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Results tagged with incompleteness
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user 1329
30
votes
Can proof by contradiction work without the law of excluded middle?
Gödel's incompleteness is dragged in for a reason that I can discern. Gödel's incompleteness provides a sentence $G$ such that neither $G$ nor $\lnot G$ is provable. … So how is Gödel's incompleteness relevant here?
P.S. I apologize for the previous version of the supplemental which was rude. …
- 31.2k
6
votes
Did Wheeler really believe that physics was undecidable?
The inference "the universe would be completely computable, so no undecidable/uncomputable things could exist" is invalid.
In the effective topos, where everything is computable, there are many undec …
- 31.2k
5
votes
Accepted
Why decision problem definition ignores Gödel incompleteness theorem?
There is an important class of decisions problems which have no solutions because of Gödel's incompleteness theorem. …
- 31.2k
4
votes
Does the first incompleteness theorem imply that any Turing complete programming language mu...
Gödel's incompleteness theorems do not apply to them, because the formal systems do not even incorporate first-order logic. …
- 31.2k