29 ideas
| 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] |
| 20429 | Most of us are too close to our own motives to understand them [Fry] |
| 20424 | Imaginative life requires no action, so new kinds of perception and values emerge in art [Fry] |
| 20427 | Everyone reveals an aesthetic attitude, looking at something which only exists to be seen [Fry] |
| 20433 | 'Beauty' can either mean sensuous charm, or the aesthetic approval of art (which may be ugly) [Fry] |
| 20430 | In life we neglect 'cosmic emotion', but it matters, and art brings it to the fore [Fry] |
| 20431 | Art needs a mixture of order and variety in its sensations [Fry] |
| 20423 | If graphic arts only aim at imitation, their works are only trivial ingenious toys [Fry] |
| 20428 | Popular opinion favours realism, yet most people never look closely at anything! [Fry] |
| 20432 | When viewing art, rather than flowers, we are aware of purpose, and sympathy with its creator [Fry] |
| 20425 | In the cinema the emotions are weaker, but much clearer than in ordinary life [Fry] |
| 20426 | For pure moralists art must promote right action, and not just be harmless [Fry] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |