28 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] |
| 14212 | A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis] |
| 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] |
| 14213 | Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 14210 | A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis] |
| 9757 | A person viewed as an agent makes no sense without its own future [Korsgaard] |
| 9758 | To make sense of personal identity, focus on agency rather than experience [Korsgaard] |
| 14215 | Causal theories of reference make errors in reference easy [Lewis] |
| 14209 | Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis] |
| 9759 | Theory of action focuses on explanation and prediction; practical action on justification and choice [Korsgaard] |
| 9760 | Self-concern may be a source of pain, or a lack of self-respect, or a failure of responsibility [Korsgaard] |
| 9761 | Personal concern for one's own self widens out into concern for the impersonal [Korsgaard] |