17 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
18469 | God might necessitate that something happen, but He is not the truth-maker for it [Smith,B] |
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] |
22392 | Morality is inescapable, in descriptive words such as 'dishonest', 'unjust' and 'uncharitable' [Foot] |
23685 | Reason is not a motivator of morality [Foot, by Hacker-Wright] |
23691 | Rejecting moral rules may be villainous, but it isn't inconsistent [Foot] |
22391 | Saying we 'ought to be moral' makes no sense, unless it relates to some other system [Foot] |
22389 | Morality no more consists of categorical imperatives than etiquette does [Foot] |