19 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] |
9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
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] |
9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
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] |
9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
7295 | Maybe induction is only reliable IF reality is stable [Mitchell,A] |
9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |