46 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] |
| 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] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 20547 | We should respect the right of people to live in their own way, even if it is irrational [Swift] |
| 20564 | Anti-colonial movements usually invoke the right of their 'people' to self-determination [Swift] |
| 20535 | Isn't it more rational to maximise the average position, but with a safety net? [Swift] |
| 20537 | Hypothetical contracts have no binding force [Swift] |
| 20542 | Cosmopolitans reject the right of different states to distribute resources in different ways [Swift] |
| 20559 | Democracy is bad, but the other systems are worse [Swift] |
| 20561 | Since all opinions are treated as equal in democracy, it implies there are no right answers [Swift] |
| 20562 | Design your democracy to treat citizens equally, or to produce better citizens? [Swift] |
| 20563 | Design your democracy to yield political stability, or good decisions? [Swift] |
| 20560 | Teledemocracy omits debate and deliberation, which are important parts of good decisions [Swift] |
| 20554 | Multiculturalism is a barrier to the whole state being a community [Swift] |
| 20553 | Liberals mistakenly think individuals choose their values, without reference to the community [Swift] |
| 20556 | The best way to build a cohesive community is to be involved in a war [Swift] |
| 20557 | Membership and inclusion in a community implies non-membership and exclusion [Swift] |
| 20555 | Liberals are concerned to protect individuals from too much community [Swift] |
| 20540 | Redistributing wealth treats some people as means, rather than as ends [Swift] |
| 20551 | Men have had the power to structure all of our social institutions [Swift] |
| 20545 | Maybe a freedom is from a restraint, and also in order to do something [Swift] |
| 20550 | Opportunity should ignore extraneous factors, or foster competence, or ignore all disadvantages [Swift] |
| 20536 | Inequalities are needed, as incentives to do the most important jobs [Swift] |
| 20548 | A person can desire redistibution of wealth, without it being for reasons of equality [Swift] |
| 20541 | You can't necessarily sell your legitimate right to something, even if you produced it [Swift] |
| 20546 | Libertarians about property ignore the fact that private property is a denial of freedoms [Swift] |
| 20533 | Justice can be seen as fairness or entitlement or desert [Swift] |