Contents -- Introduction 11 -- 1. Purpose and scope of this book 11 -- 2. Acknowledgements 12 -- Chapter 1. The Cognitive and Morphodynamical Turns 15 -- 1. Introduction 15 -- 2. Morphodynamics in cognitive semiolinguistics 16 -- 2.1. Characteristics of the cognitive turn 16 -- 2.2. The path-breaking point of view of Morphodynamics 20 -- 3. Three main examples of a cognitive approach to language 22 -- 3.1. Ray Jackendoff 22 -- 3.2. Ronald Langacker 25 -- 3.3. Len Talmy 32 -- 4. Previous cognitive perspectives 35 -- 5. The problem of formalization and modeling 38 -- 5.1. The limits of formalism 38 -- 5.2. Computationalism: the symbolic/physical dualism 40 -- 5.3. Mathematization vs. Formalization 43 -- 5.4. Modeling and schematization 43 -- 5.5. Morphodynamical models and connectionist models 44 -- 6. Semantic realism and pheno-physics 45 -- 6.1. Thom's squish and pure "etic" linguistics 45 -- 6.2. The phenomenological question 48 -- 6.3. Pheno-physics and ecological information 51 -- 6.4. Realist phenomenology 53 -- 7. Morphodynamics and complex systems 54 -- 8. The problem of Universals 55 -- 9. Morphological schemata and proto-linguistics 60 -- Chapter 2. Things 63 -- 1. Introduction 63 -- 2. The eidetic kernel of the concept of form 64 -- 2.1. Verschmelzung and Sonderung 64 -- 2.2. The t with some current ideas 65 -- 2.3. The origin of the Verschmelzung concept 66 -- 2.4. Qualitative discontinuities and segmentation 66 -- 3. Objective correlates of phenomenological descriptions 67 -- 3.1. Topological-geometrical explanation 67 -- 3.2. Morphodynamical explanation and pheno-physics 68 -- 3.3. Example: elds of oscillators 69 -- 4. A rst cognitive explanation: Marr and wavelet analysis 70 -- 5. Global contour extraction 77 -- 6. Variational segmentation models in low-level vision 77 -- 6.1. Transforming the signal into a geometric observable 77.

6.2. The Mumford-Shah model 78 -- 6.3. The link with diffusion equations 81 -- 7. Scale-space analysis 82 -- 7.1. Multiscale differential geometry 82 -- 7.2. Scale-space morphogenesis of images 84 -- 7.3. Anisotropic diffusion and morphological analysis 87 -- 7.4. Generalizations 90 -- 7.5. A few mathematical remarks about contour diffusion 90 -- 8. Gestaltic applications 92 -- 8.1. Examples 92 -- 8.2. Crest, ridges and cut locus 93 -- 9. Skeletonization 93 -- 9.1. Harry Blum's contour diffusion and grass re models 93 -- 9.2. Neural implementation of cut loci 94 -- 9.3. Properties and structure of cut loci 95 -- 9.4. Leyton's works 95 -- 9.5. The neurophysiological relevance of skeletonization 96 -- 9.6. Skeletonization and mereological constituency 96 -- 9.7. Multi-scale cut locus 98 -- 10. The binding problem and oscillator networks 99 -- 10.1. Cortical brations 100 -- 10.2. The binding problem and the labeling hypothesis 102 -- 10.3. Networks of oscillators 103 -- 10.4. Synchronized oscillations and segmentation 107 -- 10.5. Returning to the morphological nucleus 108 -- 11. Models for the Clark/Pylyshyn debate 109 -- 11.1. A. Clark: Feature-placing and proto-objects 109 -- 11.2. Z. Pylyshyn: Visual indexes and preconceptual objects 111 -- 12. From 2D to 3D 113 -- 12.1. Looking back on David Marr's perceptual theory 113 -- 12.2. Marr's 2 1 / D sketch and Husserl's adumbrations 114 -- Chapter 3. Relations 119 -- 1. Introduction 119 -- 1.1. The gestaltic conception of relations 119 -- 1.2. Scope of this study 122 -- 2. Talmy's Gestalt semantics 124 -- 2.1. Active semantics 125 -- 2.2. Basic structuring schemata 126 -- 3. What is "cognitive topology"? 130 -- 3.1. Convexi cation 131 -- 3.2. Skeletonization 132 -- 4. Operations on schemata: the 'across' puzzle 132 -- 4.1. Invariant of transversality 132 -- 4.2. Variants of transversality 133.

4.3. Plasticity of perceptual-semantic schemata 134 -- 4.4. Virtual structures 136 -- 4.5. Other examples of virtual structures: ctive motion 138 -- 5. Modeling principles and algorithms 139 -- 5.1. Gestalt computation 139 -- 5.2. Spreading activation 140 -- 5.3. Links with other works 140 -- 5.4. Morphological algorithms 141 -- 6. Numerical simulations based on cellular automata 150 -- 6.1. Example 1: "the ball in the box" 151 -- 6.2. Example 2: "the bird in the cage" 155 -- 6.3. Remarks 156 -- 6.4. Example 3: "the lamp above the table" 157 -- 6.5. Links with Kosslyn's works 159 -- 6.6. Example 4: "zigzagging across the woods" 160 -- 7. Wave dynamics in spiking neural networks 161 -- 7.1. Dynamic pattern formation in excitable media 161 -- 7.2. Spatio-temporal patterns in neural networks 162 -- 7.3. Wave propagation and morphodynamical routines 163 -- 7.4. Two wave categorization models 164 -- Chapter 4. Processes: What is an "Attractor Syntax"? 171 -- 1. Introduction 171 -- 2. Dynamical models of syntax 171 -- 2.1. Weak CN vs. strong CN 172 -- 2.2. Elementary vs. non-elementary CN syntax 172 -- 3. Theoretical strategy: using the "morphological turn" 173 -- 3.1. The concept of "structure" and Morphodynamics 173 -- 3.2. Cognitive processing 174 -- 3.3. The con gurational de nition of roles 174 -- 3.4. The link with spatial cognition 174 -- 3.5. The shift of mathematical level: "kernel sentences" 174 -- 4. Connectionism and the theory of dynamical systems 175 -- 4.1. The CNC main thesis and its precursors 175 -- 4.2. CN networks and dynamical systems 175 -- 4.3. Harmony theory 181 -- 4.4. The morphodynamical and PTC agendas 182 -- 5. Fodor and Pylyshyn's arguments against connectionism 183 -- 5.1. The general structure of the F-P arguments 183 -- 5.2. Comments: the problem of a dynamical structuralism 188.

5.3. The main point of the F-P argument 191 -- 5.4. Towards a geometry of syntax 192 -- 6. Refutation of the F-P argument: the main problem 193 -- 7. Connectionist binding and con gurational roles 196 -- 7.1. Smolensky's tensorial product 196 -- 7.2. Dynamical binding 199 -- 7.3. The need for a con gurational de nition of roles 200 -- 8. The link with Chalmers' criticism of F-P arguments 202 -- 9. The epistemology of the morphodynamical paradigm 203 -- Chapter 5. From Morphodynamics to Attractor Syntax 205 -- 1. Introduction 205 -- 2. Christopher Zeeman's initial move 205 -- 3. The general morphodynamical model 209 -- 3.1. The internal dynamics and the internal states 209 -- 3.2. The criterion of selection of the actual state 211 -- 3.3. The external control space 211 -- 3.4. The eld of dynamics 212 -- 3.5. Stuctural stability 212 -- 3.6. Categorization 213 -- 3.7. Retrieving the morphologies 213 -- 3.8. Fast/slow dynamics 214 -- 3.9. Lyapunov functions 214 -- 3.10. The reduction to gradient systems 215 -- 3.11. Contents and complex attractors 215 -- 3.12. Critical points, jets and Morse theory 215 -- 3.13. Normal forms and residual singularities 217 -- 3.14. The local ring of a singularity 218 -- 3.15. Universal unfoldings and classi cation theorems 220 -- 4. A few examples: cusp, swallowtail, butter y 221 -- 4.1. The cusp 221 -- 4.2. The swallowtail 223 -- 4.3. The butter y 226 -- 5. Applications of Morphodynamics 228 -- 5.1. Dynamical functionalism 228 -- 5.2. Actantial interactions and verbal nodes 231 -- 5.3. Actantial paradigms and their temporal syntagmation 233 -- 5.4. Actantial graphs and their combinatorics 234 -- 5.5. Summary of the principles 237 -- 6. Import and limits of Thom's paradigm 239 -- 7. Morphodynamics and Attractor Syntax 240 -- 7.1. The mathematization of Fillmore's scenes 240 -- 7.2. The localist hypothesis (LH) 242.

7.3. The uses of external dynamics 243 -- 8. Force dynamics from Talmy to Brandt 246 -- 8.1. The key idea 246 -- 8.2. Eve Sweetser's systematization 249 -- 8.3. Modal dynamics according to P. Aa. Brandt 249 -- Chapter 6. Attractor Syntax and Perceptual Constituency 259 -- 1. "From pixels to predicates": the seven pillars of cognition 259 -- 2. Apparent motion and the perception of intentionality 259 -- 3. From actantial graphs to cognitive archetypes 261 -- 3.1. Cognitive archetypes 261 -- 3.2. Reformatting actantial graphs 263 -- 4. Contour diffusion and singular encoding of relations 264 -- 4.1. The general strategy for solving the main problem 264 -- 4.2. Contour diffusion, cobordism, and Morse theorem 265 -- 4.3. The example of the Association relation 266 -- 4.4. Generating potentials 267 -- 4.5. Processes and potential deformations 269 -- 4.6. Morse theory 269 -- 4.7. Representing positional information 272 -- 5. Contour propagation and the cut locus theory 273 -- Conclusion 275 -- Bibliography 279 -- Index 299 -- List of abbreviations 305.