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] |
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] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
7096 | We may still admire a person's character even if the traits are involuntary [Statman] |
7098 | There is a new sort of moral scepticism, about the possibility of moral theories [Statman] |
7099 | With a broad concept of flourishing, it might be possible without the virtues [Statman] |
7100 | Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman] |
7102 | Promises create moral duties that have nothing to do with character [Statman] |
7095 | Moral education is better by concrete example than abstract principle [Statman] |
7094 | Friends express friendship even when no utility is involved [Statman] |
7093 | Behaviour may be disgusting or inhumane, but violate no duty [Statman] |
7104 | The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman] |
7103 | Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman] |