33 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] |
| 13134 | We negate predicates but do not negate names [Westerhoff] |
| 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] |
| 13117 | How far down before we are too specialised to have a category? [Westerhoff] |
| 13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
| 13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
| 13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
| 13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
| 13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
| 13124 | Categories can be ordered by both containment and generality [Westerhoff] |
| 13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
| 13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
| 13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
| 13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
| 13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
| 22456 | Maybe virtues conflict with each other, if some virtue needs a vice for its achievement [Foot] |