11 ideas
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
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] |
19701 | Fallibilism is consistent with dogmatism or scepticism, and is not alternative to them [Dougherty] |
19700 | It is best to see the fallibility in the reasons, rather than in the agents or the knowledge [Dougherty] |
19702 | We can't normally say that we know something 'but it might be false' [Dougherty] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |