9 ideas
21960 | Ordinary language is the beginning of philosophy, but there is much more to it [Austin,JL] |
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
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] |
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
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] |