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] |
19271 | No rule can be fully explained [Kripke] |
19269 | 'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke] |
7305 | Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A] |
19270 | If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke] |
11076 | Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna] |
11075 | The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna] |
12709 | Motion is not absolute, but consists in relation [Leibniz] |