21 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] |
10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
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] |
19558 | Our own intuitions about whether we know tend to vacillate [Cohen,S] |
19561 | We shouldn't jump too quickly to a contextualist account of claims to know [Cohen,S] |
19563 | The context sensitivity of knowledge derives from its justification [Cohen,S] |
19560 | Contextualism is good because it allows knowledge, but bad because 'knowing' is less valued [Cohen,S] |
19559 | Contextualists slightly concede scepticism, but only in extremely strict contexts [Cohen,S] |