32 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] |
16588 | I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine] |
22979 | Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine] |
22977 | I can distinguish different smells even when I am not experiencing them [Augustine] |
22982 | Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine] |
22981 | Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine] |
22980 | Memory contains innumerable principles of maths, as well as past sense experiences [Augustine] |
22983 | We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine] |
22978 | Memory is so vast that I cannot recognise it as part of my mind [Augustine] |
22984 | Without memory I could not even speak of myself [Augustine] |
5982 | If the future does not exist, how can prophets see it? [Augustine] |
22976 | Memories are preserved separately, according to category [Augustine] |
1757 | The Electra: she knows this man, but not that he is her brother [Eucleides, by Diog. Laertius] |
3028 | The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides] |
22985 | Everyone wants happiness [Augustine] |
5984 | Maybe time is an extension of the mind [Augustine] |
22888 | To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon] |
5980 | How can ten days ahead be a short time, if it doesn't exist? [Augustine] |
5979 | If the past is no longer, and the future is not yet, how can they exist? [Augustine] |
5981 | The whole of the current year is not present, so how can it exist? [Augustine] |
5978 | I know what time is, until someone asks me to explain it [Augustine] |
5983 | I disagree with the idea that time is nothing but cosmic movement [Augustine] |
5977 | Heaven and earth must be created, because they are subject to change [Augustine] |
22887 | If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon] |
5976 | If God is outside time in eternity, can He hear prayers? [Augustine] |