21 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
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] |
14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
5987 | Alcmaeon was the first to say the brain is central to thinking [Alcmaeon, by Staden, von] |
24043 | Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle] |