 23579 | Soldiers will only protect civilians if they feel safe from them [Walzer] |
| 23586 | What matters in war is unacceptable targets, not unacceptable weapons [Walzer] |
| 23591 | If the oppressor is cruel, nonviolence is either surrender, or a mere gesture [Walzer] |
| 23592 | We can only lead war towards peace if we firmly enforce the rules of war [Walzer] |