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1answer
42 views

Can we determine which statements are incomplete due to Godel?

Due to Godel's incompleteness theorems we know that there are true statements in a system that cannot be proven with that system. My questions are 1) can we tell which statements in a system are the ...
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1answer
81 views

Have I understood the whole Incompleteness business correctly?

I am reading Gödel-Escher-Bach and a good dialogue by Eliezer Yudkowsky and I think I might have understood the nature of the Completeness and Incompleteness theorems (at least regarding Peano ...
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1answer
383 views

Is there any direct application of Gödel's Theorems outside of logic?

Gödel's incompleteness theorems was a major achievement with ramifications outside the field of mathematics itself. Are there any direct applications of the theorem(s), or any of the methods pioneered ...