14 ideas
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] |
13168 | My formal unifying atoms are substantial forms, which are forces like appetites [Leibniz] |
13169 | I call Aristotle's entelechies 'primitive forces', which originate activity [Leibniz] |
13170 | The analysis of things leads to atoms of substance, which found both composition and action [Leibniz] |
13171 | Substance must necessarily involve progress and change [Leibniz] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
13167 | We need the metaphysical notion of force to explain mechanics, and not just extended mass [Leibniz] |