10 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
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] |
9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
8070 | It would be better to point to failings of character, than to moral wrongness of actions [Anscombe] |
8065 | 'Ought' and 'right' are survivals from earlier ethics, and should be jettisoned [Anscombe] |
8069 | Between Aristotle and us, a Judaeo-Christian legal conception of ethics was developed [Anscombe] |