Cognitive Morphodynamics: Dynamical Morphological Models of Constituency in Perception and Syntax (European Semiotics / Sémiotiques Européennes)

✍ Scribed by Jean Petitot

• Publisher: Peter Lang AG, Internationaler Verlag der Wissenschaften
• Year: 2011
• Tongue: English
• Leaves: 312
• Edition: New
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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 fit 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: fields of oscillators 69
4. A first 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 grassfire 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 fibrations 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. Convexification 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: fictive 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 configurational definition 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 configurational roles 196
7.1. Smolensky’s tensorial product 196
7.2. Dynamical binding 199
7.3. The need for a configurational definition 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 field 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 classification theorems 220
4. A few examples: cusp, swallowtail, butterfly 221
4.1. The cusp 221
4.2. The swallowtail 223
4.3. The butterfly 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