26 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] |
11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
11116 | Being a physical object is our most fundamental category [Jubien] |
11117 | Haecceities implausibly have no qualities [Jubien] |
11119 | De re necessity is just de dicto necessity about object-essences [Jubien] |
11118 | Modal propositions transcend the concrete, but not the actual [Jubien] |
11108 | Your properties, not some other world, decide your possibilities [Jubien] |
11111 | Modal truths are facts about parts of this world, not about remote maximal entities [Jubien] |
11105 | We have no idea how many 'possible worlds' there might be [Jubien] |
11107 | If there are no other possible worlds, do we then exist necessarily? [Jubien] |
11106 | If all possible worlds just happened to include stars, their existence would be necessary [Jubien] |
11112 | Possible worlds just give parallel contingencies, with no explanation at all of necessity [Jubien] |
11109 | If other worlds exist, then they are scattered parts of the actual world [Jubien] |
11113 | Worlds don't explain necessity; we use necessity to decide on possible worlds [Jubien] |
11110 | We mustn't confuse a similar person with the same person [Jubien] |
21097 | Modern monarchies are (like republics) rule by law, rather than by men [Hume] |