36 ideas
6161 | Structuralism is neo-Kantian idealism, with language playing the role of categories of understanding [Rowlands] |
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] |
6163 | If bivalence is rejected, then excluded middle must also be rejected [Rowlands] |
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] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
6155 | Supervenience is a one-way relation of dependence or determination between properties [Rowlands] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
6154 | It is argued that wholes possess modal and counterfactual properties that parts lack [Rowlands] |
6157 | Tokens are dated, concrete particulars; types are their general properties or kinds [Rowlands] |
6159 | Strong idealism is the sort of mess produced by a Cartesian separation of mind and world [Rowlands] |
6152 | Minds are rational, conscious, subjective, self-knowing, free, meaningful and self-aware [Rowlands] |
6173 | Content externalism implies that we do not have privileged access to our own minds [Rowlands] |
6174 | If someone is secretly transported to Twin Earth, others know their thoughts better than they do [Rowlands] |
6158 | Supervenience of mental and physical properties often comes with token-identity of mental and physical particulars [Rowlands] |
6168 | The content of a thought is just the meaning of a sentence [Rowlands] |
6167 | Action is bodily movement caused by intentional states [Rowlands] |
6177 | Moral intuition seems unevenly distributed between people [Rowlands] |
6156 | The 17th century reintroduced atoms as mathematical modes of Euclidean space [Rowlands] |
6170 | Natural kinds are defined by their real essence, as in gold having atomic number 79 [Rowlands] |
6178 | It is common to see the value of nature in one feature, such as life, diversity, or integrity [Rowlands] |