14 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| 13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| 13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
| 13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
| 13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
| 13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| 13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |