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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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Index 299

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Index Aahrus, 12 Abeles, 162, 163 Ajdukiewicz, 65 Ajjanagadde, 199 Albertazzi, 13 Alvarez, 87, 89 Ambrosio, 80 Amit, 15, 176, 214 Anderson, 240, 242 Andler, 13, 40, 171, 172, 230 Arnold, 115, 213, 221 Azencott, 177, 178 Bach, 55 Baire, 217 Bak, 215 Bassili, 260 Bellemare, 13, 94, 149, 150 Bergen, 234 Berkeley, 187 Berkeley (Univ.), 157 Bermudez, 112 Bialek, 162 Biederman, 97 Bienenstock, 13, 163, 171, 199 Birkhoff, 213 Blakemore, 260 Bloomfield, 56 Blum, 93–95, 127, 154 Bonhoeffer, 163 Bonnet, 80 Bowen, 214 Bozzi, 13 Brady, 95 Brandt, 11–13, 43, 240, 246, 249–252, 254– 258, 276 Brault, 87 Brooks, 18 Buser, 71 Caen, 13, 171 Campbell, 163 Carlson, 140 Casati, 14 Cessac, 179 Chafe, 35 Chalmers, 202, 203 Chambon, 53 Chang, 234 Chenciner, 213 Chomsky, 36, 39, 46, 57, 58, 190, 240 Churchland, 40 Citti, 80, 107 Clark, 109–112 Cole, 55 Comrie, 55, 56 Cooper, 40 Coquet, 13 Coseriu, 56–58 Coullet, 69, 70, 105, 179 Courte`s, 252 Cowan, 103 CREA, 13, 14 Crisanti, 179 Culioli, 35 Daido, 105, 106 Dal Maso, 80 Damasio, 161 David, 80 De Giorgi, 80 Decety, 260 300 INDEX Descle´s, 13, 243, 244, 261–263 Dirac, 71, 82, 83 Dougherty, 141 Doursat, 13, 14 Doya, 180 Doyon, 179 Dreyfus, 42 Durgin, 260 Eco, 13 E´cole Polytechnique, 13 Edelman, 199 Emilsson, 70 Engel, 102 Ermentrout, 104 Evans, G., 112 Evans, L.C., 92 Feigenbaum, 179 Feldman, 157 Fergusson, 56 Fillmore, 33, 35, 238, 240–242, 261 FitzHugh, 163...

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