15 ideas
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
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] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
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] |
9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
9969 | The empty set is the purest abstract object [Jubien] |
4921 | Quantum states in microtubules could bind brain activity to produce consciousness [Penrose] |