23 ideas
22358 | Scientific objectivity lies in inter-subjective testing [Popper] |
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] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [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] |
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] |
22188 | Give Nobel Prizes for really good refutations? [Gorham on Popper] |
7780 | Falsification is the criterion of demarcation between science and non-science [Popper, by Magee] |
16830 | We don't only reject hypotheses because we have falsified them [Lipton on Popper] |
6794 | If falsification requires logical inconsistency, then probabilistic statements can't be falsified [Bird on Popper] |
6795 | When Popper gets in difficulties, he quietly uses induction to help out [Bird on Popper] |
3856 | Good theories have empirical content, explain a lot, and are not falsified [Popper, by Newton-Smith] |
7779 | There is no such thing as induction [Popper, by Magee] |
3860 | Science cannot be shown to be rational if induction is rejected [Newton-Smith on Popper] |
2798 | Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich] |
2799 | Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich] |