21 ideas
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] |
15086 | Absolute necessity might be achievable either logically or metaphysically [Hale] |
8261 | Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale] |
15080 | 'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale] |
15081 | A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale] |
15082 | Metaphysical necessity says there is no possibility of falsehood [Hale] |
15085 | 'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale] |
15088 | Logical necessities are true in virtue of the nature of all logical concepts [Hale] |
15087 | Conceptual necessities are made true by all concepts [Hale] |
20795 | Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus] |
20794 | How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus] |