31 ideas
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| 4748 | Anselm of Canterbury identified truth with God [Anselm, by Engel] |
| 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] |
| 20100 | Classical liberalism seeks freedom of opinion, of private life, of expression, and of property [Micklethwait/Wooldridge] |
| 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] |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| 10481 | Models in model theory are structures, not sets of descriptions [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] |
| 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] |
| 20097 | The welfare state aims at freedom from want, and equality of opportunity [Micklethwait/Wooldridge] |
| 20099 | For communists history is driven by the proletariat [Micklethwait/Wooldridge] |
| 20098 | Fans of economic freedom claim that capitalism is self-correcting [Micklethwait/Wooldridge] |
| 20096 | Roman law entrenched property rights [Micklethwait/Wooldridge] |
| 21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
| 21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
| 21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
| 21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [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] |