34 ideas
22496 | Wisdom only implies the knowledge achievable in any normal lifetime [Foot] |
23877 | Most people won't question an idea's truth if they depend on it [Weil] |
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] |
23878 | Weakness of will is the inadequacy of the original impetus to carry through the action [Weil] |
23694 | All criterions of practical rationality derive from goodness of will [Foot] |
23686 | Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright] |
23693 | Practical rationality must weigh both what is morally and what is non-morally required [Foot] |
23687 | Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright] |
23879 | In a violent moral disagreement, it can't be that both sides are just following social morality [Weil] |
22493 | Sterility is a human defect, but the choice to be childless is not [Foot] |
22492 | Virtues are as necessary to humans as stings are to bees [Foot] |
22491 | Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot] |
22497 | Deep happiness usually comes from the basic things in life [Foot] |
22498 | Happiness is enjoying the pursuit and attainment of right ends [Foot] |
23695 | Good actions can never be justified by the good they brings to their agent [Foot] |
22499 | We all know that just pretending to be someone's friend is not the good life [Foot] |
22495 | Someone is a good person because of their rational will, not their body or memory [Foot] |
22502 | Refraining from murder is not made good by authenticity or self-fulfilment [Foot] |
23880 | When war was a profession, customary morality justified any act of war [Weil] |