17 ideas
| 23766 | Don't be tossed to and fro with every wind of doctrine, by cunning deceptive men [Paul] |
| 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] |
| 13195 | To explain a house we must describe its use, as well as its parts [Leibniz] |
| 13193 | Active force is not just potential for action, since it involves a real effort or striving [Leibniz] |
| 13194 | God's laws would be meaningless without internal powers for following them [Leibniz] |
| 13196 | All qualities of bodies reduce to forces [Leibniz] |
| 13192 | Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz] |