43 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 20547 | We should respect the right of people to live in their own way, even if it is irrational [Swift] |
| 19407 | We want good education and sociability, rather than lots of moral precepts [Leibniz] |
| 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] |