22 ideas
14092 | Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms [Rosen] |
14100 | Figuring in the definition of a thing doesn't make it a part of that thing [Rosen] |
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] |
17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
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] |
14096 | Explanations fail to be monotonic [Rosen] |
14097 | Things could be true 'in virtue of' others as relations between truths, or between truths and items [Rosen] |
14095 | Facts are structures of worldly items, rather like sentences, individuated by their ingredients [Rosen] |
14093 | An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations [Rosen] |
14094 | The excellent notion of metaphysical 'necessity' cannot be defined [Rosen] |
14101 | Are necessary truths rooted in essences, or also in basic grounding laws? [Rosen] |
14099 | 'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around [Rosen] |
14098 | An acid is just a proton donor [Rosen] |