10.3—
Computation, Mathematization, and Connectivity

It is here that the computer paradigm may prove to be of considerable worth. What computer science provides is a rigorous set of terms and methods for talking about certain kinds of systems: systems whose distinctive characteristic is their functional organization. What can be characterized in functional terms can be described rigorously by computer science. Now in order for this to be of use to psychology, several things must be the case. First, psychological phenomena must be functionally describable. And here the sense of "function" is the technical mathematical sense. To put it differently, psychological phenomena must be such as to he describable by an algorithm or effective procedure expressible in the form of a machine table. Here computer science

supplies two things: first, a language (or set of languages) for the rigorous specification of algorithms; and second, an assurance that a very large class of algorithms (the finite ones) have a structure that can be instantiated by a physical system. So the computer paradigm might do two things here for psychology: it might provide a rigorous language for characterizing the system of causal interrelations between psychological phenomena, and at the same time provide assurance that this characterization can be realized in a physical mechanism that does not simply flout every law of nature. In short, the computer paradigm might provide the right tools for the mathematization of at least some part of psychology.

If computer science might directly provide the right tools for psychology to progress towards mathematical maturity, it might thereby indirectly provide an important contribution towards connective maturity as well. Of course, computation is not the right sort of notion to provide everything needed for connective maturity. Computation is an abstract or formal notion, and is therefore neutral, in important ways, about what sorts of things it describes. This is not to say that it does not itself specify functionally delimited kinds, but rather that in so doing it remains absolutely agnostic about (a ) what the nature of these kinds may be, apart from their formal interrelations, and (b ) how these functions are realized. A single computational description could apply equally well to a set of silicon chips, a network of cells, a structure of gears and levers, a set of galaxies, or the changes in affections of a Cartesian immaterial substance. Hence, even the best imaginable computational description of cognition would, in and of itself, do nothing about connecting psychology with other disciplines. For all that computational description buys us, it might still turn out that the things so described are not brain processes after all, but processes in an immaterial soul without even any analogous processes taking place in a brain. To be sure, the fact that computational structures can be physically instantiated is "bracing stuff" to someone who feels committed both to cognitivism and to materialism. It shows that the evidence for intentional realism may not be evidence against materialism, and vice versa. But the claim that cognitive processes are functionally describable has no consequences for the debate over whether materialism is correct in its ontological claims.

Nor does any computational description of cognitive processes have any direct consequences for how they are realized in the nervous system. This is, of course, a famous benefit of the computational approach: it allows for the possibility of the realization of equivalent functions in vastly

different architectures—human, angelic, Martian, or Macintosh. The strongest constraint the computational description might place upon the realizing system is that it share the functional structure characteristic of the realized cognitive process. That is, if cognitive phenomenon C is realized through a realizing system R , and C is characterized by functional structure F , it must be the case that R is also characterized by F .

But while this does not directly connect psychology with, say, neuroscience, it may provide just the sort of link that is needed to forge a connection between the two. The brain, after all, is a complex and bewildering set of interrelated units, and those who wander in its tractless wastes are constantly groping to discern what are the significant units and relations. The availability of careful characterizations of cognitive processes is the sort of thing that might serve, if not as a Rosetta stone for the brain, at least as a hastily scribbled map. Indeed, the grand appeal of the functionalist strategy in empirical psychology lies largely in the fact that starting "top-down" and unlocking black boxes one stage at a time has often seemed to be the only way one can proceed if one is interested in phenomena lying at a higher level than, say, on-center off-surround structures. As a somewhat idealized characterization, sometimes the only way to proceed is to get as clear as possible on the form of the process you wish to describe and then look for some candidate realizing system that has the right "shape" to match it.

It thus appears that progress towards mathematical maturity is one of the more likely roads towards connective maturity as well. The link between the two is not hard and fast: one might get a good descriptive functional psychology without making much progress in seeing how the functional structures are realized in the brain, much as we have no microexplanations for gravity or magnetism. But then again, progress in mathematization might bring connective progress in its wake, as combinatorial chemistry was eventually supplemented by a structurally oriented chemistry that is strongly linked to physics. One simply does not know in advance how the cards will fall.