20 ideas
19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
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] |
13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
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] |
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
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] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
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] |
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] |