27 ideas
4901 | Truth has to be correspondence to facts, and a match between relations of ideas and relations in the world [Perry] |
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] |
4885 | Identity is a very weak relation, which doesn't require interdefinability, or shared properties [Perry] |
23283 | Necessity implies possibility, but in experience it matters which comes first [Williams,B] |
4899 | Possible worlds thinking has clarified the logic of modality, but is problematic in epistemology [Perry] |
4898 | Possible worlds are indices for a language, or concrete realities, or abstract possibilities [Perry] |
4887 | We try to cause other things to occur by causing mental events to occur [Perry] |
4884 | Brain states must be in my head, and yet the pain seems to be in my hand [Perry] |
4888 | It seems plausible that many animals have experiences without knowing about them [Perry] |
4891 | If epiphenomenalism just says mental events are effects but not causes, it is consistent with physicalism [Perry] |
4900 | Prior to Kripke, the mind-brain identity theory usually claimed that the identity was contingent [Perry] |
4892 | If physicalists stick with identity (not supervenience), Martian pain will not be like ours [Perry] |
4889 | Although we may classify ideas by content, we individuate them differently, as their content can change [Perry] |
4896 | The intension of an expression is a function from possible worlds to an appropriate extension [Perry] |
4897 | A proposition is a set of possible worlds for which its intension delivers truth [Perry] |
4890 | A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry] |