12 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] |
9915 | V = L just says all sets are constructible [Putnam] |
13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
9913 | The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam] |
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] |
9914 | It is unfashionable, but most mathematical intuitions come from nature [Putnam] |
3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |