58 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] |
22190 | If a theory is more informative it is less probable [Gorham] |
22189 | Why abandon a theory if you don't have a better one? [Gorham] |
22192 | Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham] |
22194 | Structural Realism says mathematical structures persist after theory rejection [Gorham] |
22195 | Structural Realists must show the mathematics is both crucial and separate [Gorham] |
22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
22193 | Consilience makes the component sciences more likely [Gorham] |
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] |
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] |
23571 | States can rightly pre-empt real and serious threats [Walzer] |
23572 | Just wars are self-defence, or a rightful intercession in another's troubles [Walzer] |
23581 | The aim of reprisals is to enforce the rules of war [Walzer] |
23582 | Reprisal is defensible, as an alternative to war [Walzer] |
23588 | With nuclear weapons we have a permanent supreme emergency (which is unstable) [Walzer] |
23580 | States need not endure attacks passively, and successful reprisals are legitimate [Walzer] |
23587 | Nuclear bombs are not for normal war; they undermine the 'just war', with a new morality [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] |
23573 | For moral reasons, a just war must be a limited war [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] |
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] |
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] |
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] |
22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |