21 ideas
19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
19067 | A successful proof requires recognition of truth at every step [Dummett] |
19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
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] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |