16 ideas
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| 22269 | We must fight fiercely to hang on to the few pleasures which survive into old age [Montaigne] |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| 535 | The gods are just personified human benefits [Prodicus] |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |