25 ideas
9327 | Organisms understand their worlds better if they understand themselves [Gulick] |
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] |
9325 | In contrast with knowledge, the notion of understanding emphasizes practical engagement [Gulick] |
9326 | Knowing-that is a much richer kind of knowing-how [Gulick] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
9319 | Is consciousness a type of self-awareness, or is being self-aware a way of being conscious? [Gulick] |
9320 | Higher-order theories divide over whether the higher level involves thought or perception [Gulick] |
9321 | Higher-order models reduce the problem of consciousness to intentionality [Gulick] |
9322 | Maybe qualia only exist at the lower level, and a higher-level is needed for what-it-is-like [Gulick] |
9324 | From the teleopragmatic perspective, life is largely an informational process [Gulick] |