25 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
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] |
13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
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] |
10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [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] |
13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
5126 | A carelessly thrown brick is condemned much more if it hits someone [Smith,A, by Harman] |
20991 | People prepare our dinner from their own self-interest, not from humanity [Smith,A] |
20680 | Selfish profit-seeking increases collective wealth, so greed is good, and egoism is altruism [Smith,A, by Harari] |