In previous comment threads I detected a conflation of two objections to interactionist substance dualism. One I will call the traditional objection, the other the pairing objection. The first is radically misconceived, while the second has merit.
The Traditional Objection
It is a given that mind affects body, and body mind. Suddenly remembering the bottle of single-malt Scotch that Harry gave me for my birthday, I am inspired to get out of my chair and pour myself some. After consuming a generous portion, I note that my mental state has altered appreciably. The mental event of remembering causes the physical event of drinking which in turn elicits the mental state of elation. But how are such interactions possible if mind and body/brain are distinct types of substance, one spatial the other nonspatial? As Elliot Sober put it recently:
If the mind is immaterial, then it does not take up space. But if it lacks spatial location, how can it be causally connected to the body? When two events are causally connected, we normally expect there to be a physical signal that passes from one to the other. How can a physical signal emerge from or lead to the mind if the mind is no place at all?
It is difficult to see what this objection is supposed to be. If Sober is saying that all causation must involve physical contact between cause and effect, then he simply begs the question against the dualist. He simply asserts something that the dualist denies. If I assert proposition p, and you assert either the negation of p or a proposition equivalent to the negation of p, then you have not refuted me, but merely opposed me. It is essential to see that if you merely contradict what I say, you have not given me a reason to abandon what I say.
If interactionist dualism is true, then there are cases of causation that do not operate by physical contact. One cannot refute this by saying, or implying, that all cases of causation operate by physical contact. At this point I will be told that dualist interaction is unintelligible. But why? If you say that it is because dualist interaction does not fit the physical-physical pattern, then again you beg the question. If you say that every case of causation involves an intervening mechanism, but there isn't one in the dualist case, then you beg the question in a slightly more subtle way. For what the dualist holds is that there are cases of direct causation. It is not clear that all physical-physical causation is indirect, but even if it were, this putative fact is not a reason to think that all cases of causation are indirect.
But how does mental-physical causation work? If this is a demand for a specification of the intervening mechanism, then the question rests on a false presupposition, namely, that there must be such a mechanism. If, on the other hand, the demand is for a specification of the causally relevant properties and covering laws, then I see no reason why this demand cannot be met.
If one thinks clearly about this, one sees that the traditional objection is quite worthless: it gives the interactionist dualist no reason to abandon his view.
The Pairing Objection
The Pairing Objection is much more serious, and much more interesting. Let m1 and m2 be mental tokens of type M and b1 and b2 brain tokens of type B, and suppose that M-type events cause B-type events. Suppose m1 and m2 both occur at time t, and b1 and b2 both occur at a slightly later time t*. Suppose further that m1 is in Tim's mind, m2 in Tom's mind, b1 in Tim's brain and b2 in Tom's brain. What makes it the case that m1 causes b1 rather than b2, and that m2 causes b2 rather than b1? What insures that m1 is paired with b1 and m2 with b2? How, on dualist interactionist assumptions, can we insure that the picture looks like this:
m1 --> b1
m2 --> b2
and not like this:
m1 --> b2
m2 --> b1?
Note that one cannot appeal to spatial contiguity to establish the right pairings for the simple reason that m1 and m2 are not in space. Thus one cannot say that m1 pairs with b1 because it is nearer in space to b1 than to b2. It is also clear that neither temporal contiguity nor temporal precedence can establish the right pairings. For both mental events occur at t, and both brain events at the later time t*.
One will be tempted to say that a mind controls the body it is embodied in, not some other body. This is true, but doesn't solve the pairing problem since embodiment is a causal notion: Tim is embodied in that body over which he has (some) causal control, but what insures that this is Tim's body? It is circular to say that Tim's mind causes changes in Tim's body rather than Tom's because Tim's mind is embodied in Tim's body — given that Tim's mind is embodied in that body over which he has causal influence.
The Pairing Objection can be met if we reject an assumption on which it is based. The assumption is that an event-sequence is a causal sequence in virtue of its falling under a law of nature. The assumption, in other words, is that what makes m1 the cause of b1 is the fact that the m1-b1 sequence instantiates the law that every M-event causes a B-event. On this assumption, there is nothing to distinguish the m1-b1 sequence from the m1-b2 sequence. For they are alike in being instances of the law, and as noted, nothing else distinguishes them.
Borrowing from Michael Tooley (Sosa and Tooley, p. 173), the assumption can also be put as follows:
Weak Reductionism with Respect to Causal Relations. Any two worlds that agree with respect to all of the non-causal properties of, and relations between, particular events or states of affairs, and with respect to all causal laws, must also agree with respect to all of the causal relations between states of affairs.
Spatial contiguity, temporal contiguity, and temporal precedence are examples of non-causal relations. Clearly, on the above assumption there is no way to distinguish the two different pairings displayed above. This implies that the Pairing Problem may be construable as an objection to Weak Reductionism with respect to Causal Relations rather than as an objection to interactionist dualism. In other words, an interactionist dualist who understands his position will not subscribe to Weak Reductionism as just stated; he will adopt a realist theory of causation according to which certain event-sequences are intrinsically causal.
What we need, however, is an independent reason to reject Weak Reductionism, a reason independent of the mind-body problem. If the Pairing Problem arises in a purely physical situation, then we have an independent, non-question-begging reason to abandon Weak Reductionism with respect to Causal Relations. So consider the following set-up. (What follows was suggested to me by John Foster's "A Defense of Dualism" in The Case for Dualism, pp. 14-15.)
There are two light bulbs, B1 and B2, in an enclosed space. They are indistinguishable: they are of the same wattage and manufacture, each is connected to a 120V AC power source, etc. When either of the bulbs is on, it causes the temperature in the enclosure to increase by X degrees in an interval of time I. Suppose that this is because of a law of nature according to which running a current through a filament causes it to emit heat.
Suppose B1 and B2 are both switched on at the same time, t, and kept on for interval I. During I, the temperature in the enclosure increases by 2X degrees. Clearly, each light's being on causes its own temperature increase in the enclosed space. There are two distinct physical causes c1 and c2 and two distinct effects e1 and e2.
But what makes c1 the cause of e1 rather than the cause of e2, and c2 the cause of e2 rather than the cause of e1? The causal pairings are not fixed by the causal law and the non-causal conditions. This shows that there must be more to causation than instantiation of a law. It shows that Weak Reductionism with respect to Causal Relations is false, or at least not obviously true.
If we abandon the assumption that causal relations can be completely explained in terms of non-causal properties/relations and causal laws, then the problem of psychophysical causal pairings no longer arises. If, on the other hand, we hold fast to Weak Reductionism, then, since the Pairing Problem arises both in the mental-physical and the physical-physical case, this problem cannot be taken to be an objection to interactionist dualism.