32 ideas
| 20768 | Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius] |
| 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] |
| 3926 | The human heart has a natural concern for public good [Hume] |
| 3929 | No moral theory is of any use if it doesn't serve the interests of the individual concerned [Hume] |
| 3925 | Personal Merit is the possession of useful or agreeable mental qualities [Hume] |
| 3049 | The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius] |
| 3922 | Justice only exists to support society [Hume] |
| 23560 | If we all naturally had everything we could ever desire, the virtue of justice would be irrelevant [Hume] |
| 3549 | Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas] |
| 3918 | Moral philosophy aims to show us our duty [Hume] |
| 3919 | Conclusions of reason do not affect our emotions or decisions to act [Hume] |
| 3928 | Virtue just requires careful calculation and a preference for the greater happiness [Hume] |
| 3923 | No one would cause pain to a complete stranger who happened to be passing [Hume] |
| 3924 | Nature makes private affections come first, because public concerns are spread too thinly [Hume] |
| 3921 | The safety of the people is the supreme law [Hume] |
| 3927 | Society prefers helpful lies to harmful truth [Hume] |
| 3920 | If you equalise possessions, people's talents will make them unequal again [Hume] |