35 ideas
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| 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] |
| 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] |
| 11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
| 11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
| 11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
| 11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
| 11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
| 11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
| 11886 | There are problems both with individual essences and without them [Mackie,P] |
| 11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
| 11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
| 11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
| 11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
| 11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
| 11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
| 11892 | Things may only be counterparts under some particular relation [Mackie,P] |
| 11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
| 11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
| 11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
| 11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |
| 1558 | Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus] |