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Cognitive Morphodynamics

Dynamical Morphological Models of Constituency in Perception and Syntax

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Jean Petitot

This book – written in collaboration with René Doursat, director of the Complex Systems Institute, Paris – adds a new dimension to Cognitive Grammars. It provides a rigorous, operational mathematical foundation, which draws from topology, geometry and dynamical systems to model iconic «image-schemas» and «conceptual archetypes». It defends the thesis that René Thom’s morphodynamics is especially well suited to the task and allows to transform the morphological structures of perception into Gestalt-like, abstract, proto-linguistic schemas that can act as inputs into higher-level specific linguistic routines.
Cognitive Grammars have drawn upon the view that the deep syntactic and semantic structures of language, such as prepositions and case roles, are grounded in perception and action. This study raises difficult problems, which thus far have not been addressed as a mathematical challenge. Cognitive Morphodynamics shows how this gap can be filled.

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Chapter 2. Things 63

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CHAPTER 2 Things 1. Introduction In this first technical chapter we address the first class of entities from the Things/Relations/Processes trilogy of cognitive grammars. As we have seen in the previous chapter, every form (and, in particular, every shape) results from the emergence of qualitative discontinuities on a substrate space. Rather evi- dent for physical and visual forms, this rule is also a universal semiolinguistic principle. As it was strongly emphasized by Louis Hjelmslev, and restated later by Algirdas J. Greimas, every form results from the articulation of an amor- phous “materia”, that is, from the discretization of an underlying continuum by means of discontinuities. We will show that even at the most primitive and elementary levels of the phenomenology of visual perception, the constitution of boundaries that de- limit homogeneous regions—what is called the segmentation problem—already raises considerable difficulties when attempting to elaborate segmentation mod- els conform to the advances of visual neuroscience and computational vision. Ronald Langacker’s concept of “scanning” (Chapter 1, Section 3.2.2) pointed towards a difficult technical problem requiring sophisticated mathematical tools. We want to introduce these tools in the present chapter, as we will use them again in subsequent parts of this book. • In Section 2 we begin with a pure phenomenological description of 2D image segmentation. We think that the best description was given by Edmund Husserl in the early twentieth century, following ideas from his master Carl Stumpf, one of the founders of the Gestalt theory. • We then present...

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