38 ideas
| 23728 | Analysis aims to express the full set of platitudes surrounding a given concept [Smith,M] |
| 23744 | Defining a set of things by paradigms doesn't pin them down enough [Smith,M] |
| 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] |
| 23743 | Capturing all the common sense facts about rationality is almost impossible [Smith,M] |
| 23739 | Goals need desires, and so only desires can motivate us [Smith,M] |
| 23724 | A pure desire could be criticised if it were based on a false belief [Smith,M] |
| 23736 | A person can have a desire without feeling it [Smith,M] |
| 23723 | In the Humean account, desires are not true/false, or subject to any rational criticism [Smith,M] |
| 23735 | Subjects may be fallible about the desires which explain their actions [Smith,M] |
| 23738 | Humeans (unlike their opponents) say that desires and judgements can separate [Smith,M] |
| 23742 | If first- and second-order desires conflict, harmony does not require the second-order to win [Smith,M] |
| 23746 | Objective reasons to act might be the systematic desires of a fully rational person [Smith,M] |
| 23733 | Motivating reasons are psychological, while normative reasons are external [Smith,M] |
| 23740 | Humeans take maximising desire satisfaction as the normative reasons for actions [Smith,M] |
| 23745 | We cannot expect even fully rational people to converge on having the same desires for action [Smith,M] |
| 23731 | 'Externalists' say moral judgements are not reasons, and maybe not even motives [Smith,M] |
| 23732 | A person could make a moral judgement without being in any way motivated by it [Smith,M] |
| 23729 | Moral internalism says a judgement of rightness is thereby motivating [Smith,M] |
| 23730 | 'Rationalism' says the rightness of an action is a reason to perform it [Smith,M] |
| 23727 | Expressivists count attitudes as 'moral' if they concern features of things, rather than their mere existence [Smith,M] |
| 23741 | Is valuing something a matter of believing or a matter of desiring? [Smith,M] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |