11 ideas
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
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] |
20660 | At one level maths and nature are very similar, suggesting some deeper origin [Wolfram] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
3178 | A fast machine could pass all behavioural tests with a vast lookup table [Block, by Rey] |
20659 | Space and its contents seem to be one stuff - so space is the only existing thing [Wolfram] |