I think this requires a thorough debate on what it is to be human; not just the limitations but also the extremes. What are the limits of human experience?
Just to bring one example, if one assumes the brain is just a neural net, then one can justify that one can build a better artificial neural net. But the brain is more than point-to-point interactions at the synapses, there are electromagnetic fields that communicate between neurons. (What are EEGs otherwise?) This implies that the geometry of the brain is as much part of its function as its electro-bio-chemistry. But that means that to build a better brain means building... a better brain!
This is just one example, but in essence, to assume limitations on human abilities because one has a preconceived model that builds in such limitations is not in itself proof that being able to surpass that model is the same as being "better" than human.
Great reply,
David Bohm wrote a book, Thought as a System.
I think we know too little to comfortably (ie based on evidence) put to rest the argument of how a mind functions. I do take an emergent perspective on intelligence and that colours what I think can ground a mind. The brain can ground a mind and a brain will have physical limitations. To what extent those the physical limitations of the brain are also limitations on the mind is not known.
But, let's just say we accept the brain is some form of neural net - the reality is we're not even close to building a neural net that matches the scale of the brain. That's even before going into how we train that neural net. In a practical sense, the level of sophistication is not there yet.