19 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] |
10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
10284 | There are three different standard presentations of semantics [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] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm] |
21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
1421 | A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm] |
21245 | The word 'God' can be denied, but understanding shows God must exist [Anselm] |
21246 | Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm] |
21247 | Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm] |
1420 | Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm] |