9 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] |
10558 | Abstract objects are actually constituted by the properties by which we conceive them [Zalta] |
10557 | Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta] |
15788 | Syntax and semantics are indeterminate, and modern 'semantics' is a bogus subject [Quine, by Lycan] |