22 ideas
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
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] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
15464 | The distinction between dispositional and 'categorical' properties leads to confusion [Lewis] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
15463 | All dispositions must have causal bases [Lewis] |
15461 | A 'finkish' disposition is real, but disappears when the stimulus occurs [Lewis] |
15462 | Backtracking counterfactuals go from supposed events to their required causal antecedents [Lewis] |