12 ideas
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] |
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
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] |
9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |