Thus far my arguments have been largely negative, to insist that there is no reason to assume discrete categorization in phonetics. The implication is to pull the discreteness rug out from under phonology. So if phonetics cannot explain the discreteness of phonology, how can we account for the distinct phonological objects we linguists so clearly observe there? Languages seem to exhibit discretely different places of articulation, manners, vowel heights, etc, in the units used to spell lexical entries. Where could these come from? But first note that linguistics is not unique in trying to account for the nature of structured things, invariant identities under transformation. Such issues lie at the heart of biology and other fields. Indeed, the notion of an `object' or identity turns out to be just as problematic even computer science (Brian Smith, 1996).
If one assumes that cognition is a continuous-time dynamical process embedded in neural tissue and an external physical environment, then a new set of theoretical tools become appropriate - the tools of dynamical systems (see Port and van Gelder, 1995 and Kelso, 1995). Morphological structures arise in this world on many temporal and spatial scales, from the individual stars and galaxies of astronomy, to species and self-organizing skin patterns in biology, to molecular valences or tornadoes in physics. Simple integer ratios are found even in the resonant frequencies of uniform tubes and strings. None of these spatio-temporal forms can be explained by simple `analysis into their parts' and cannot be constructed by `merely assembling together their structural atoms' - like the way that phonological structures are assembled from phonetic atoms. Instead, they seem to generate themselves over time.
René Thom coined the term morphogenesis to describe the process of the creation of a form as a temporally stable pattern, typically exhibiting some specific symmetries (often periodic ones in space or time) from within a flux of dissipating energy. The mechanisms by which such self-organizing dynamics creates an `object' (or other more complex forms) are beginning to be understood at a mathematical level of abstraction [Kelso et al., 1994, Haken, 1983, Kelso, 1995]. If we abandon the dogma that `language is a formal system', we may see that phonological structures, as structured events in time, are phenomena that are not completely unrelated to other domains of biology, and may be explained in similar ways. Cognition is a system that runs in continuous time following dynamical laws. In some situations, it produces discrete `object'-like structures in space-time. In the case of speech, for example, the relevant space is an abstract one that can be derived from either articulation or acoustics.
Such a theory of phonology, rather than merely providing a specification of parameters that some (yet unimagined) production and perception implementational systems are supposed to carry out in real time, a dynamical description will show (or at least suggest) just how such phonological objects could be both produced and perceived. Obviously it will be a challenging task to develop a theory of phonology along these lines. But it seems clear that this is where the future of our discipline lies. The theory of language must show at least how abstract linguistic structures that are invariant across a community of speakers as well as between production and perception could be created as stable `morphs' of a community of speaker-hearers [Port, 1986].