36 ideas
| 4262 | If the only aim was consistent beliefs then new evidence and experiments would be irrelevant [Goldman] |
| 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] |
| 4045 | Children may have three innate principles which enable them to learn to count [Goldman] |
| 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] |
| 4044 | Rat behaviour reveals a considerable ability to count [Goldman] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 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] |
| 4048 | Infant brains appear to have inbuilt ontological categories [Goldman] |
| 4043 | Elephants can be correctly identified from as few as three primitive shapes [Goldman] |
| 4049 | The way in which colour experiences are evoked is physically odd and unpredictable [Goldman] |
| 4047 | Gestalt psychology proposes inbuilt proximity, similarity, smoothness and closure principles [Goldman] |
| 8830 | A belief can be justified when the person has forgotten the evidence for it [Goldman] |
| 6871 | We can't only believe things if we are currently conscious of their justification - there are too many [Goldman] |
| 6872 | Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman] |
| 6874 | Internal justification needs both mental stability and time to compute coherence [Goldman] |
| 8832 | If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman] |
| 6873 | Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman] |
| 8829 | Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman] |
| 6875 | Reliability involves truth, and truth is external [Goldman] |
| 8831 | Introspection is really retrospection; my pain is justified by a brief causal history [Goldman] |