34 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] |
| 4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
| 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] |
| 9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
| 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] |
| 18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
| 10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
| 9264 | Persons are distinguished by a capacity for second-order desires [Frankfurt] |
| 9266 | A person essentially has second-order volitions, and not just second-order desires [Frankfurt] |
| 9267 | Free will is the capacity to choose what sort of will you have [Frankfurt] |
| 9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
| 4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
| 9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
| 4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |
| 9265 | The will is the effective desire which actually leads to an action [Frankfurt] |
| 20015 | Freedom of action needs the agent to identify with their reason for acting [Frankfurt, by Wilson/Schpall] |
| 9270 | A 'wanton' is not a person, because they lack second-order volitions [Frankfurt] |
| 9269 | A person may be morally responsible without free will [Frankfurt] |