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] |
17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
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] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |