21 ideas
291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
22864 | Philosophy is the study and criticsm of cultural beliefs, to achieve new possibilities [Dewey] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
22873 | Liberalism should improve the system, and not just ameliorate it [Dewey] |
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] |
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] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
22869 | Knowledge is either the product of competent enquiry, or it is meaningless [Dewey] |
22867 | The quest for certainty aims for peace, and avoidance of the stress of action [Dewey] |
22870 | No belief can be so settled that it is not subject to further inquiry [Dewey] |
22866 | Mind is never isolated, but only exists in its interactions [Dewey] |
293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |
22872 | Liberals aim to allow individuals to realise their capacities [Dewey] |
22880 | The things in civilisation we prize are the products of other members of our community [Dewey] |
22879 | 'God' is an imaginative unity of ideal values [Dewey] |
22877 | We should try attaching the intensity of religious devotion to intelligent social action [Dewey] |
22878 | Religions are so shockingly diverse that they have no common element [Dewey] |