28 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] |
16706 | Generation is when local motions aggregate to become a single subject [Nicholas of Autrecourt] |
17472 | Thick mechanisms map whole reactions, and thin mechanism chart the steps [Weisberg/Needham/Hendry] |
17471 | Using mechanisms as explanatory schemes began in chemistry [Weisberg/Needham/Hendry] |
17465 | Lavoisier's elements included four types of earth [Weisberg/Needham/Hendry] |
17468 | Over 100,000,000 compounds have been discovered or synthesised [Weisberg/Needham/Hendry] |
17470 | Water molecules dissociate, and form large polymers, explaining its properties [Weisberg/Needham/Hendry] |
17473 | It is unlikely that chemistry will ever be reduced to physics [Weisberg/Needham/Hendry] |
17474 | Quantum theory won't tell us which structure a set of atoms will form [Weisberg/Needham/Hendry] |
17475 | For temperature to be mean kinetic energy, a state of equilibrium is also required [Weisberg/Needham/Hendry] |
17469 | 'H2O' just gives the element proportions, not the microstructure [Weisberg/Needham/Hendry] |
17467 | Isotopes (such as those of hydrogen) can vary in their rates of chemical reaction [Weisberg/Needham/Hendry] |
17466 | Mendeleev systematised the elements, and also gave an account of their nature [Weisberg/Needham/Hendry] |