Bennett on Non-Reductive Physicalism

I just re-read Karen Bennett’s paper Exclusion, Again. In this paper she argues that causal exclusion arguments provide a nice overall argument for physicalism but do not cut against non-reductive physicalism as usually thought.
Here is how she defines non-reductive physicalism.

Let us begin with the ‘physicalism’ part. It is notoriously hard to define it adequately, but I can at least offer up the same slogans as everyone else. Physicalists not only endorse the completeness of physics, but also think that all the facts are physical facts—that there is nothing ‘over and above’ the physical. Physicalists believe that everything globally supervenes6 on the physical as a matter of metaphysical necessity (see Lewis 1983, Chalmers 1996, and Jackson 1998; see Hawthorne 2002 for interesting challenges to their definitions). That is, physicalists deny that it is merely nomologically impossible for there to be a world physically just like this one but mentally different. There are no special psychophysical laws that link or tether the mental to the physical, and that can be broken.

She is officially neutral on the issue of the a priori entailment of the mental by the physical but she clearly rejects the metaphysical possibility of zombie worlds. So, what, then, is non-reductive about her view?

Nonreductive physicalists do not think—or, at any rate, should not think—that mental events and properties really are not identical to any physical ones. All we think is that they are not identical to any standard physical ones. We have no reason to deny that they are identical to physical events and properties reachable by extension or analogy with standard ones. Let me try to put this marginally more carefully, by loosely distinguishing between a narrow and a broad sense of ‘physical’.

What she means by this seems to be the following. On the one hand we have ‘narrow’ physical properties, events, or objects, which means that they figure in the laws of a ‘clearly physical’ science. So she will count neurons as narrow physical objects because they figure in neuroscience. She will also count electrons and elements, etc. On the other hand there are what she calls ‘broad’ physical properties, events, or objects, which means that we can construct the thing in question out of the narrow properties in some ‘clearly articulated’ way. So,

Broadly physical properties are those constructed from narrowly physical ones by means of property-forming operations like disjunction, conjunction, and quantification (though presumably not negation!). Broadly physical events are those constructed from narrowly physical ones by means of various forms of spatio-temporal, mereological, and modal gerrymandering. And so on. This list is merely supposed to give the general idea, and presumably needs to be expanded and tweaked in various ways.

Given these two notions she formulates non-reductive physicalism as the view that mental states are broadly physical but not narrowly physical. She thus finds it to be a mistake on the part of the non-reductive physicalist to claim that mental properties are not physical at all. They are physical, just not in the narrow sense. There is no neurological state that she will want to say is identical to the mental state, though the mental state is constructed out of those narrow states. So on her view the functional characterization of mental states picks out some narrow physical property as its realizer. When thought of in this way, she continues, non-reductive physicalism has no worries with casual exclusion but dualists do.
The crux of the argument is that if one really wants to maintain a role for the mental in causation you must endorse some kind of over-determination and if that is the case then the following two counterfactuals must be non-vacuously true (which I take to mean; true because the antecedent is true):

(O1) if m had happened without p, e would still have happened and 

(O2) if p had happened without m, e would still have happened.

These are supposed to capture our ordinary understanding of overdetermination. Had there been only one of the causes the effect would have been produced by the other cause, and vice versa. The real action is over (O2). She argues that only a physicalist can interpret it in the required way. That is, only the physicalist can say that it is either vacuous or false. A physicalist will think it is vacuously true just in case she thinks that it is impossible that p happen without m. If that is false then (O2) is vacuously true. The dualist has to deny this (zombie worlds are worlds where p happens without m and e happens) and so the dualist cannot say that (O2) can ever be vacuously true. The physicalist can also say that it is false. How? Bennett argues that (O2) is false when we have p ‘out of context’. So, if we replicate the brain state that is pain in the normal brain in some petri dish or if that state were hooked up in some strange/unusual fashion it will be false that e would still come about. The effect depends on the state being in a normally functioning brain in an environment, etc. So in those cases (O2) is false. Bennett then goes on to argue that the dualist cannot take this option. This is because,

doing so would abandoning standard ways of evaluating counterfactuals. For the dualist, the closest world in which the C-fibers fire without pain is not a world in which various surrounding physical facts go differently. It is not a world in which the C-fiber firing takes place in a petri dish, or otherwise without crucial background conditions that actually obtain. It is instead a world in which the psychophysical law linking firing C-fibers in such and such circumstances to pains is violated. It is not a full-blown zombie world, mind you—that would clearly involve the kinds of “big, widespread, diverse violations of law” that Lewis says it is of the first importance to avoid (1979, 47). It is instead simply a world in which just that particular physical occurrence fails to give rise to the sort of mental one that usually accompanies it. That is merely a “small, localized, simple violation of law,” that allows us to “maximize the spatio- temporal region throughout which perfect match of particular fact prevails” (47-48). This one tiny little violation of psychophysical law is a lot easier to accomplish—if it can be accomplished at all—than a big sweeping change in circumstances.

If all of this is right, she concludes, then only the non-reductive physicalist (or the reductive physicist) can avoid the exclusion problem.
But this doesn’t seem right to me. It is wrong to say that the closest possible world where we have p without m is one where there is a small violation of the bridging laws. At least not if one is thinking in terms of the kind of dualism that Dave Chalmers advocates. Since he thinks that consciousness and mental activity are functionally invariant, under normal conditions, he can happily accept that in the cases that Bennett cites (O2) will be false. Sure they do in fact think that there are worlds like the ones that Bennett talks about where the is a local violation of a law and sure Bennett does not really think that there are any such worlds (I tend to agree) but the point is that the worlds that Bennett thinks falsify (O2) are closer to the actual world on both accounts. In those worlds no laws are violated. So the property dualist can say that (O2) is false when you have p without m in the way that Bennett talks about (i.e. p without the general background conditions that let p function normally) but that it is true when you have p without m in the law-violating way. Thus the property dualist can think that (O2) is false in the usual cases, just like the non-reductive physicalist.