23 ideas
18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
18789 | Intuitionist logic looks best as natural deduction [Mares] |
18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
18782 | The connectives are studied either through model theory or through proof theory [Mares] |
18783 | Many-valued logics lack a natural deduction system [Mares] |
18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
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] |
18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
490 | Everything happens by reason and necessity [Leucippus] |
18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |