(2016) Classical problems, non-classical proposals [revised-2017]

At least since Aristotle (Poetics, XX), and as emphasized by Saussure (1916), the dual character of linguistic terms –comprising both sound and meaning- has been recognized as central to natural language. Generative Linguistics has traditionally separated sound and meaning systems, and their respective representations (Chomsky, 1965, et seq.), so that only syntax derives structure, whereas the sound and meaning components are purely interpretive: a departure from European structuralism, according to which sound and meaning are intimately related and in tension (Tesniere, 1959), and also aspects of Glossematics (Hjelmslev, 1961), in which two continua, expression and content, are partitioned in what is called the form of expression and the form of content. In this talk we depart from the Generative model, and explore the consequences of adopting a ‘syntax-as-partitioning’ approach where sound and meaning are in tension, configuring a dynamical frustration (Binder, 2008; Saddy, 2016). We propose that we are dealing with ultrametric high-dimensional fields which configure vector spaces. Given a perturbation to this system, these are parametrized and operated on syntactically. Following Saddy and expanding on Krivochen (2016), we consider the consequences of adopting a field-theoretic approach whereby syntax is a set of topological operations which, by changing the landscape of the off-phase sound (‘phonotactic’) and meaning (‘conceptual’) fields, creates structured manifolds. When syntactic operations change the topological properties of the fields from ultrametric to metric, those manifolds get closer and intersect, triggering the fading of a dimensional attractor and squeezing the core properties of the manifolds into a lower-dimensional, metrized, normal space by means of the center manifold theorem (CMT, Carr, 2006). This approach follows Tesnière and Hjelmslev insofar as (a) the computational operations available in both high-dimensional and low-dimensional spaces are defined by the sound/meaning antinomie; and (b) syntax is not a set of functions operating over discrete symbols but a fundamentally topological mechanism operating over continuous spaces, partitioning them and providing them with a metric, creating manifolds, and getting those closer together until they intersect. A derivation, we claim, oscillates between high- and low- dimensional spaces cyclically, atomizing structure via the CMT.This approach leads to a straightforward definition of derivational cycles in syntactic computations over manifolds, and separates hard conditions from soft conditions in language as a dynamical system. We expand on the idea that a dependency can be established only if the relevant elements belong to the same workspace when the dependency is established. A cycle is thus defined by the dynamics of the metric-ultrametric interface via the CMT. They are both maximal and minimal units: they are minimally interpretable because nothing smaller can be assigned a semantic interpretation. They are maximally generable, because once a critical value for the manifold being generated is reached, a dimensional attractor fades, and no further structure can be built up in that derivational current.