17 ideas
11257 | The Pythagoreans were the first to offer definitions [Politis, by Politis] |
11235 | 'True of' is applicable to things, while 'true' is applicable to words [Politis] |
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] |
11277 | Maybe 'What is being? is confusing because we can't ask what non-being is like [Politis] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
11248 | Necessary truths can be two-way relational, where essential truths are one-way or intrinsic [Politis] |
19399 | Prime matter is nothing when it is at rest [Leibniz] |