10 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] |
15312 | We get the idea of power by abstracting from ropes, magnets and electric shocks [Priestley] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
15311 | Attraction or repulsion are not imparted to matter, but actually constitute it [Priestley] |