32 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] |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| 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] |
| 23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
| 21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
| 21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 23418 | Liberal state legitimacy is based on a belief in justice, not in some conception of the good life [Kymlicka] |
| 23414 | Liberals say state intervention in culture restricts people's autonomy [Kymlicka] |
| 23410 | Modern liberals see a community as simply a society which respects freedom and equality [Kymlicka] |
| 23409 | Community can focus on class or citizenship or ethnicity or culture [Kymlicka] |
| 23413 | Feminism has shown that social roles are far from fixed (as communitarians tend to see them) [Kymlicka] |
| 23419 | Communitarianism struggles with excluded marginalised groups [Kymlicka] |
| 23415 | Participation aids the quest for the good life, but why should that be a state activity? [Kymlicka] |
| 23411 | Communitarians see justice as primarily a community matter, rather than a principle [Kymlicka] |
| 23412 | Justice resolves conflicts, but may also provoke them [Kymlicka] |