24 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] |
| 14329 | Some dispositional properties (such as mental ones) may have no categorical base [Price,HH] |
| 9032 | Before we can abstract from an instance of violet, we must first recognise it [Price,HH] |
| 9035 | If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH] |
| 9034 | There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH] |
| 9036 | There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH] |
| 9037 | Intelligent behaviour, even in animals, has something abstract about it [Price,HH] |
| 9033 | Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH] |
| 9030 | Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH] |
| 9029 | If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH] |
| 9031 | The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH] |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |