16 ideas
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 18383 | Plantinga says there is just this world, with possibilities expressed in propositions [Plantinga, by Armstrong] |
| 11891 | Possibilities for an individual can only refer to that individual, in some possible world [Plantinga, by Mackie,P] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| 20704 | A possible world contains a being of maximal greatness - which is existence in all worlds [Plantinga, by Davies,B] |