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] |
17879 | Axiomatising set theory makes it all relative [Skolem] |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
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] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
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] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
13197 | The notion of substance is one of the keys to true philosophy [Leibniz] |
13198 | Gravity is within matter because of its structure, and it can be explained. [Leibniz] |