20 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] |
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] |
9169 | A statement can be metaphysically necessary and epistemologically contingent [Putnam] |
5819 | Conceivability is no proof of possibility [Putnam] |
8406 | Not all explanations are causal, but if a thing can be explained at all, it can be explained causally [Sanford] |
9168 | I can't distinguish elm trees, but I mean by 'elm' the same set of trees as everybody else [Putnam] |
5820 | 'Water' has an unnoticed indexical component, referring to stuff around here [Putnam] |
9170 | We need to recognise the contribution of society and of the world in determining reference [Putnam] |
5817 | Language is more like a cooperative steamship than an individual hammer [Putnam] |
8407 | A totality of conditions necessary for an occurrence is usually held to be jointly sufficient for it [Sanford] |
5818 | If water is H2O in the actual world, there is no possible world where it isn't H2O [Putnam] |