19 ideas
8000 | He who is ignorant of the history of philosophy is doomed to repeat it [Santayana, by MacIntyre] |
23269 | Philosophy must start from clearly observed facts [Galen] |
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] |
23266 | The spirit in the soul wants freedom, power and honour [Galen] |
23219 | Stopping the heart doesn't terminate activity; pressing the brain does that [Galen, by Cobb] |
23264 | Philosophers think faculties are in substances, and invent a faculty for every activity [Galen] |
23220 | The brain contains memory and reason, and is the source of sensation and decision [Galen] |
23265 | The rational part of the soul is the desire for truth, understanding and recollection [Galen] |
23268 | We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life [Galen] |