There's no evidence that the psyche is solely a product of neurological function. That's a theory driven by materialist-reductionist philosophy. No one is arguing that brain states can not or do not affect mental states, but no one has proved that the psyche is only a result of brain activity.
Correct me if I'm wrong, but no one ever gave a credible hypothesis of how a not-imaginary psyche in this sense could exist in reality; or how the 'immaterial' can be distinguished from the imaginary.
Is consciousness in the brain?
What do we mean by 'consciousness' here? The waking state? Alertness? Self-awareness? And what do you make of the >
Global Workspace< hypothesis, which has some experimental support? Besides, one thing we've seen demonstrated again and again is that consciousness is greatly overrated and that just about all the heavy lifting in brain function is done by the non-conscious brain. An easy example is, where are these words I'm typing in the quarter second before I type them since they're not being formulated in my conscious brain, any more than my speech is (you may have come across Auden's noted dictum, 'How do I know what I think till I hear what I say?')
Now one might have supposed that contemporary neuroscientists could tell you where consciousness is to be found, but no, its location has never been discovered.
It seems fair to point out that no one else can show where 'consciousness' is to be found either; but meanwhile brain research according to scientific method is the only systematic enquiry into that and related phenomena.
Nor has that of longterm memory, or of tacit memory. (This is almost equally interesting, but I cannot discuss it here.) Moreover, no one has explained how the sense information coming along the neural pathways in the brain is transformed into conscious experience. This is the problem of qualia, one of the most discussed issues in contemporary philosophy.
I'm not up to date with research into long term memory but I dare say that again only the scientific researchers are systematically examining such problems. As for qualia, it took me a while to work out what the problem was supposed to be, because I don't see any problem. Instead of being like Arnie's terminator and having all our sensory data displayed in numbers down the side of our vision, we, like all the other macrocritters, take our sensory data on board in forms that draw the most direct response. I suspect that your experience of light in the 620-740 nm waveband striking your eye and sending red signals down the optic nerve is not significantly different to mine or anyone else's with normal sight. I suspect that my experience of banana, or olive oil, or wine, or bacon is not significantly different to yours or to anyone else's because the same evolved mechanisms of sense and of interpretation are being used (though of course the connotations may differ).
The End of Materialism by Graham Duncan Martin
However, I'm content to drop it here, since our presuppositions will only result in predictable wheel-spinning.
In the 14 years since he wrote his book, he's had ample opportunity to win the argument, but as far as I can tell he's scarcely been noticed by the scientists. And all he seems to be doing in that brief summary you've linked is saying it's inexplicable, it can't be solved, science doesn't know &c &c instead of noting first that the mapping and describing of the brain and its functions is a massive task, that it's been a work in progress since the 18th century, that in the 20th century the questions began began to be defined, so that when in the 90s new tools for brain research arrived the whole range of enquiry got a massive boost, and that real steady progress has been the story ever since. Does he even have an alternative hypothesis that's expressed in falsifiable terms so it can be the subject of testing?