24 ideas
2764 | Full coherence might involve consistency and mutual entailment of all propositions [Blanshard, by Dancy,J] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
19080 | Coherence tests for truth without implying correspondence, so truth is not correspondence [Blanshard, by Young,JO] |
8250 | So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra] |
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] |
10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
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] |
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] |
10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [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] |
8719 | There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend] |
8971 | There are objects of which it is true that there are no such objects [Meinong] |
8718 | Meinong says an object need not exist, but must only have properties [Meinong, by Friend] |
7756 | Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan] |
15781 | The objects of knowledge are far more numerous than objects which exist [Meinong] |