12 ideas
17879 | Axiomatising set theory makes it all relative [Skolem] |
9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
16369 | There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati] |