19 ideas
15527 | Defining terms either enables elimination, or shows that they don't require elimination [Lewis] |
13838 | A decent modern definition should always imply a semantics [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] |
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] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
15453 | The main rivals to universals are resemblance or natural-class nominalism, or sparse trope theory [Lewis] |
15452 | We could not uphold a truthmaker for 'Fa' without structures [Lewis] |
15530 | A logically determinate name names the same thing in every possible world [Lewis] |
15531 | The Ramsey sentence of a theory says that it has at least one realisation [Lewis] |
15528 | A Ramsey sentence just asserts that a theory can be realised, without saying by what [Lewis] |
15526 | There is a method for defining new scientific terms just using the terms we already understand [Lewis] |
15529 | It is better to have one realisation of a theory than many - but it may not always be possible [Lewis] |