The problem of intentionality vis-à-vis physicalism is not an empirical problem; it is a categorical problem. Formal operations, for instance, are determinate in a way that physical operations cannot be. Intellection is, for instance, universally abstract in a way that physical “signs” cannot be. The contents of sensory experience are analytically non-identical with the physical correlates we infer as their causal substrate. And as for intentionality…
Intentionality and physical order are simply, categorically mutually irreducible. This is hardly a “pet claim” of Thomists. Read some J. Levine, or J. Searle, C. S. Pierce, or F. Brentano, or J. Kim, or W. Vallicella, or S. Kripke, or K. Gödel, or D. Melser. Indeed, read some D. Dennett: he is so committed to physicalism, and yet aware of the intentionality problem, that he denies the latter on behalf of the former.
The issue is simply not one that can be overcome by “more brain studies.” Intentionality, and its related immateriality, is, like purpose and action, simply not reducible to behavioral categories. Intentionality, purpose, action, formal order––these are simply “their own things” and not to be trifled with. Certainly, it is true to say that intellection occurs “naturally” insofar as it is metaphysically contiguous with the operations of its natural agents; but this must be qualified by the fact that nature, thus, operates with both material and immaterial powers.
In any case, consider the following scenarios (which I borrow from Richard Taylor in Action and Purpose):
a. A man attending a debate raises his hand in order to get the attention of debater Q, and thereby both attracts the attention of debater Q and scares off a fly.
b. A man attending a debate raises his hand in order to get the attention of the moderator, and thereby both attracts the attention of the moderator and scares off a fly.
c. A man attending a debate raises his hand in order to scare off a fly, and thereby both attracts the attention of debater Q and scares off the fly.
Behaviorally, and I should say neurologically, these events are indiscernible. Only on the supposition of a distinct purpose (”in order to”) can they be differentiated. Likewise with intentionality. Physically indiscernible phenomena can have different intentionality, different meaning. Physical causation is, to palm off of Walker Percy and Pierce, metaphysical dyadic, whereas language–-qua intentionality in action––is conceptually triadic, and, indeed, intersubjectively tetradic. Physical things only stand in formal, theoretical bonds with each others as we evoke those bonds by the intentional, immaterial power of referential language. An atom simply does not and cannot “refer to” something else; but language can and, incessantly, does “conscript” an atoms, and hordes or atoms, for such bonds.
Someone might, however, object that there could be neurological difference between a, b, and c. If neurologists discover which neuronal firings cause pain and various thoughts, then they could discover which combination of neuron firings n1 produce the impulse, “Get X’s attention.” In this case, the physicalist could produce a fancy detailed neurological story about how n1 causes some other set of neuron firings n2, which produce the thought “Raise your hand to get X’s attention.” It does seem coherent to say that in each of the “¬¬p in order to q” cases, the different q’s are discernible.
In reply, I would ask, "Which set of neuronal impulses, call it nx, accounts for the intentional ascription of intentional action to n1 and n2 for a., b. and c.?" And which neurons, in turn, account for the ascription between nx and that second-order ascription of intentionality? And so on. The terms of an intentional system may be, indeed are, scientifically measurable, but intentionality itself is not measurable, and therefore not a physical reality. Nothing intentional (which, again, does not mean "purposive" but rather "notionally directed at") simply and naturally falls out from any nx; nx orders n1 and n2 only if we can produce an intentional bond from outside the neuronal complex under observation.
The critic that invokes n1 and n2 as pure descriptions of all behavior is oblivious to the fact that we can only imagine a coherent difference between the a., b. and c. actions at the neural level because we already know how those actions are formally (viz., teleologically) distinct. We know the brain phenomena will be different "on the inside" because we already know the actions in which they are involved are formally different "on the outside." If, however, we strip away the explanations of the actions that I gave in listing them, they are effectively indiscernible. Without already knowing why we are observing different happenings in the brain, we can't coherently say the brain happenings correspond to distinct actions. For all the "action blind" observer knows, he is simply seeing minutely different neural patterns which result in visibly indistinguishable limb motions. Even if we suppose we could ask the person what he intended after each neural-behavioral episode, we would still just be resorting to the categorically autonomous, and truly explanatory, category of purpose and formal action. Even if we could observe a man’s brain on the sly, so he weren’t conscious of later having to talk about his intentions, we could only “decode” the neural activity by translating it into, and correlating it with, his stated aims.
But perhaps the physicalist is still not satisfied. "It seems," he goes on, "that there might very well be a physical difference between a neural pattern for 'raising one’s hand in order to get somebody’s attention' and 'raising one’s hand to brush away a fly'. Neural patterns are presumably very complex, with plenty of room for internal variation even when the external effects—the raising of the hand—are identical."
But, in reply, let us ask, "Would the raising of two separate men’s hands for the (same) purpose of shooing a fly be the same action?" Clearly, yes. Let us then ask, "Seeing as their actions are formally identically, would their neural states be proportionately identical?" It seems not. The formal determinateness of an action-for-some-end is irreducibly incommensurable with the complexities of specific neural acts.
Arguably, of course, since two different men are doing the swatting, they would be doing two technically different acts in spacetime, and this spatiotemporal difference could be construed as providing analogously sufficient identity between neural types of happenings and formal actions. Presumably, the same kinds of brain-stuff are involved in the same kinds of actions, so there is a rough but satisfactory identity between their actions and their brain events.
This a weak retort, however, for a couple reasons. First, the original scenario of two men doing exactly the same action-for-a-purpose preempts such a rough identity. Second, more importantly, if the same man were asked to repeat his own action-for-the-same-purpose numerous times, it seems incredible that each formally identical action would correlate to one and the same neural process every time. Presumably, given enough time, the man’s brain cells would change to such an extent that it would literally be different neurons and chemicals involved in the same action. Furthermore, imagine if we had the man perform the action for ten minutes, then had him drink two Jolt colas and perform it another ten minutes, and then had him take a Valium to perform it ten more minutes. Over thirty minutes, his brain would undergo vast amounts of neurochemical changes, which, while admittedly peripheral to his successful performance of the action, would certainly alter the specific properties of his relevant brain matter in performing the action (e.g., a hand-raise impulse mingled with a stifle-giggle or yawn impulse).
All the while, of course, the action remains one and the same. If it did not remain one and the same, on a purely formal level, there would be no way, let alone desire, to compare the neural happenings with the behavioral. I.e., if we didn’t already grasp that he is doing one and the same action in a formally identical way, we would not have any one thing to explore in relation to his brain states. We would just have numerous materially discrete happenings that we would correlate by Humean fiat.
Aside from these technical difficulties in the brain-reductionist platform, Taylor’s Action and Purpose provides much food for thought about how odd the idea of “mental desires” is for explaining action in sheer causal terms. If desires cause actions, what causes the desires? Do we have a certain desire to have a certain desire? Only if one is willing to reduce all behavior to sheer caused events is one able to circumvent this regress into a desire-cause spiral. There is a categorical difference between “a man’s hand being caused to go up and x occurring in succession” and “a man raising his hand in order to bring about x”. If action, as distinct from mere bodily movements, is just a pinball of neuronal fireworks, no one can be said to act rationally, i.e., for a cogent end, for an intelligible reason. Causes are not rational but actions are. Thus, if actions just are behavior, then there are no rational actions. But, of course, ends and reasons are integral to our entire taking-of an event to be an action as opposed to a mere happening in the first place. Smoke is caused to go up, but that is not an action. A man’s hand goes up for some reason but that is not simply a causal event.
A related problem for the causal reductionist is Popper’s argument that, without an extra-mental, formally discrete grasp of the event under analysis, we have no purely physical basis for calling this neurochemical or physical occurrence the “beginning” of the event and that occurrence the “end.” What is there about this particular neural firing, or this particular phoneme, considered physically, that dictates its formal, intentional place in our analysis? (Hint: nothing.)
Related to this is D. Melser’s claim (in a way, very reminiscent of Taylor’s criticisms in Action and Purpose) that a science of language and behavior are strictly impossible, since understanding language––i.e., knowing what's going on when certain sounds are emitted––requires cooperative use of it with the speaker being viewed. But since science by definition limits itself to an objective, non-participatory “view,” a purely scientific observer is asymptotically removed from "what it takes" to understand language. And if one cannot understand what is happening when one observes what is happening, one can't reasonably explain what is happening. The more objective science becomes, the less traction or right it has for “getting” the language events and treating them as meaningful (i.e., intentional); and the more involved science becomes in the meaning and use of language, the less objective it is. See the last section of his essay here http://www.derekmelser.org/essays/essayverbal.html