21 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] |
21075 | The state of nature always involves the threat of war [Kant] |
20569 | Kant made the social contract international and cosmopolitan [Kant, by Oksala] |
21079 | The a priori general will of a people shows what is right [Kant] |
21077 | Each nation should, from self-interest, join an international security constitution [Kant] |
21078 | A constitution must always be improved when necessary [Kant] |
21076 | Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant] |
20570 | There is now a growing universal community, and violations of rights are felt everywhere [Kant] |
20571 | There are political and inter-national rights, but also universal cosmopolitan rights [Kant] |
21073 | Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant] |
21074 | Some trust in the enemy is needed during wartime, or peace would be impossible [Kant] |