20 ideas
9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
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] |
9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |
20761 | If existence is absurd it can never have a meaning [Beauvoir] |