13 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] |
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] |
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] |
22375 | Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot] |
22377 | Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot] |
22378 | We can't affirm a duty without saying why it matters if it is not performed [Foot] |
22376 | Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |