17 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] |
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] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
19382 | Abstracta are abbreviated ways of talking; there are just substances, and truths about them [Leibniz] |
7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |