18 ideas
21918 | Sufficient Reason can't be proved, because all proof presupposes it [Schopenhauer, by Lewis,PB] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [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] |
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] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
21920 | No need for a priori categories, since sufficient reason shows the interrelations [Schopenhauer, by Lewis,PB] |
21362 | Necessity is physical, logical, mathematical or moral [Schopenhauer, by Janaway] |
21361 | For Schopenhauer, material things would not exist without the mind [Schopenhauer, by Janaway] |
21919 | Object for a subject and representation are the same thing [Schopenhauer] |
21917 | The four explanations: objects by causes, concepts by ground, maths by spacetime, ethics by motive [Schopenhauer, by Lewis,PB] |
21921 | Concepts are abstracted from perceptions [Schopenhauer, by Lewis,PB] |
21363 | Motivation is causality seen from within [Schopenhauer] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |