26 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] |
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] |
11993 | Jones may cease to exist without some simple property, but that doesn't make it essential [Kung] |
11997 | A property may belong essentially to one thing and contingently to another [Kung] |
11992 | Aristotelian essences underlie a thing's existence, explain it, and must belong to it [Kung] |
11995 | Some peripheral properties are explained by essential ones, but don't themselves explain properties [Kung] |
11996 | Some non-essential properties may explain more than essential-but-peripheral ones do [Kung] |
21278 | All the signs of design found in a watch are also found in nature [Paley] |
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] |