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] |
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] |
19520 | Evidentialism is not axiomatic; the evidence itself inclines us towards evidentialism [Conee] |
19521 | If pure guesses were reliable, reliabilists would have to endorse them [Conee] |
19522 | More than actual reliability is needed, since I may mistakenly doubt what is reliable [Conee] |
19523 | Reliabilism is poor on reflective judgements about hypothetical cases [Conee] |
19555 | People begin to doubt whether they 'know' when the answer becomes more significant [Conee] |
19557 | Maybe low knowledge standards are loose talk; people will deny that it is 'really and truly' knowledge [Conee] |
19556 | Maybe knowledge has fixed standards (high, but attainable), although people apply contextual standards [Conee] |
12890 | That standards vary with context doesn't imply different truth-conditions for judgements [Conee] |
12892 | Maybe there is only one context (the 'really and truly' one) for serious discussions of knowledge [Conee] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |