22 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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
17402 | Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri] |
17399 | Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev] |
17400 | Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri] |
17401 | Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |