13 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [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] |
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] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
3597 | Foundations need not precede other beliefs [Wittgenstein] |
3596 | Total doubt can't even get started [Wittgenstein, by Williams,M] |
4721 | If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein] |