Materialism, however, bears the burden of several very serious difficulties, including the following three: 1) No one knows what matter is; 2) Some popular interpretations of quantum mechanics seem to entail that matter is just a wave function, a mathematical posit, that has no objective existence; And 3) the most significant feature of minds - consciousness - seems inexplicable on any materialist ontology.
Here are some excerpts from what Frank says about this:
Materialism holds the high ground these days in debates over that most ultimate of scientific questions: the nature of consciousness. When tackling the problem of mind and brain, many prominent researchers advocate for a universe fully reducible to matter. ‘Of course you are nothing but the activity of your neurons,’ they proclaim. That position seems reasonable and sober in light of neuroscience’s advances, with brilliant images of brains lighting up like Christmas trees while test subjects eat apples, watch movies or dream. And aren’t all the underlying physical laws already known?Indeed, the problem of conscious experience has caused many philosophers, like Thomas Nagel in his book Mind and Cosmos, for instance, to abandon materialism altogether.
....In the very public version of the debate over consciousness, those who advocate that understanding the mind might require something other than a ‘nothing but matter’ position are often painted as victims of wishful thinking, imprecise reasoning or, worst of all, an adherence to a mystical ‘woo’.
....There is, however, a significant weakness hiding in the imposing-looking materialist redoubt. It is as simple as it is undeniable: after more than a century of profound explorations into the subatomic world, our best theory for how matter behaves still tells us very little about what matter is. Materialists appeal to physics to explain the mind, but in modern physics the particles that make up a brain remain, in many ways, as mysterious as consciousness itself.
When I was a young physics student I once asked a professor: ‘What’s an electron?’ His answer stunned me. ‘An electron,’ he said, ‘is that to which we attribute the properties of the electron.’ That vague, circular response was a long way from the dream that drove me into physics, a dream of theories that perfectly described reality.
Like almost every student over the past 100 years, I was shocked by quantum mechanics, the physics of the micro-world. In place of a clear vision of little bits of matter that explain all the big things around us, quantum physics gives us a powerful yet seemly paradoxical calculus. With its emphasis on probability waves, essential uncertainties and experimenters disturbing the reality they seek to measure, quantum mechanics made imagining the stuff of the world as classical bits of matter (or miniature billiard balls) all but impossible.
....Some neuroscientists think that they’re being precise and grounded by holding tightly to materialist credentials. Molecular biologists, geneticists, and many other types of researchers – as well as the non-scientist public – have been similarly drawn to materialism’s seeming finality. But this conviction is out of step with what we physicists know about the material world – or rather, what we don’t know.
....if one wants to apply the materialist position to a concept as subtle and profound as consciousness, something more must clearly be asked for. The closer you look, the more it appears that the materialist (or ‘physicalist’) position is not the safe harbor of metaphysical sobriety that many desire.
Explaining conscious experience, the sensation of red or the taste of sweet, is what philosophers have referred to as the "Hard" problem and it has proven to be intractable on any materialist account. Indeed, it's a mystery on any account. For an explanation of what philosophers mean by this go here (also here and here). Frank adds this:
....Some consciousness researchers see the hard problem as real but inherently unsolvable; others posit a range of options for its account. Those solutions include possibilities that overtly project mind into matter.If, as some versions of quantum physics insist, there really is no material entity until we observe it then it would seem that what everything reduces to is not matter, but an observing mind. If that's the case then some form of idealism would seem to be true.
Consciousness might, for example, be an example of the emergence of a new entity in the Universe not contained in the laws of particles. There is also the more radical possibility that some rudimentary form of consciousness must be added to the list of things, such as mass or electric charge, that the world is built of. Regardless of the direction ‘more’ might take, the unresolved democracy of quantum interpretations means that our current understanding of matter alone is unlikely to explain the nature of mind. It seems just as likely that the opposite will be the case.
But if mind is the ultimate reality, where did it come from? It didn't evolve since evolution can only act on material entities like molecules of DNA.
Perhaps our minds are derivatives of a universal mind which has generated everything that we perceive and holds everything in being. That may seem bizarre, but it's certainly no more bizarre than the idea that matter is, at bottom, simply an abstract wave function with no objective existence.