44 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 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] |