If matter could think, then matter would not be matter as currently understood.
Alternatively, thinking would not be thinking as currently understood. One man's modus ponens...
Can abstracta think? Sets count as abstracta. Can a set think? Could the set of primes contemplate itself and think the thought, I am a set, and each of my members is a prime number? Given what we know sets to be from set theory, sets cannot think. It is the same with matter. Given what we know or believe matter to be from current physics, matter cannot think. To think is to think about something, and it is this aboutness or intentionality that proves embarrassing for materialism. I have expatiated on this over many, many posts and I won't repeat myself here. (Here is a characteristic post.) Please remind yourself of the obvious: physics is not materialism. Physics is science; materialism is philosophy.
Thinking involves change but sets, being abstracta, cannot change. Ergo, sets cannot think. Given what we believe thinking to be from current philosophy, matter cannot think. But it clearly does. We are prime examples. So we need to rethink our thinking about thinking.
But couldn't matter have occult powers, powers presently hidden from our best physics, including the power to think? Well, could sets have occult powers that a more penetrating set theory would lay bare? Should we pin our hopes on future set theory? Obviously not. Why not? Because it makes no sense to think of sets as subjects of intentional states. We know a priori that the set of primes cannot lust after the set of evens. It is impossible in a very strong sense: it is broadly logically impossible.
Of course, there is a big difference between sets and brains. We know enough about sets to know a priori that sets cannot think. But perhaps we don't yet know enough about the human brain. So I don't dogmatically claim that matter could not have occult or hidden powers. Maybe the meat between my ears does have the power to think. But then that meat is not matter in any sense we currently understand. And that is my point. You can posit occult powers if you like, and pin your hopes on a future science that will lay them bare; but then you are going well beyond the empirical evidence and engaging in high-flying speculations that ought to seem unseemly to hard-headed empiricistic and scientistic types.
If the meat between our ears has the power to think then maybe thinking is not thinking in whatever sense we currently understand it. We should look for a better understanding of thinking rather than for occult powers in matter That's my point. Sorry to labour it.
Such types are known to complain about spook stuff and ghosts-in-machines. But to impute occult powers, powers beyond our ken, to brain matter does not seem to be much of an improvement. For that is a sort of dualism too. There are the properties and powers we know about, and the properties and powers we know nothing about but posit to avoid the absurdities of identity materialism and eliminativism. There is also the dualism of imagining that matter when organized into human brains is toto caelo different from ordinary hunks of matter. There is also a dualism within the brain as between those parts of it that are presumably thinking and feeling and those other parts that perform more mundane functions. Why are some brain states mental and others not? Think about it. (I have a detailed post on this but I don't have time to find it.)
I suppose, like Bill, that there could be further powers inherent in matter as yet unknown to science. But I prefer to work within our present understanding of matter. That means that we have to reconceptualise the mental. And this is proper work for philosophy.
One might ask, Is there a dualism between those parts of a car engine that are propelling the car and those other parts that perform more mundane functions?
The materialist operates with a conception of matter tied to current physics. On that conception of matter, it is simply unintelligible to to say that brains feel or think. If he nonetheless ascribes mental powers to matter, then he abandons materialism for something closer to panpsychism.
But we could also say that the antimaterialist operates with a conception of thinking tied to late nineteenth century philosophical phenomenology, and on that conception of thinking it is simply unintelligible to say that brains think or feel.
It is worth noting that the reverent gushing of the neuro-scientistic types over the incredible complexity (pound the lectern!) of the brain does absolutely nothing to reduce the unintelligibility of the notion that it is brains or parts of brains that are the subjects of intentional and qualitative mental states. For it is unintelligible how ramping up complexity can trigger a metabasis eis allo genos, a shift into another genus. Are you telling me that meat that means is just meat that is more complex than ordinary meat? You might as well say that the leap from unmeaning meat to meaning meat is a miracle. Some speak of 'emergence.' But that word merely papers over the difficulty, labeling the problem without solving it. Do you materialists believe in miracle meat or mystery meat? Do you believe in magic? In a young girl's brain?
Of course, greater complexity pure and simple cannot be the whole story. The organisation of matter is clearly significant. The contrast between a single-celled living organism and a similar quantity of inert matter is one primarily of structure, though that structure will possess some minimal level of complexity also. Does this count as a shift into another genus? If so, does that mean we must accept a fundamental duality of the living and the non-living, just as we are asked to accept a duality of the mental and the material? Better to say that living is what suitably organised matter can do. Likewise thinking. Which is mysterious.