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It is well-known that Godel's incompleteness theorems restricted the reachability of symbolic-AI, which is dependent on mathematical logic.

But, I am wondering whether it has any impact on the connectionist AI.

I don't think it has any impact on the capability of connectionist AI because of the following reasons I am aware of

  1. Connectionist-AI is more focused on generalization and is not about mathematical logic..
  2. Universal approximation theorem, contrary to Godel's incompleteness theorems says that connectionist-AI is capable of achieving all bounded-continuous functions. I am not sure about the implications of Godel's incompleteness theorems on either unbounded or discrete functions.

So, the incompleteness theorems seem to have no impact on the connectionist AI.

Do the theorems also restrict the reachability of connectionist-AI?

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