29 ideas
20320 | Truth is what unites, and the profound truths create a community [Jaspers] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
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] |
20318 | My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers] |
20321 | The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers] |
20325 | Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [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] |
20315 | 'Existenz' is the potential being, which I could have, and ought to have [Jaspers] |
20316 | Every decision I make moves towards or away from fulfilled Existenz [Jaspers] |
4050 | We only allow voluntary euthanasia to someone who is both sane and crazed by pain [Kamisar] |
4051 | People will volunteer for euthanasia because they think other people want them dead [Kamisar] |