10 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] |
6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |