The question of reduction of the human mind is something many humanists, as well as many STEM people get wrong, but it is quite easy to explain to software developers. The key is this: computation breaks reduction. And by reduction I mean explaining something as the sum of its components, rather than simply describing it as such (although the word explaining requires a definition here which I cannot give). The intractability of simple aggregation of variables makes reduction nigh impossible -- which is why we have physicists, chemists and biologists rather than just physicists -- but computation does so in a much more fundamental way (though it can be said that computation is involved, or emerges, in those aggregations, too). So while an algorithm running on a computer could be described as the physical interactions of electrons in the CPU, explaining and studying the algorithm as a physical process is nearly useless. No computer scientist would reduce a sorting algorithm to physics, and would probably claim that the reduction -- even though it is theoretically possible -- is completely meaningless, as the algorithm transcends the hardware it runs on.

The concept of universal computation says that a machine that is able to perform just a few simple operations, can not only simulate the entire universe it is in, but any universe at all -- with any natural laws. The physical world can therefore contain something that is more general than the world itself. Of course, this is not quite so but only an approximation. As the machine needs to be actually built of earthly materials, it does not have enough degrees of freedom to describe the exact universe it resides in, but even as a bounded approximation, reduction is severely limited.

Of course, much of the "reductionst" study of the mind indeed operates at the "software" level, the algorithm level -- not the hardware level. But the thing about universal computation is that even that is not enough. A computer software can simulate another computer, and the simulated computer cannot be reduced to the workings of the "virtual machine" it runs in. The number of levels of simulation is, of course, bounded by computing resources, but I think it's quite possible that there is at least one simulation layer in the brain.

So while reduction is always necessary to understand the foundations of the next level of abstractions, it can never be a full explanation or even a full explanation mechanism. This is doubly so when computation is involved.

"Reducing" the mind to neurobiology, therefore, does not change Shakespeare being a better explanation to human behavior than neural networks. The two might well operate at two irreducible levels of abstractions, and even if one gives rise to the other, it does not form a sufficient "explanation" (whatever that means).

Dismissing the "reality" or applicability of "literary logic" (e.g. the moon is made of cheese) makes as much sense as dismissing software as less real or less fundamental than the hardware it runs on -- even if the software is simulation a world ruled by laws very different from those governing matter.