40 ideas
| 1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
| 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] |
| 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] |
| 3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
| 23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
| 23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
| 23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
| 23128 | The opposite of liberalism is dogmatism [Gopnik] |
| 23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
| 23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
| 23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
| 23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
| 23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
| 23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
| 23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
| 23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
| 23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
| 23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
| 23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
| 23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
| 23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
| 23136 | Liberal free speech is actually paid speech [Gopnik] |
| 23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |
| 1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
| 1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
| 1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |