Is there doubt as to whether a neuron can be represented computationally?
1. You have to solve the interaction problem (how does the mind interact with the physical world?)
2. You need to explain why the world is not physically closed without blatantly violating physical theory / natural laws.
3. From the fact that the mind is nonphysical, it does not follow that computationalism is false. On the contrary, I'd say that computationalism is still the best explanation of how human thinking works even for a dualist. (All the alternatives are quite mystical, except maybe for hypercomputationalism.)
2. If the world is not physically closed then physical theory and natural laws are not violated, since they would not apply to anything beyond the physical world.
3. True, but if the mind can be shown to perform physically uncomputable tasks, then we can infer the mind is not physical. In which case we can also apply Occam's razor and infer the mind is doing something uncomputable as opposed to having access to vast immaterial computational resources.
Finally, calling a position names, such as 'mystical', does nothing to determine the veracity of the position. At best it is counter productive by distracting from the logic of the argument.
> if the mind can be shown to perform physically uncomputable tasks
That's true. Many people have tried that and many people believe they can show it. Roger Penrose, for example. These arguments are usually based on complexity theory or the Halting Problem and involve certain views about what mathematicians can and cannot do. As I've said, I've personally not been convinced by any of those arguments.
Your mileage may differ. Fair enough. Just make sure that you do not "know the answer" already when starting to think about the problem, because that's what many people seem to do when they think about these kind of problems and it's a pity.
> calling a position names, such as 'mystical', does nothing to determine the veracity of the position. At best it is counter productive by distracting from the logic of the argument.
That wasn't my intention, I use "mystical" in this context in the sense of "does not provide any better understanding or scientifically acceptable explanation." Many of the (modern) arguments in this area are inferences to the best explanation.
By the way, correctly formulated computationalism does not presume physicalism. It is fully compatible with dualism.
I know the Lucas Godel incompleteness theorem type arguments. Whether successful or not, the counter arguments are certainly fallacious. E.g. just because I form a halting problem for myself does not mean I am not a halting oracle for uncomputable problems.
But, I have developed a more empirical approach, something that can be solved by the average person, not dealing with whether they can find the Godel sentence for a logic system.
Also, there is a lot of interesting research showing that humans are very effective at approximating solutions to NP complete problems, apparently better than the best known algorithms. While not conclusive proof in itself, such examples are very surprising if there is nothing super computational about the human mind, and less so if there is.
At any rate, there are a number of lines of evidence I'm aware of that makes the uncomputable mind a much more plausible explanation for what we see humans do, ignoring the whole problem of consciousness. I'm just concerned with empirical results, not philosophy or math. As such, I don't really care what some journal's idea of the burden of proof is. I care about making discoveries and moving our scientific knowledge and technology forward.
Additionally, this is not some academic speculation. If the uncomputable mind thesis is true, then there are technological gains to be made, such as through human in the loop approaches to computation. Arguably, that is where all the successful AI and ML is going these days, so that serves as yet one more line of evidence for the uncomputable mind thesis.