12 ideas
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
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] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
18671 | The ground for an attitude is not a thing's 'goodness', but its concrete characteristics [Ewing] |