They appear to have sharp categorial distinctions because there are loci of relative stability within a dimension of
variation. The degree of“discreteness vs. gradedness”in a dimension then reflects the relative steepness of stability
gradients in the neighborhood of such loci. The discrete categories of a functional description are therefore to be
regarded as a useful approximation to the behavior of the relevant part of the neural substrate, with the recognition
that there will be situations where the approximation breaks down and we must resort to more elaborate modes of
functional description.^8
The second proble min bringing neural and functional descriptions into potential align ment is, I think, more severe. It
arises from the fact that the functional description of language is inherently combinatorial. For example, we cannot
simplysay thatthepositioninstate-space encoded byFig. 1.1 is thesum ofthepositionsofallitsspeech sounds. Each
speech sound is a position inphonological spacethat excludesallother positions. To simplysum them wouldbetosay
thatthe phonologicalpart of state-space invokedby thesentence is simultaneouslyð,ə,I, 1 , and so on—a total mush.
Rather itis necessary to specify theoverallstate (inpart)asðfollowed by a followed byəand so on. But itis notclear
how to set up a binary relation such as “followed by” in terms of a state-space. Similar difficulties emerge in
instantiatinghierarchical treestructures in terms ofa state-space.Moreover, because thesizeofutterances isunlimited,
the state-space also must be unlimited. We will come back to this problem in Chapter 3, concluding that neural
modelers for the most part have not come to grips with the depth of this problem. It thus remains a significant
challenge to the possibility of melding the neural and functional approaches.
Thesefirst twosections have engaged in a very abstract discussion, not an ideal way to start an exposition of linguistic
theory. But itisnecessaryinorder tosituatetheinquiryproperly. In1965 lifewas perhapssimpler: Chomskycouldjust
say (1965: 4):“in the technical sense, linguistic theory is mentalistic, since it is concerned with discovering a mental
reality underlying actual behavior.” He clarifies this statement in a footnote (p. 193) that states the standard
functionalist line of the period.
The mentalist, in this traditional sense, need make no assumptions about the possible physiological basis for the mental reality that he studies.
In particular, he need not deny that there is such a basis. One would guess, rather, that it is the mentalistic studies that
26 PSYCHOLOGICAL AND BIOLOGICAL FOUNDATIONS
(^8) Smolensky (1999 : 594) proposes the hypothesis of“Symbolic Approximation”:“In the domain of language, the patterns of activation constituting mental representations
admit abstract,higher-level descriptionsthatare closelyapproximatedby thekinds ofdiscrete,abstract structures posited by symboliclinguistictheory.”Making appropriate
substitutions for Smolensky's intentional terms“mental,”“representations,”and“symbolic,”this is essentially what is envisioned here.