18 ideas
23248 | Early empiricists said reason was just a useless concept introduced by philosophers [Galen, by Frede,M] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
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] |
9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |