23 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
20320 | Truth is what unites, and the profound truths create a community [Jaspers] |
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] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [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] |
20323 | Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers] |
20322 | I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers] |
20324 | My freedom increases as I broaden my vision of possiblities and motives [Jaspers] |
20321 | The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers] |
20318 | My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers] |
20325 | Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers] |
7073 | I am a creative nothing, out of which I myself create everything [Stirner] |
20315 | 'Existenz' is the potential being, which I could have, and ought to have [Jaspers] |
20317 | Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers] |
20319 | We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers] |
20316 | Every decision I make moves towards or away from fulfilled Existenz [Jaspers] |