22 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] |
16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
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] |
16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
8510 | 'Socrates is wise' means a concurrence sum contains a member of a similarity set [Williams,DC] |
8508 | A 'trope' is an abstract particular, the occurrence of an essence [Williams,DC] |
8509 | A world is completely constituted by its tropes and their connections [Williams,DC] |
16981 | With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke] |
4942 | The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke] |
16984 | I don't think possible worlds reductively reveal the natures of modal operators etc. [Kripke] |
9385 | The very act of designating of an object with properties gives knowledge of a contingent truth [Kripke] |
4943 | Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke] |
16983 | Probability with dice uses possible worlds, abstractions which fictionally simplify things [Kripke] |