24 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
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] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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] |
14637 | Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael] |
14636 | Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael] |
14640 | Maybe essential properties have to be intrinsic, as well as necessary? [McMichael] |
14638 | Essentialism is false, because it implies the existence of necessary singular propositions [McMichael] |
22370 | Big central government only exists as a focus for anger - not to act [Fisher] |
22368 | It is hard to imagine the end of capitalism [Fisher] |
22369 | Are students consumers or products of education? [Fisher] |
14639 | Individuals enter into laws only through their general qualities and relations [McMichael] |