As I understand the Pairing Objection to substance dualism it goes like this. 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?
For example, what insures that Tim's desire for sex causes changes in his brain and body that eventuate in certain familiar actions as opposed to causing changes in Tom's brain and body? 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 on substance dualism. 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 about causation 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, eds. Causation, Oxford 1993, 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 construed 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. To say that an event-sequence is intrinsically causal is to say that its causality does not derive from instantiation of a law.
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. The precedence and contiguity conditions are the same. 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.
Since the Pairing Problem cannot possibly arise if Cartesian egos are spatial, the dualist could also take the view that they are spatial even if immaterial: they are located where their corresponding brains are located. See William G. Lycan, Giving Dualism Its Due, p. 12: "It may be wondered wherein minds are immaterial, if they are spatially located. In at least two ways: They do not have other physical properties such as mass or charge; and unlike brain matter, they are not made of atoms or subatomic particles."
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