Valerie Hartcastle and Istvan Berkely both regard this as a matter of definition:
[Hartcastle:] I take it that part of what is driving this discussion is the question whether our brains could be a computer. It would be unfortunate if our definition of what a computer is ruled it out of hand, contrary to any well-developed and well-informed intuitions regarding this matter.However, they disagree as to whether this posed a problem for the magic paper account:
[Berkeley:] It seems to me to be a requirement that brains should count as being computational in at least some respects. This is because, as Hayes' noted (Sec. 3.9), machines like IBM XTs are called computers due to their similarities to human computers. It would seem to me that an account of computation which failed to capture this intuition would simply be defective.
[Hartcastle:] Hayes claims that computers have to operate over patterns that behave as syntactic formuli. Whether connectionist machines have syntax and can be described as manipulating patterns to produce output is a well-known dispute in philosophy and cognitive science. I don't want to answer that question here; I don't know the answer. I do though want to flag this as an area of concern. Hayes appears to have already assumed the answer is yes in the definition.This isn't obvious. If one looks closely enough at the way a computer works, the symbols in the memory will not be instantiated by any particular pattern of electrical charge, especially if the machine does clever things like memory paging and online file management. Since a computational simulation of a computer is itself a computer (much as my Powerbook consists mostly of software), it could well be that the computer described by Freeman is itself rather a simple device serving as an interpreter for a more complex machine whose ``cognitive currency'' consists of symbols which are quite intricate dynamic patterns in the simpler machine's memory.
Worse, if brains work at all like the way Walter Freeman thinks, for example, then Hayes's definition is really in trouble (or brains just aren't computers). If our cognitive currency can be described as limit cycles in phase space whose patterns are generated and maintained by the underlying activation of neurons (but not by any particular pattern of individual neuronal activity), then it is difficult, if not impossible, to describe what is happening as operations over syntax.
However, all of this is conjecture, and I concede to Hartcastle that if something like Freeman's model is accepted as the proper account of brain functioning, then it becomes a nontrivial task to show how the brain can be a syntactic computer. It seems clear that the human CNS is capable of producing and processing syntax, and of encoding information that is externally expressed in syntax, all of which strongly suggest that it might work by storing and manipulating syntax; but this is not a conclusive demonstration.
[Berkeley:] Hayes position makes it quite clear that PDP models should count as computational too. Firstly, most connectionist systems are instantiated as virtual machines upon Von Neumann architectures, and as a consequence would count as computational. Secondly, what little evidence that exists with respect to the internal structures of connectionist systems, seems to indicate that such systems contain representations (in Dretske's sense) and may even, in certain circumstances be described as having operations which manipulate those representations. Indeed, in some cases I would go as far as claiming that connectionist systems contain ``rules.'' (Berkeley et al. 1995)