I dedicate this post to Victor Reppert who thinks along similar lines, and shares my love of the oldies.
If matter could think, then matter would not be matter as currently understood.
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 can't repeat myself here. (Here is a characteristic post.)
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.
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 mudane 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.)
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. I seem to recall Reppert making this point recently.
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, labelling the problem without solving it. Do you materialists believe in miracle meat or mystery meat? Do you believe in magic?