29 ideas
| 1642 | We must fight fiercely for knowledge, understanding and intelligence [Plato] |
| 1645 | The desire to split everything into its parts is unpleasant and unphilosophical [Plato] |
| 287 | Good analysis involves dividing things into appropriate forms without confusion [Plato] |
| 1644 | Dialectic should only be taught to those who already philosophise well [Plato] |
| 20478 | In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato] |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 11278 | What does 'that which is not' refer to? [Plato] |
| 1643 | If statements about non-existence are logically puzzling, so are statements about existence [Plato] |
| 7022 | To be is to have a capacity, to act on other things, or to receive actions [Plato] |
| 1641 | Some alarming thinkers think that only things which you can touch exist [Plato] |
| 10784 | Whenever there's speech it has to be about something [Plato] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 16122 | Good thinkers spot forms spread through things, or included within some larger form [Plato] |
| 10422 | The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato] |
| 15855 | If we see everything as separate, we can then give no account of it [Plato] |
| 1637 | A soul without understanding is ugly [Plato] |
| 1636 | Wickedness is an illness of the soul [Plato] |
| 1638 | Didactic education is hard work and achieves little [Plato] |