67 ideas
| 4643 | The Principle of Sufficient Reason does not presuppose that all explanations will be causal explanations [Baggini /Fosl] |
| 4633 | You cannot rationally deny the principle of non-contradiction, because all reasoning requires it [Baggini /Fosl] |
| 4635 | Dialectic aims at unified truth, unlike analysis, which divides into parts [Baggini /Fosl] |
| 4632 | 'Natural' systems of deduction are based on normal rational practice, rather than on axioms [Baggini /Fosl] |
| 4631 | In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use [Baggini /Fosl] |
| 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] |
| 4638 | The principle of bivalence distorts reality, as when claiming that a person is or is not 'thin' [Baggini /Fosl] |
| 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] |
| 4640 | If identity is based on 'true of X' instead of 'property of X' we get the Masked Man fallacy ('I know X but not Y') [Baggini /Fosl, by PG] |
| 4647 | 'I have the same car as you' is fine; 'I have the same fiancée as you' is not so good [Baggini /Fosl] |
| 4639 | Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects [Baggini /Fosl] |
| 4646 | Is 'events have causes' analytic a priori, synthetic a posteriori, or synthetic a priori? [Baggini /Fosl] |
| 4645 | 'A priori' does not concern how you learn a proposition, but how you show whether it is true or false [Baggini /Fosl] |
| 4582 | Basic beliefs are self-evident, or sensual, or intuitive, or revealed, or guaranteed [Baggini /Fosl] |
| 4644 | A proposition such as 'some swans are purple' cannot be falsified, only verified [Baggini /Fosl] |
| 4584 | The problem of induction is how to justify our belief in the uniformity of nature [Baggini /Fosl] |
| 4583 | How can an argument be good induction, but poor deduction? [Baggini /Fosl] |
| 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] |
| 4634 | Abduction aims at simplicity, testability, coherence and comprehensiveness [Baggini /Fosl] |
| 4637 | To see if an explanation is the best, it is necessary to investigate the alternative explanations [Baggini /Fosl] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 4629 | Consistency is the cornerstone of rationality [Baggini /Fosl] |
| 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] |
| 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] |
| 23587 | Nuclear bombs are not for normal war; they undermine the 'just war', with a new morality [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] |
| 23614 | Even aggressor soldiers are not criminals, so they have equal rights with their opponents [Walzer] |
| 23589 | Kidnapped sailors and volunteers have different obligations to the passengers [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] |