25 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
10365 | We might use 'facta' to refer to the truth-makers for facts [Mellor, by Schaffer,J] |
18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
10284 | There are three different standard presentations of semantics [Hodges,W] |
10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
8568 | A property is merely a constituent of laws of nature; temperature is just part of thermodynamics [Mellor] |
8564 | There is obviously a possible predicate for every property [Mellor] |
8566 | We need universals for causation and laws of nature; the latter give them their identity [Mellor] |
8565 | If properties were just the meanings of predicates, they couldn't give predicates their meaning [Mellor] |
4785 | Causal statements relate facts (which are whatever true propositions express) [Mellor, by Psillos] |
8567 | Singular causation requires causes to raise the physical probability of their effects [Mellor] |
8408 | Probabilistic causation says C is a cause of E if it increases the chances of E occurring [Mellor, by Tooley] |