21 ideas
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
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] |
8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
8193 | Verification is not an individual but a collective activity [Dummett] |
8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |