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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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Introduction 11

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Introduction 1. Purpose and scope of this book The purpose of this book is to present mathematical models of the relations between perception and language. If we had to condense it into one formula, we could say that it tries to show that syntax is to perception what algebraic topology is to differentiable manifolds: spanning several levels of categorization, it identifies in the visual geometry of perceptual scenes abstract invariants that can be reformatted and redescribed as syntactic constituent-structures. Al- gebraic topology examines the universe of differentiable manifolds and makes explicit rough information about their global structure. This is made possible by categorizing these structures into algebraic structures such as homotopy, homology, and cohomology groups. In this book we will look at the universe of images and try to make explicit rough information concerning their morpholog- ical structure. We will show that this is possible if we use specific mathematical theories for categorizing the structures into non-symbolic syntactic scripts or frames, which can then be translated into symbolic syntactic structures. Our investigation takes place in the context of a naturalist approach to structures conceived in the structuralist sense. Claude Le´vi-Strauss famously claimed that “social sciences will be structural sciences or will not be” (“les sciences humaines seront structurales ou ne seront pas”). We would like to add that “social sciences will be natural sciences or will not be”. Of course, this statement can have some plausibility only if we broaden the classical concept of natural...

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