16 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] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [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] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |