31 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] |
| 11181 | Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)] |
| 11184 | Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [Marcus (Barcan)] |
| 11180 | Essentialist sentences are not theorems of modal logic, and can even be false [Marcus (Barcan)] |
| 11186 | 'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical [Marcus (Barcan)] |
| 11185 | 'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted [Marcus (Barcan)] |
| 12177 | Human artefacts may have essences, in their purposes [Popper] |
| 11182 | If essences are objects with only essential properties, they are elusive in possible worlds [Marcus (Barcan)] |
| 11183 | The use of possible worlds is to sort properties (not to individuate objects) [Marcus (Barcan)] |
| 11187 | In possible worlds, names are just neutral unvarying pegs for truths and predicates [Marcus (Barcan)] |
| 12176 | Science does not aim at ultimate explanations [Popper] |
| 11189 | Dispositional essences are special, as if an object loses them they cease to exist [Marcus (Barcan)] |
| 12175 | Galilean science aimed at true essences, as the ultimate explanations [Popper] |
| 12179 | Essentialist views of science prevent further questions from being raised [Popper] |