17 ideas
8942 | Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher] |
13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
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] |
13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
22328 | I just confront the evidence, and let it act on me [Ramsey] |
22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |