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] |
| 15510 | Classes are a host of ethereal, platonic, pseudo entities [Goodman] |
| 9920 | Two objects can apparently make up quite distinct arrangements in sets [Goodman, by Burgess/Rosen] |
| 10657 | The counties of Utah, and the state, and its acres, are in no way different [Goodman] |
| 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] |
| 7956 | If all and only red things were round things, we would need to specify the 'respect' of the resemblance [Goodman, by Macdonald,C] |
| 7957 | Without respects of resemblance, we would collect blue book, blue pen, red pen, red clock together [Goodman, by Macdonald,C] |
| 7952 | If we apply the same word to different things, it is only because we are willing to do so [Goodman, by Macdonald,C] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 16978 | If conceivability is a priori coherence, that implies possibility [Tahko] |
| 16975 | Essences are used to explain natural kinds, modality, and causal powers [Tahko] |
| 16976 | Scientific essentialists tend to characterise essence in terms of modality (not vice versa) [Tahko] |
| 16977 | If essence is modal and laws are necessary, essentialist knowledge is found by scientists [Tahko] |