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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 1. The Cognitive and Morphodynamical Turns 15

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CHAPTER 1 The Cognitive and Morphodynamical Turns 1. Introduction In the 1970’s and early 1980’s a number of works were devoted to the use of morphodynamical models—that is, dynamical mathematical models of forms, patterns and structures—in structural and semiolinguistic disciplines. We dedi- cated three books and several papers to their applications in phonetics (analysis of the relationships between audio-acoustics and phonological categorization, models of categorical perception), actantial theory1 (case grammars, structural syntax), and structural semiotics (semantic categorization, models of Greimas’ narrative schemes and Le´vi-Strauss’ canonical formula of myth). These models came from natural sciences and participated in the increasingly radical natu- ralization of mind undertaken by cognitive science. To emphasize this point, we qualified them to be part of a Physics of Meaning (see [279]). In parallel, during the 1980’s the development of cognitive grammars led to a complete reversal of the theoretical status of the syntactic-semantic structures of natural languages. The convergence of profound theoretical transformations resulted in a spectacular progress of dynamical approaches—first with connec- tionist models of neural networks, then with dynamical models proper, the latter being a natural generalization of the former. In fact, as Daniel Amit [11] has shown, introducing a hypothesis of full feedback and recurrence in a neural network allowed to reinterpret Hebbian reverberation as the stabilization of its dynamics into one of several attractors during a “psychological” time (a few hundred ms).2 As Tim van Gelder [393] states: If connectionism was the most dramatic theoretical revolution...

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