25 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] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [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] |
14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
12031 | Essences are taken to be qualitative properties [Adams,RM] |
12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |