17 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
14231 | We should always apply someone's theory of meaning to their own utterances [Liggins] |
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] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [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] |
14232 | We normally formalise 'There are Fs' with singular quantification and predication, but this may be wrong [Liggins] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
14233 | Nihilists needn't deny parts - they can just say that some of the xs are among the ys [Liggins] |
299 | What is fine is always difficult [Plato] |
297 | What is fine is the parent of goodness [Plato] |
298 | While sex is very pleasant, it should be in secret, as it looks contemptible [Plato] |