16 ideas
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |