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] |
9470 | Modal logic is not an extensional language [Parsons,C] |
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] |
9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
15565 | Events have inbuilt essences, as necessary conditions for their occurrence [Lewis] |
15566 | Events are classes, and so there is a mereology of their parts [Lewis] |
15567 | Some events involve no change; they must, because causal histories involve unchanges [Lewis] |
15561 | The events that suit semantics may not be the events that suit causation [Lewis] |
15564 | An event is a property of a unique space-time region [Lewis] |
15563 | Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis] |
15562 | Causation is a general relation derived from instances of causal dependence [Lewis] |