It is a big mistake to think that most computability theory applies to AI, including Gödel’s Theorem. People start off wrong by talking about AI “algorithms.” The term applies more correctly to concepts like gradient descent. But the inferences of the resulting neural nets is not an algorithm. It is not a defined sequence of operations that produces a defined result. It is better described as a heuristic, a procedure that approximates a correct result but provides no mathematical guarantees.
Other aspects of ANN that show that Gödel doesn’t apply is that they are not formal systems. Formal system is a collection of defined operations. The building blocks of ANN could perhaps be built into a formal system. Petri nets have been demonstrated to be computationally equivalent to Turing machines. But this is really an indictment on the implementation. It’s the same as using your PC, implementing a formal system like its instruction set to run a heuristic computation. Formal system can implement informal systems.
I don’t think you have to look at humans very hard to see that humans don’t implement any kind of formal system and are not equivalent to Turing machines.
Other aspects of ANN that show that Gödel doesn’t apply is that they are not formal systems. Formal system is a collection of defined operations. The building blocks of ANN could perhaps be built into a formal system. Petri nets have been demonstrated to be computationally equivalent to Turing machines. But this is really an indictment on the implementation. It’s the same as using your PC, implementing a formal system like its instruction set to run a heuristic computation. Formal system can implement informal systems.
I don’t think you have to look at humans very hard to see that humans don’t implement any kind of formal system and are not equivalent to Turing machines.