This is absurd. If you can mathematically model atoms, you can mathematically model any physical process. We might not have the computational resources to do it well, but nothing in principle puts modeling what's going on in our heads beyond the reach of mathematics.
A lot of people who argue that cognition is special to biological systems seem to base the argument on our inability to accurately model the detailed behavior of neurons. And yet kids regularly build universal computers out of stuff in Minecraft. It seems strange to imagine the response characteristics of low-level components of a system determine whether it can be conscious.
I'm not saying that we won't be able to eventually mathematically model cognition in some way.
But GP specifically says neural nets should be able to do it because they are universal approximators (of Lebesgue integratable functions).
I'm saying this is clearly a nonsense argument, because there are much simpler physical processes than cognition where the answers are not Lebesgue integratable functions, so we have no guarantee that neural networks will be able to approximate the answers.
For cognition we don't even know the problem statement, and maybe the answers are not functions over the real numbers at all, but graphs or matrices or Markov chains or what have you. Then having universal approximators of functions over the real numbers is useless.
A lot of people who argue that cognition is special to biological systems seem to base the argument on our inability to accurately model the detailed behavior of neurons. And yet kids regularly build universal computers out of stuff in Minecraft. It seems strange to imagine the response characteristics of low-level components of a system determine whether it can be conscious.