50 ideas
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 19718 | Indefeasibility does not imply infallibility [Grundmann] |
| 19717 | Can a defeater itself be defeated? [Grundmann] |
| 19716 | Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann] |
| 19715 | You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann] |
| 19713 | Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann] |
| 19714 | Knowledge requires that there are no facts which would defeat its justification [Grundmann] |
| 19719 | 'Moderate' foundationalism has basic justification which is defeasible [Grundmann] |
| 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] |