15 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] |
13152 | We can talk of 'innumerable number', about the infinite points on a line [Newton] |
13151 | Not all infinites are equal [Newton] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
11127 | If concepts just are mental representations, what of concepts we may never acquire? [Peacocke] |
15863 | The principles of my treatise are designed to fit with a belief in God [Newton] |
8340 | I do not pretend to know the cause of gravity [Newton] |
13150 | The motions of the planets could only derive from an intelligent agent [Newton] |
12178 | That gravity should be innate and essential to matter is absurd [Newton] |