21 ideas
3745 | Must sentences make statements to qualify for truth? [O'Connor] |
3742 | Beliefs must match facts, but also words must match beliefs [O'Connor] |
3744 | The semantic theory requires sentences as truth-bearers, not propositions [O'Connor] |
3749 | What does 'true in English' mean? [O'Connor] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
3746 | Logic seems to work for unasserted sentences [O'Connor] |
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] |
3747 | Events are fast changes which are of interest to us [O'Connor] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
490 | Everything happens by reason and necessity [Leucippus] |
3748 | Without language our beliefs are particular and present [O'Connor] |
3743 | We can't contemplate our beliefs until we have expressed them [O'Connor] |