21 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] |
2526 | Philosophers regularly confuse failures of imagination with insights into necessity [Dennett] |
2523 | That every mammal has a mother is a secure reality, but without foundations [Dennett] |
2528 | Does consciousness need the concept of consciousness? [Dennett] |
2525 | Maybe language is crucial to consciousness [Dennett] |
2527 | Unconscious intentionality is the foundation of the mind [Dennett] |
2530 | Could a robot be made conscious just by software? [Dennett] |
2524 | A language of thought doesn't explain content [Dennett] |
2529 | Maybe there can be non-conscious concepts (e.g. in bees) [Dennett] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |