17 ideas
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| 9969 | The empty set is the purest abstract object [Jubien] |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |