We must now look at the task of reconciling mind and physics, shifting from psychological to physical, from enjoyed to contemplated. In this area we are presented with physical systems, namely brains, whose operations clearly have a great deal to do with mind, and which are, under the more conventional ways of thinking about physics, located in space. Can this line of thought lead us to conclude that, despite the contrary appearance from introspection, minds are in fact really located in space?
To begin with I want to clear out of the way the two arguments for the localisation of mind presented by Lockwood (1991), though these do not depend on any particular view of the relation of mind to brain.
The first argument is as follows. Suppose we are given two mental events A and B for which it can be said that A comes before B. It is a tenet of special relativity that whenever two events are related by ``before'' there exists a frame of reference in which they are in the same place. So ``place'' must be a property of mental events. This argument clearly begs most of the question by assuming that special relativity is applicable to mental events. Indeed, the argument does not even hold for physical events, because it involves a confusion between ``event'' in the general sense and ``event'' in the technical sense in relativity of a point-event. The tenet quoted above is only true for point events.
The second argument is more serious, however. Whatever we may think about mind, most of us hold that our decisions have physical consequences -- so a given decision affects a particular region of space-time. Let us call P the region that is capable in principle of being affected by a given decision. If we believe that causality is a universal physical principle, then P will be what is called a future set, with the property that if x is in P and if y is after x (in the causal sense) then y is also in P. Similarly, our decision depends on (is affected by) a particular region Q of space time which is a past set (defined by replace ``after'' by ``before''). Moreover -- again by appealing to widely believed causal principles -- P and Q will have no overlap, because, if they did, there would be a causal ``vicious circle'' with an event that was influenced by the decision but which also influenced the decision.
Lockwood now wishes to argue that this situation will itself define a region in space-time within which the decision is located, thus establishing the principle that mental events do have a location in space-time. That is, he claims that given the two sets P and Q as described, there is some region R with the property that every point in R lies to the past of the whole of P and to the future of the whole of Q. The trouble is that there is no reason whatever why this should be so, unless we beg the question by assuming in the first place that mental events are indeed located in space-time. Without such a question-begging assumption, it is entirely possible to construct examples of sets P and Q for which there is no such R. The argument therefore fails.
There is a further problem with this argument. Even if a set R did exist, that would only indicate that the action of the mental event was spatially restricted. The mental event itself could be non-located -- provided, of course, that one does not assume at the outset that the only sort of action possible is an action between located entitites that are in contact, which would again beg the question.
Having, I hope, burried this red herring, we must return to the problems posed by the physical description, and address the different ways in which the connection between mind and brain can be formulated. I will sketch some of these in turn.