28 ideas
16123 | Whenever you perceive a community of things, you should also hunt out differences in the group [Plato] |
16125 | To reveal a nature, divide down, and strip away what it has in common with other things [Plato] |
16124 | No one wants to define 'weaving' just for the sake of weaving [Plato] |
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] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [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] |
18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
5961 | The soul gets its goodness from god, and its evil from previous existence. [Plato] |
9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
283 | The question of whether or not to persuade comes before the science of persuasion [Plato] |
5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
282 | Non-physical beauty can only be shown clearly by speech [Plato] |
281 | The arts produce good and beautiful things by preserving the mean [Plato] |
22559 | Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle] |
279 | Only divine things can always stay the same, and bodies are not like that [Plato] |