16 ideas
| 2661 | Dialectic is speech cast in the form of logical argument [Cicero] |
| 2673 | There cannot be more than one truth [Cicero] |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
| 2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
| 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] |
| 2664 | If we have complete healthy senses, what more could the gods give us? [Cicero] |
| 2665 | How can there be a memory of what is false? [Cicero] |
| 20800 | Every true presentation can have a false one of the same quality [Cicero] |
| 2672 | Virtues must be very detached, to avoid being motivated by pleasure [Cicero] |