15 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] |
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| 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] |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |