13 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] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
19400 | Possibles demand existence, so as many of them as possible must actually exist [Leibniz] |
19401 | God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz] |
19402 | The actual universe is the richest composite of what is possible [Leibniz] |
16006 | Either Abraham rises higher than universal ethics, or he is a mere murderer [Kierkegaard] |
7577 | Abraham was willing to suspend ethics, for a higher idea [Kierkegaard] |