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Are there any uses or applications for Gödel's theorems (other than their mere implications)?
by nthcolumn 9y ago
Are there any uses or applications for Gödel's theorems (other than their mere implications)?
- drdeca 9y agoMaybe stuff with Löb's theorem?
- atqtion 9y ago> Are there any uses or applications for Gödel's theorems (other than their mere implications)? Theorems are implications, so I'm not quite sure what you mean. There are practical applications of Gödel's theorems, if that's what you mean. His incompleteness theorems are useful for determining when to give up on a certain class of approaches toward a problem. I think this is what you meant by "implication", but the importance of this knowledge is difficult to over-state. His completeness theorems form the groundwork for first-order theorem proving, which has plenty of practical applications.
- kazinator 9y agoGödel's theorem is about "this sentence has no proof (in formal system S)", which is only resembles the direct self-contradiction in the Liar Paradox. Unprovable isn't false. If any axiom could talk, it could say that about itself. "I'm true, but unprovable; I'm an axiom, darn it!"