30 ideas
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] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [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] |
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] |
7647 | The imagination alone perceives all objects; it is the soul, playing all its roles [La Mettrie] |
7645 | When falling asleep, the soul becomes paralysed and weak, just like the body [La Mettrie] |
23225 | The soul's faculties depend on the brain, and are simply the brain's organisation [La Mettrie] |
7652 | Man is a machine, and there exists only one substance, diversely modified [La Mettrie] |
7650 | All thought is feeling, and rationality is the sensitive soul contemplating reasoning [La Mettrie] |
7651 | With wonderful new machines being made, a speaking machine no longer seems impossible [La Mettrie] |
24073 | Capitalists use their exceptional power to impose their own rules, and make the state their ally [Davies,W] |
24070 | Economies have material, economic and capitalist layers [Davies,W] |
24074 | Capitalism must mainly rely either on the labour market, or on the financial markets [Davies,W] |
24072 | Capitalism is the anti-market, with opacity, monopolies, powers, exceptional profits and wealth [Davies,W] |
24071 | Markets are transparent, with known prices and activity, and minimal profits [Davies,W] |
7648 | The sun and rain weren't made for us; they sometimes burn us, or spoil our seeds [La Mettrie] |
7646 | There is no abrupt transition from man to animal; only language has opened a gap [La Mettrie] |
7649 | There is no clear idea of the soul, which should only refer to our thinking part [La Mettrie] |