[Nebullis]

Sorry to disillusion you, but the class of computations possible for a neural network with finitely many neuron each of which has finitely many states is describable by a formal system. Goedel's result applies. The only thing you get by going to neural networks is run-time efficiencies.

Think of the patterns produced by cellular automatons. And imagine the infinite states possible with genetic algorithms. Neural nets have evolved.

[AndrewC]

And imagine the infinite states possible with genetic algorithms.

Please explain how this is possible?

[The_Reader_David]

Not to the point. Neural "evolution" evidenced by systems in the neural network approach to AI is still inside a formal system to which Goedel's theorem applies. Again stochatic algorithms only (with high probability) gain run-time efficiency. What computations are possible within the system doesn't change, and thus the "jumping outside the system" evidenced by Goedel's behavior in discovering and proving his theorem, and applying it to all formal systems sufficient to describe the natural numbers as a subsystem, cannot be done by anything computationally equivalent to a push-down automaton (e.g. a computer, a finite-state neural network with an infinite memory stack (or many such stacks),...).