26 ideas
21900 | Deleuze relies on Spinoza (immanence), Bergson (duration), and difference (Nietzsche) [May] |
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] |
23513 | Single neurons can carry out complex functions [Seth] |
23514 | The cerbellum has a huge number of neurons, but little involvement in consciousness [Seth] |
23516 | Maybe a system is conscious if the whole generates more information than its parts [Seth] |
23519 | The self is embodied, perspectival, volitional, narrative and social [Seth, by PG] |
23518 | Modern AI is mostly machine-based pattern recognition [Seth] |
23517 | Volition is felt as doing what you want, with possible alternatives, and a source from within [Seth] |
23515 | Human exceptionalism plagues biology, and most other human thinking [Seth] |
21898 | For existentialists the present is empty without the pull of the future and weight of the past [May] |
21905 | Liberal theory starts from the governed, not from the governor [May] |