19 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] |
14348 | An 'antidote' allows a manifestation to begin, but then blocks it [Corry] |
14347 | A 'finkish' disposition is one that is lost immediately after the appropriate stimulus [Corry] |
14350 | If a disposition is never instantiated, it shouldn't be part of our theory of nature [Corry] |
14351 | Maybe an experiment unmasks an essential disposition, and reveals its regularities [Corry] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
14346 | Dispositional essentialism says fundamental laws of nature are strict, not ceteris paribus [Corry] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |