31 ideas
6259 | Why can't a wise man doubt everything? [Montaigne] |
6263 | No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne] |
23122 | Montaigne was the founding father of liberalism [Montaigne, by Gopnik] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
6258 | Virtue is the distinctive mark of truth, and its greatest product [Montaigne] |
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] |
6262 | We lack some sense or other, and hence objects may have hidden features [Montaigne] |
6260 | Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
6261 | The soul is in the brain, as shown by head injuries [Montaigne] |
7496 | Rules and duties are based on the will, as that is all we control [Montaigne] |
7495 | Apart from the fear, dying is an easy duty [Montaigne] |
22269 | We must fight fiercely to hang on to the few pleasures which survive into old age [Montaigne] |
20482 | Virtue inspires Stoics, but I want a good temperament [Montaigne] |
20480 | There is not much point in only becoming good near the end of your life [Montaigne] |
20481 | Nothing we say can be worse than unsaying it in the face of authority [Montaigne] |
20479 | People at home care far more than soldiers risking death about the outcome of wars [Montaigne] |