16 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |