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] |
15789 | Lewis's distinction of 'existing' from 'being actual' is Meinong's between 'existing' and 'subsisting' [Lycan on Lewis] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
15790 | Lewis can't know possible worlds without first knowing what is possible or impossible [Lycan on Lewis] |
15791 | What are the ontological grounds for grouping possibilia into worlds? [Lycan on Lewis] |
19698 | Deviant causal chain: a reason causes an action, but isn't the reason for which it was performed [Davidson, by Neta] |