12 ideas
10051 | The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism [Kneale,W and M] |
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] |
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] |
19480 | Process philosophy places the dynamic nature of being at the centre of our theories [Seibt] |
19479 | Reductionists identify processes by their 'owner', but tornadoes etc. are processes without owners [Seibt] |
19481 | Traditionally small things add up to processes, but quantum mechanics reverses this [Seibt] |