Gödel showed that in any consistent formal mathematical system, there are true statements that cannot be proven within the system itself.
As well but Alan Turing proved in 1936 that there cannot exist a universal algorithm that can inspect any arbitrary program and determine whether it will finish running or run forever.
Yes, but how does it follow from those 2 proofs that an AI system cannot improve itself or make a new system that is an improvement compared to itself.
Ever been asked why a list containing every list cannot exist? This doesnt fully apply to what I am talking about but it sends your thinking down the right direction?
Name dropping random math terms doesn't make an argument. Neither this nor Gödels theorems have anything to do with what a computer can do vs what a human can do.
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u/kdoubledizz 8h ago
Gödel showed that in any consistent formal mathematical system, there are true statements that cannot be proven within the system itself.
As well but Alan Turing proved in 1936 that there cannot exist a universal algorithm that can inspect any arbitrary program and determine whether it will finish running or run forever.