The introspective ability to hold abstract concepts in the mind is the source of the statement that humans can do so.

It is what Aristotle called the intellectual soul, not qualia. Qualia is an experience and has no relation to holding abstract concepts. As I already wrote, Turing machines cannot do it for they suffer from multiple realizability, any abstract concept can be implemented in multiple physical constructs and any physical construct can be interpreted to be any number of different abstract items. I have not written that only "wetware" can do it, I have written that turing machines cannot do it and that no purely physical construct can do it (including purely newtonian/quantum wetware).

Uh... but the neural networks (and Bayesian networks) do hold abstract concepts, and are implementable by Turing machines. So it appears that your assertion is wrong.

They do not hold concepts, they are simply physical items behaving in accord with physical principles. You as a human interpret them (wrongly) to hold concepts. You can as well interpret them to be something else. None of your interpretations change the physics and the physics have no mention of abstract concepts and can be interpreted to be any number of things. None of the interpretations make that particular interpretation a concrete implementation of it.

So if we are not purely physical constructs, what are we? Are you a dualist?

human

Are you are dualist? In the sense of Descartes' Dualism?