30 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] |
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] |
5311 | If observation goes up a level, we expect the laws of the lower level to remain in force [Wilson,EO] |
5312 | A child first sees objects as distinct, and later as members of groups [Wilson,EO] |
5309 | Beliefs are really enabling mechanisms for survival [Wilson,EO] |
5310 | Philosophers study the consequences of ethics instead of its origins [Wilson,EO] |
5313 | The rules of human decision-making converge and overlap in a 'human nature' [Wilson,EO] |
5316 | We undermine altruism by rewarding it, but we reward it to encourage it [Wilson,EO] |
5318 | Pure hard-core altruism based on kin selection is the enemy of civilisation [Wilson,EO] |
5317 | The actor is most convincing who believes that his performance is real [Wilson,EO] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
5308 | The only human purpose is that created by our genetic history [Wilson,EO] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
5314 | Cultural evolution is Lamarckian and fast, biological evolution is Darwinian and slow [Wilson,EO] |
5315 | Over 99 percent of human evolution has been in the hunter-gatherer phase [Wilson,EO] |
5320 | It is estimated that mankind has produced 100,000 religions [Wilson,EO] |