13 ideas
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| 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] |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| 8921 | Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman] |
| 8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |