20 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] |
12184 | Logical necessity overrules all other necessities [McFetridge] |
15083 | The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale] |
15084 | In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale] |
12180 | Logical necessity requires that a valid argument be necessary [McFetridge] |
12181 | Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge] |
12183 | It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge] |
12192 | The mark of logical necessity is deduction from any suppositions whatever [McFetridge] |
12182 | We assert epistemic possibility without commitment to logical possibility [McFetridge] |
12187 | Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge] |
12186 | Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |