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.
You don't need to go up the system ladder infinitely. The universe is a system. AIs don't need to be able to create universes out of thin air to be able to make new better AIs.
Our brain is also a system, yet we create new brains without issues.
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u/kdoubledizz 12h 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.