17 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] |
| 22142 | In future, only logical limits can be placed on divine omnipotence [Anon (Par), by Boulter] |
| 16716 | It is heresy to require self-evident foundational principles in order to be certain [Anon (Par)] |
| 6231 | There is a self-determing power in each person, which makes them what they are [Cudworth] |
| 1866 | It is heresy to teach that history repeats every 36,000 years [Anon (Par)] |
| 1865 | It is heresy to teach that natural impossibilities cannot even be achieved by God [Anon (Par)] |
| 1864 | It is heresy to teach that we can know God by his essence in this mortal life [Anon (Par)] |