52 ideas
| 17651 | Without words or other symbols, we have no world [Goodman] |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| 17652 | Truth is irrelevant if no statements are involved [Goodman] |
| 15510 | Classes are a host of ethereal, platonic, pseudo entities [Goodman] |
| 9920 | Two objects can apparently make up quite distinct arrangements in sets [Goodman, by Burgess/Rosen] |
| 10657 | The counties of Utah, and the state, and its acres, are in no way different [Goodman] |
| 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] |
| 12394 | If the result is bad, we change the rule; if we like the rule, we reject the result [Goodman] |
| 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] |
| 17656 | Being primitive or prior always depends on a constructional system [Goodman] |
| 17661 | We don't recognise patterns - we invent them [Goodman] |
| 17659 | Reality is largely a matter of habit [Goodman] |
| 17657 | We build our world, and ignore anything that won't fit [Goodman] |
| 17654 | A world can be full of variety or not, depending on how we sort it [Goodman] |
| 14292 | Dispositions seem more ethereal than behaviour; a non-occult account of them would be nice [Goodman] |
| 7956 | If all and only red things were round things, we would need to specify the 'respect' of the resemblance [Goodman, by Macdonald,C] |
| 7957 | Without respects of resemblance, we would collect blue book, blue pen, red pen, red clock together [Goodman, by Macdonald,C] |
| 7952 | If we apply the same word to different things, it is only because we are willing to do so [Goodman, by Macdonald,C] |
| 17653 | Things can only be judged the 'same' by citing some respect of sameness [Goodman] |
| 12191 | Counterfactuals are true if logical or natural laws imply the consequence [Goodman, by McFetridge] |
| 17660 | Discovery is often just finding a fit, like a jigsaw puzzle [Goodman] |
| 411 | If we succeed in speaking the truth, we cannot know we have done it [Xenophanes] |
| 412 | If God had not created honey, men would say figs are sweeter [Xenophanes] |
| 17658 | Users of digital thermometers recognise no temperatures in the gaps [Goodman] |
| 17650 | We lack frames of reference to transform physics, biology and psychology into one another [Goodman] |
| 18749 | Goodman argued that the confirmation relation can never be formalised [Goodman, by Horsten/Pettigrew] |
| 17646 | Goodman showed that every sound inductive argument has an unsound one of the same form [Goodman, by Putnam] |
| 17655 | Grue and green won't be in the same world, as that would block induction entirely [Goodman] |
| 20440 | Art is a referential activity, hence indefinable, but it has a set of symptoms [Goodman] |
| 20439 | Artistic symbols are judged by the fruitfulness of their classifications [Goodman, by Giovannelli] |
| 8113 | Art is like understanding a natural language, and needs a grasp of a symbol system [Goodman, by Gardner] |
| 20438 | A performance is only an instance of a work if there is not a single error [Goodman] |
| 20437 | A copy only becomes an 'instance' of an artwork if there is a system of notation [Goodman] |
| 17649 | If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman] |
| 1640 | The basic Eleatic belief was that all things are one [Xenophanes, by Plato] |
| 4794 | We don't use laws to make predictions, we call things laws if we make predictions with them [Goodman] |
| 3055 | Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius] |
| 408 | Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes] |
| 407 | Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes] |