25 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] |
8915 | How we refer to abstractions is much less clear than how we refer to other things [Rosen] |
8917 | The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen] |
8912 | Nowadays abstractions are defined as non-spatial, causally inert things [Rosen] |
8913 | Chess may be abstract, but it has existed in specific space and time [Rosen] |
8914 | Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen] |
8916 | Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen] |
8918 | Functional terms can pick out abstractions by asserting an equivalence relation [Rosen] |
8919 | Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen] |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |