20 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
17990 | Instances of minimal truth miss out propositions inexpressible in current English [Hofweber] |
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] |
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] |
17988 | Quantification can't all be substitutional; some reference is obviously to objects [Hofweber] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
17644 | Metaphysical realism is committed to there being one ultimate true theory [Putnam] |
17648 | It is an illusion to think there could be one good scientific theory of reality [Putnam] |
17989 | Since properties have properties, there can be a typed or a type-free theory of them [Hofweber] |
17643 | Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam] |
17642 | The old view that sense data are independent of mind is quite dotty [Putnam] |
17991 | Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber] |
17645 | An alien might think oxygen was the main cause of a forest fire [Putnam] |