15 ideas
18261 | A simplification which is complete constitutes a definition [Kant] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
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] |
18260 | If we knew what we know, we would be astonished [Kant] |
23683 | Moral norms are objective, connected to facts about human goods [Foot, by Hacker-Wright] |
23684 | Morality gives everyone reasons to act, irrespective of their desires [Foot, by Hacker-Wright] |
23690 | We all have reason to cultivate the virtues, even when we lack the desire [Foot, by Hacker-Wright] |
22379 | The meaning of 'good' and other evaluations must include the object to which they attach [Foot] |