Morphology, Neurogeometry, Semiotics: A Festschrift in honor of Jean Petitot 's 80th birthday

Foreword
Contents
1 Introduction
	1.1 Jean Petitot: A Multiverse of Science and Humanities
	1.2 Neurogeometry and Mathematics
	1.3 Semiotics and Aesthetics
	1.4 Epistemology and Phenomenology
	1.5 Selected List of Publications of Jean Petitot
		1.5.1 Authored Books
		1.5.2 Edited Books
		1.5.3 Special Issues of Journals
		1.5.4 Papers
	References
Part I Mathematics
2 On Objectivity and Meaning in Mathematics
	2.1 Conclusion
	References
3 Le vrai, le faux, l\'insignifiant
	3.1 Limites, bords, frontières, ellipsis…
	3.2 La rigueur formelle contre le sens?
		3.2.1 Rigueur et logique
		3.2.2 La Variété infinie et joyeuse des formes
		3.2.3 Quel langage?
		3.2.4 La rigueur ... a posteriori
	3.3 Oublier les cas trop particuliers ellipsis…
		3.3.1 Le général et le particulier : Poincaré
		3.3.2 Transversalité, stratifications : Thom
		3.3.3 Orbites ou pseudo-orbites ? : Laskar
		3.3.4 Information et probabilité : Shannon
	3.4 ellipsis… ou les détails trop précis
	3.5 Du faux lorsqu\'il se révèle fécond
		3.5.1 Une erreur célèbre de Poincaré
		3.5.2 Questions d\'échelle ou: quand l\'insignifiant devient signifiant
		3.5.3 Une erreur de Thom
		3.5.4 D\'autres erreurs fécondes
		3.5.5 Des dogmes utiles
	3.6 Même pas faux!
	References
4 Concept, Sense and Reality
	4.1 Results
	4.2 Examples
	4.3 The Scheme of Meaning
	4.4 From Things to Relations
	4.5 A Quick Tour of History
	4.6 A Scheme of Knowledge
	4.7 Two Ancient Schools
	References
Part II Neurogeometry
5 The Manifold Man
	5.1 The Man of Many Humanities
	5.2 Meeting the Man
	5.3 Teaching Interdisciplinarity—The Journal of Physiology (Paris) Experience
	5.4 Teaching Interdisciplinarity at the Ecole Polytechnique
	5.5 Geometry and Brain Sciences
	5.6 Final Words
	References
6 Enchanted and Actual Spaces
	6.1 Introduction
	6.2 Formal Geometries
		6.2.1 Alberti and Scenographic Geometry
		6.2.2 The Geometry from a Picture Viewer\'s Perspective
		6.2.3 Pictures and Windows
	6.3 Conclusions
	References
7 Cortical Functional Architectures as Contact and Sub-riemannian Geometry
	7.1 Introduction
	7.2 From Functional Geometry to Differential Structure via Contactization, Symplectization and Sub-riermannian Lifting
		7.2.1 The Retinal Plane
		7.2.2 Simple Cells, Modeled via Contactization and Symplectization
		7.2.3 Complex Cells as Extension of Simple Cells Space as Contact or Subriemannian Structures
		7.2.4 Further Extension: Hierarchically Higher Families of Cells
	7.3 From Differential Structure to Lie Groups Representation as Models of Receptive Profiles
		7.3.1 The Retinal Plane: A Commutative Group
		7.3.2 Simple Cells Receptive Profiles
		7.3.3 Complex Cells Receptive Profiles
		7.3.4 Receptive Profiles of Hierarchically Higher Cells
	7.4 Cortical Connectivity and Horizontal Curves
		7.4.1 Fiber Bundle Structure and the Hypercolumnar Structure
		7.4.2 Cortical Connectivity of Simple Cells
		7.4.3 Cortical Connectivity of Complex Cells
		7.4.4 Cortical Connectivity of Hyerarchically Higer Cells
	7.5 Action and Functionality of Receptive Profiles, as Bargmann Transform
		7.5.1 Action of Receptive Profiles as Bargmann Transform
		7.5.2 Action of Intracortical Connectivity and Feature Selection
	7.6 Discussion
	References
Part III Semiotics
8 Jean Petitot, Semiotician
	8.1 A Deferred Meeting
	8.2 A Convergence of Projects
	8.3 The Petitot/Coquet Debate. Focus of His Research
	8.4 From Piero Della Francesca to Cranach the Elder
	8.5 To Conclude
	References
9 Naturalizing Semiotics. Perspectives and Limitations
	9.1 Introduction
	9.2 Structuralism: Historical Sources and Theoretical Limitations
	9.3 Natural Philosophy and the Program of Naturalization in Linguistics and Semiotics
		9.3.1 Semantic Archetypes and Semiophysics
		9.3.2 The Correct Application of Qualitative Mathematics in the Humanities. The Strategies of Petitot, Brandt, and Wildgen
	9.4 The Nature of Semiotic Phenomena and the Limits of a Morphodynamic Description
	9.5 Different Notions of Dynamics and a Range of Methodological Alternatives
	9.6 Conclusions
	References
10 Differentiality: From Saussure to Morphodynamics
	10.1 Prologue
	10.2 Introduction and Generalities
	10.3 Back to Saussure: In Search of Phenomena
	10.4 “Viewpoints” and Empirical Knowledge
	10.5 Abstraction/Generalization
	10.6 Review and Transition
	10.7 Awareness and Difference
	10.8 Wrap-Up and Return to Differentiation
	10.9 The Morphodynamic Solution
	10.10 To Conclude
	Bibliography
11 Three Fundamental Contributions by Jean Petitot to Semiotics
	11.1 The Topological Intuition of Structuralism and Interpretive Semiotics (The “Localist Hypothesis”)
	11.2 Narrativity
	11.3 The Birth of Cognitive Semiotics
	11.4 Conclusions
	References
Part IV Aesthetics
12 The Construction of Meaning in Vision—Three Examples: Bonnard, Hammershøi, Poussin
	12.1 Preamble—A Too Short Personal Note
	12.2 Pierre Bonnard, The Merchant of Four Seasons. Perceptual Grouping: The Defunctionalization of Objects and Their Refunctionalization as Significant Shapes
	12.3 Vilhelm Hammershøi. The Dynamicity of Silent Shapes
	12.4 Poussin, Venus Presenting Arms to Aeneas. Non-genericity as a Tool for Meaning-Making
		12.4.1 Attention and Visual Meaning
		12.4.2 Non-genericity in World Perception and in Image Perception
		12.4.3 Non-genericity and Semiotic Intentionality
		12.4.4 Non-genericity as a Compositional Technique
	12.5 In Guise of a Conclusion
	References
13 Plasticity and Aesthesia: Towards a Semiotics of Art Encompassing the Sensitive Dynamics
	References
Part V Epistemology
14 Minimizing Cognitive Representation
	14.1 Representation and Cognitive Philosophy
	14.2 Defining the General Problem of Cognitive Representationalism
	14.3 Defining the Problem of Minimal Cognitive Representationalism
	14.4 The Hypothesis of Hyperminimal Cognitive Representationalism
	14.5 The Minimal Representation Debate
		14.5.1 Delineating the Minimal Representation Debate
		14.5.2 Qualitatively Minimized Cognitive Representationalism: Clark\'s Proposal
		14.5.3 Qualitatively Minimized Cognitive Representationalism: Wheeler\'s Proposal
		14.5.4 Gallagher\'s Hypermaximalist Objection
	14.6 The Persistance of the Symbolic Prejudice
	References
15 Geometry and Cognition from the Foundations of Mathematics to Theories of Knowledge and Cognition
	15.1 The Origin of a Debate
	15.2 Geometry: From a Science of Space to a Science of Movement in Space
	15.3 Epistemology and Genesis
	15.4 The Constitution of Mathematical Invariants: Their Cognitive Interest
	15.5 Infinity and Geometry: From Continuity to Dynamical Systems
	15.6 Computing
	15.7 Conclusions
	References
16 The Delicate Frontier Between Schematism and Reflection
	16.1 Introduction
	16.2 First Example of Analogy: Structural Stability and an Analogy from Embryology to Development
	16.3 Second Example of Analogy: From Physical Pregnance to Biological Pregnance
	16.4 Summary and Final Remarks
	References
17 Jean Petitot’s New Enlightenment
	17.1 Introduction
	17.2 Epistemology and Transcendental Tradition
	17.3 The Naturalization of the Phenomenological Experience
	17.4 The Emancipatory Value of Science and Technology
	17.5 The Naturalization of the Social Sciences
	17.6 Gobetti, Class Struggle and Spontaneous Order
	References