19 ideas
13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [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] |
13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
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] |
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] |
9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
10286 | A 'set' is a mathematically well-behaved class [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] |
7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |