15 ideas
12302 | Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K] |
14266 | Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K] |
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] |
14268 | Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K] |
14267 | There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K] |
14264 | Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
14265 | The components of abstract definitions could play the same role as matter for physical objects [Fine,K] |