22 ideas
16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
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] |
16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
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] |
16981 | With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke] |
4942 | The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke] |
16984 | I don't think possible worlds reductively reveal the natures of modal operators etc. [Kripke] |
9385 | The very act of designating of an object with properties gives knowledge of a contingent truth [Kripke] |
4943 | Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke] |
16983 | Probability with dice uses possible worlds, abstractions which fictionally simplify things [Kripke] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |