14 ideas
| 5035 | The two basics of reasoning are contradiction and sufficient reason [Leibniz] |
| 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] |
| 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
| 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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] |
| 5038 | Assume that mind and body follow their own laws, but God has harmonised them [Leibniz] |
| 5037 | God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred [Leibniz] |