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Full Idea
I uphold the belief that for clear questions posed by reason, reason can also find clear answers.
Gist of Idea
For clear questions posed by reason, reason can also find clear answers
Source
Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5
Book Ref
-: 'Philosophia Mathematica' [-], p.12
A Reaction
[written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems.
Related Ideas
Idea 12461 We believe all mathematical problems are solvable [Hilbert]
Idea 9812 In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]
| 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] |