27 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| 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] |
| 23865 | Morality would improve if people could pursue private interests [Weil] |
| 23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
| 23871 | No central authority can initiate decentralisation [Weil] |
| 23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
| 23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
| 23863 | Only individual people of good will can achieve social progress [Weil] |
| 23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
| 23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
| 23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
| 23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |