13 ideas
19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
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] |
19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
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] |
23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |