26 ideas
2945 | Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer] |
2946 | You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer] |
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] |
9329 | Justification is coherence with a background system; if irrefutable, it is knowledge [Lehrer] |
9330 | Generalization seems to be more fundamental to minds than spotting similarities [Lehrer] |
9328 | All conscious states can be immediately known when attention is directed to them [Lehrer] |
21277 | Even an imperfect machine can exhibit obvious design [Paley] |
21275 | Unlike a stone, the parts of a watch are obviously assembled in order to show the time [Paley] |
21276 | From the obvious purpose and structure of a watch we must infer that it was designed [Paley] |
21357 | No organ shows purpose more obviously than the eyelid [Paley] |
21278 | All the signs of design found in a watch are also found in nature [Paley] |