14 ideas
21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
23476 | Logical constants seem to be entities in propositions, but are actually pure form [Russell] |
23477 | We use logical notions, so they must be objects - but I don't know what they really are [Russell] |
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] |
18273 | Logical truths are known by their extreme generality [Russell] |
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] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
22315 | There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell] |
21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |