Mental and Physical Events
Identity of properties is one thing; identity of particulars is another. Particulars can be identical without their properties all being identical. This is obvious: Superman is identical to Clark Kent but the property of being a flying man is not identical to the property of being a journalist. It is just that a single man has both these properties. This distinction has been thought useful in characterizing the relationship between the mind and the brain: hence the distinction between type identity theories and token identity theories. A type identity theory would say that the property of pain is identical to the property of C-fiber firing; a token identity theory would say that every particular instance of pain is identical with an instance of some kind of brain event or another—it need not always be C-fiber firing. The properties are different but they apply to the same particular (so a dualism of particulars is false). Thus we have “non-reductive materialism” and “anomalous monism”.  Two sets of properties, one set of particulars: mental properties are not identical to physical properties, but every instance of the former is an instance of the latter. Here is an analogy for the token identity theory: each member of the set of soldiers has a certain rank—private, corporal, captain, colonel, etc.—and (we can suppose) a certain civilian occupation—lawyer, teacher, greengrocer, tailor, etc. For any instance of the former set of attributes, we can say that he or she is identical to someone with an attribute drawn from the latter set of attributes. That is, every soldier is token identical to someone of a certain civilian occupation—what has the former property also has the latter—but it would be quite wrong to identify military ranks and civilian occupations. The property of being a colonel is not identical to the property of being a lawyer, say. No one would be a “civilianist” about military ranks, holding that ranks are type identical with civilian occupations. Yet there are no soldiers who fail (we are supposing) to also have a (prior) civilian occupation: there is no dualism here of soldiers and non-military workers—as if each soldier has a kind of shadow civilian counterpart. No, he or she just is a particular civilian worker. The same people can have different attributes. Just so events can have both the attribute of being a pain and the attribute of being a C-fiber firing—without the attributes being identical. Thus we have a weaker version of materialism, one that avoids the problems encountered by type identity theories. We have materialism without reductionism.
But do we? Is token identity theory really a form of materialism? Is it strong enough for that? And is it an adequate account of the relationship between the mind and the brain? Consider this question (which I have never seen asked): could any other type of mental event than pain have a token that is identical with a token of C-fiber firing? Could a tickle or a sensation of red be identical to an instance of C-fiber firing—in addition to instances of pain? Evidently, both colonels and corporals can be identical to people who are teachers in civilian life, so can both token pains and token tickles both be identical to tokens of the type C-fiber firing? Generally, is it possible for instances of every type of mental event to be identical to instances of the same physical type? Might every mental token be identical to a token of an identical physical type? Evidently, nothing in logic precludes this: token identity theory is consistent with total homogeneity at the physical level. There is nothing but C-fiber firing to “realize” every mental type. If that were so, then properties of the brain would have nothing to do with properties of the mind. In the same way civilian occupations have nothing to do with military ranks: these properties are determined by quite different factors (or could be). Nothing about being a tailor makes you into a colonel rather than a corporal, since tailors can be both (they can be trained to be both). Similarly, the mental type of a mental token is not determined by its physical type—it might not even be correlated with that type. Of course, if type identity were true, then we would have such determination, but not if we only have token identity. Token identity is entirely neutral on what determines mental properties: it could be acts of God or human convention or the color of your hair. Two people could have completely different mental lives while having all their physical properties in common—they could still be such that all their mental tokens are identical to physical tokens. A given mental type can be “multiply realized”, as we have been taught, but as a matter of logic it is also true that the same physical type can be “multiply manifested”, i.e. correlated with different mental types. At any rate, token identity in no way rules this out. We may then wonder whether it deserves the name “materialism”, since it is silent on what makes an organism have the mind it has. Mere token identity is a very weak relation, hardly qualifying as a less unpalatable version of classic type identity: for it says nothing about the nature or fixation of mental properties, i.e. what makes the mind the mind. What kind of mind you have has nothing to do with what kind of brain you have, according to token identity theory; the theory merely rules out the possibility that mental tokens float free of physical tokens—as soldiers might be thought (falsely) to float free of people with prior civilian lives. A monism of mental tokens allows for any old theory of mental types, or none. It is not a theory of mental types at all.
This point may be conceded (the “uniform realization” point) but it may be suggested that we need to strengthen the token identity theory in a familiar way—by invoking supervenience. We can assert that mental types are strongly dependent on brain types, so that brain type entails mental type—physical properties fix mental properties. All right, let’s go ahead and assert that: the question then is what makes it true. The crucial point is that type identity explains this but token identity does not: if mental types are physical types, then of course you can’t have one without the other; but if they aren’t, the question is left hanging. Without type identity (or something close to it) supervenience looks like a mere stipulation devoid of rationale. It leaves open the question of why the dependence goes in one direction only: why doesn’t the mind also determine the brain? How can the properties be dependent one way but not the other? We certainly don’t have supervenience in the case of the soldiers, for the obvious reason that civilian occupation doesn’t determine military rank (or shape determine color, etc.), so why is the mental case different? No answer is given—a mere logical possibility is asserted. And surely we would want to say that there must be some internal relation between the brain and the mind—something about brain properties that underlies and explains supervenience. Absent a specification of what this might be, supervenience only gives us materialism by main force: it is what we need to wheel in to bulk up token identity into something looking more like classic materialism. More strongly put, unexplained supervenience is mere postulation not a theory of the mind-brain relation. It (purportedly) fills the gap left by abandoning type identity theory but without really supplying any filler. But token identity alone is hopelessly weak as a theory of the mind-brain relation. We may note that the asymmetry of dependence postulated by supervenience is also exaggerated at best: for there must be somedetermination from the mental to the physical, as a matter of hard necessity. For example, pain is necessarily linked to withdrawal behavior (or a disposition to it), but withdrawal behavior must be physically produced by the nervous system—so pain must fix some physical aspects of the organism feeling pain (viz. a physical withdrawal mechanism). It is not completely neutral about the condition of the body. Maybe C-fibers are in fact the only ones that can figure in a causal sequence that culminates in withdrawing a limb from the painful stimulus, even though this fact is not transparent to us; in that case there is partial supervenience from the mental to the physical.  And then we will have mutual dependence between mental and physical types, which encourages a type identity theory after all. It turns out that token identity plus supervenience is not sufficient to capture the nature of the mind-brain relation, and that we must move in a more type-committed direction. So token identity alone is no good, and one-way supervenience is no good either; we can’t avoid assuming something like type identity (possibly type composition). Maybe the brain descriptions (and the mental descriptions too) have to go beyond our commonsense categories, but we can’t avoid assuming a close relation of types—and identity seems the only clear way to go. Of course, this will lead to the classic objections to type identity theory, but that is just the old familiar mind-body problem making itself felt. My point is that the attempt to circumvent the objections to type identity by retreating to token identity (with or without supervenience) is doomed, because (a) that is not really a form of materialism and (b) we evidently need to postulate a stronger relation between mind and brain than can be supplied by those theories.
We tacitly assume that physical types play some role in fixing mental types when we intuitively rule out the possibility that the same physical type may underlie different mental types in instances of token identity. We don’t even consider the possibility that token pains and tickles and sensations of red might all be identical to physical tokens of C-fiber firing, even though that is not logically precluded by token identity theories—because we assume that the mental is fixed in some way by the physical (hence the appeal of type identity theories). But mere token identity is quite compatible with homogeneity at the physical level combined with heterogeneity at the mental level (the analogue of soldiers of different military ranks all coming from people of the same civilian occupation).  But that is not a satisfactory account of the relation between mental and physical events; and supervenience as commonly understood is not sufficient to remedy the problem. Type identity seems like the only way to go—with all the problems that are attendant upon that. Token identity theory is thus an inadequate refuge from those problems. It is too much like saying that all mental events fall under physical descriptions like “occurring n miles from the equator”: that is no doubt true, but it is not a form of materialism. Many types of mental token could correspond to the same such description (all those at a certain latitude, say), but that is not a theory of what makes mental types the types they are. The brain needs to be brought into closer proximity to the mind than that, but token identity alone is not equipped to do it. Type identity, however, is. 
 Valves are similar: they can be made of very different materials, but they all require a physical mechanism consisting of opening and closing. Likewise all tables require a flat raised stable surface, which are physical features, despite varying widely in physical composition. Not all physical facts are compositional facts.
 If we were to observe this situation obtaining in the brain, we would surely conclude that mind and brain have little to do with each other. The same mental type can co-occur with different physical types (“multiple realization”) and the same physical type can co-occur with different mental types (“uniform realization”). The fact that each mental token is identical with some physical token would not alter our opinion. In fact, we observe quite strong correlations and these lead us, reasonably enough, to postulate type identities; but this is not part of the logic of token identity theories. So token identity theory cannot be construed as a relaxing of type identity theory that preserves its spirit while avoiding its difficulties.
 The type of type identity might be very different from any currently envisaged or even imaginable by us: it might have to be expressed using concepts quite alien to concepts we now use to think about mind and brain. In particular, C-fiber firing may be a far more exotic thing (by our standards) than we realize; it may have hidden depths. Type identity and mysterianism are not incompatible doctrines: the brain might have properties currently mysterious to us that are type identical with mental properties.