29 ideas
7914 | To try to be wise all on one's own is folly [Rochefoucauld] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [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] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [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] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
13795 | Properties only have identity in the context of their contraries [Elder] |
13798 | Maybe we should give up the statue [Elder] |
13797 | The loss of an essential property means the end of an existence [Elder] |
13794 | Essential properties by nature occur in clusters or packages [Elder] |
13796 | Essential properties are bound together, and would be lost together [Elder] |
7118 | La Rochefoucauld's idea of disguised self-love implies an unconscious mind [Rochefoucauld, by Sartre] |
7912 | Judging by effects, love looks more like hatred than friendship [Rochefoucauld] |
7915 | Supreme cleverness is knowledge of the real value of things [Rochefoucauld] |
7917 | Realising our future misery is a kind of happiness [Rochefoucauld] |
7913 | Virtue doesn't go far without the support of vanity [Rochefoucauld] |
7916 | True friendship is even rarer than true love [Rochefoucauld] |
9299 | We are bored by people to whom we ourselves are boring [Rochefoucauld] |