23 ideas
9184 | We can't presume that all interesting concepts can be analysed [Williamson] |
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] |
7332 | There is a huge range of sentences of which we do not know the logical form [Davidson] |
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] |
9183 | Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson] |
7772 | Compositionality explains how long sentences work, and truth conditions are the main compositional feature [Davidson, by Lycan] |
7327 | Davidson thinks Frege lacks an account of how words create sentence-meaning [Davidson, by Miller,A] |
7769 | You can state truth-conditions for "I am sick now" by relativising it to a speaker at a time [Davidson, by Lycan] |
6179 | Should we assume translation to define truth, or the other way around? [Blackburn on Davidson] |