6.7.1—
Functionalist Theories of the Mind

I believe that this is precisely the case with functional description of the mind and of language as well. Let us begin with math-functionalist theories of the mind. The founding hypothesis here is that math-functional description of the sort provided by machine tables or general-purpose programming languages provides mathematical tools adequate to the task of describing the form of mental states and processes. Mental states and processes are real-world phenomena, and describing them is bound to involve some abstraction. We treat as irrelevant things like mechanical force (though people do get banged on the head, often to the detri-

ment of their thinking) and gravitation (though it has been claimed that some individuals are affected by the full moon and NASA does psychological experiments on the effects of free-fall), and so on. Likewise we treat some physiological factors like blood sugar and hormone levels as constant much the way we treat voltage levels in a computer as constant, abstracting away from the fact that variations in these things affect real-world performance in ways that are of considerable concern to doctors and systems operators, respectively. Perhaps this strategy for mathematizing psychology will pan out in the long run. Perhaps it is fundamentally flawed, as claimed by Dreyfus (1972) and Winograd and Flores (1986). Perhaps it would work in principle, but the number of mutually dependent variables makes it impossible to carry out in practice. My concern is not with the prospects of this strategy but with what it would provide if carried out in detail. And what it would provide is precisely analogous to what, say, Newton's equations provided for classical mechanics: a mathematically exact model of mental states and processes.

Given the preceding discussion of mathematical models in general, it should be clear why a psychological machine table would not be an analysis of the nature of mental states and processes. At a rich level of description, the model is indeed a model of mental processes . But we know it is a model of those processes and not something else for the very pedestrian reason that we knew it all along: the model is a model of the mind because producing a model of the mind was our goal from the outset. Such models can be better or worse insofar as they involve better or worse approximations of the form that is really present in processes in vivo (that is, in the sense that Einstein's model is better than Newton's, and Newton's is better than Descartes's). So at the rich level of abstraction, the content of the model is not a consequence of its mathematical form alone. At this rich level we do indeed have a description in which we can identify mental states as such and characterize them in terms of their location in a network of other mental states, inputs, and outputs. However, we can do this only by assuming the individual mental states as mental states and assuming the network, and then characterizing the relations precisely in terms of the machine table. At best, we can analyze one mental state in terms of its relation to the others, holding their existence and relatedness as a kind of background assumption. But in doing this we never break out of the web of the intentional, unless it should prove possible to define all of the inner states in terms of a neutrally characterized set of inputs and outputs. But arguably this "best case" itself involves a misunderstanding. For in such a case what we are

doing is picking out a set of states by dint of an abstract description of their causal interrelations. But this by no means assures that those causal relations are the essential properties of the states involved, nor that there could not be a variety of distinct state types that could occupy isomorphic causal roles.

On the other hand, at the sparse level the "model" is now just a mathematical entity. This level of abstraction is indeed useful even for the scientist (as opposed to the mathematician) at times, such as when one is interested in seeing whether, say, classical mechanics is a special case of relativistic mechanics, and does so purely by mathematical manipulations. But it cannot tell us what the interpretations of the mathematical symbols used to express the theory might be. For example, the formulas used for information theory do not tell us whether they are being used to express a model of information or of heat—or indeed that they are being used to express any real-world properties at all. In the case of the mathematization of psychology, here all we have is the machine table, which is a representation of a function in the mathematical sense. There is nothing about the table that tells us what the domain of the table is. Indeed, it could serve equally well as a functional description of all kinds of things: some abstract objects, some interesting real-world phenomena, some monstrous meriological contrivances. If we do not start out knowing that we are talking about the mind, there is nothing about the math-functional description that will tell us that we are doing so.

In short, math-functional description cannot provide us with an analysis of the nature of mental states and processes any more than equations for entropy can teach us the difference between heat and information. What it would do is no more and no less than what other mathematical models do in the other sciences: namely, to specify exactly the mathematical form of real-world phenomena of whose existence and nature we have some kind of independent knowledge.