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Table of Contents
Intro
Introduction
Topological Visualisation, or How to Apprehend the Invisible
Feynman Diagrams: A New Way Forward in Theoretical Physics
Diagrammatics and Invariants in Knot and Braid Theory
Philosophical and Scientific Implications
Diagrammatics and Category Theory
A French Singularity in Epistemological Field: Gilles Châtelet
Phenomenology of Space (and Time) and Diagrammatic Epistemology
Towards a "Diagrammatic Critique of Aesthetics"
Acknowledgments
Contents
Part I Logic, Forms and Diagrams
The Semiotics of Laws of Form
Introduction
Finding Distinction
Finding Primary Arithmetic
Finding Logic
Finding Mathematics
The Arctic Essay
Epilogue
References
Can We "Show" the Correctness of Reasoning? On the Role of Diagrammatic Spatialization in Logical Justification
Introduction
The Eulerian Thesis: The Logical Correctness of the Diagrams "Jumps to the Eyes"
Determining the Logical Framework of Our Research
The Late Emergence of "Analytical" Logic Diagrams in a Pedagogical Context
First Section: The Cognitive Advantages of the Diagrammatic Method
Second Section: Can Diagrams Be Given the Task of Validating Reasoning?
Third Section: Can a Diagram Show ("donner à voir") the Nature of a Proposition or the Correctness of a Reasoning?
Back to Euler
Showing the Nature of a Proposition
Showing the Correctness of a Reasoning
Some Remarks on the Relationship Between the Principles of Logic and Spatiality in Syllogistic (From Aristotle to Hamilton)
Conclusion: Summary and Discussion
References
Articles and Monographs
Proceedings of International Colloquia
Catégorification et méthode
Le polynôme de Jones
Sterographic Projections in Dimension 1 and 2 (Figs. 4 and 5)
Origins of Birational Geometry and Classification
Cremona Transformations (Fig. 6)
de Jonquiéres Transformations (Fig. 8)
Classical Problems and Rational Parametrizations: Curves and Surfaces
Classical Problems and Rational Parametrizations: Cubics
The Classical Turn in Algebraic Geometry
References
Knots, Diagrams and Kids' Shoelaces. On Space and their Forms
Introductive Remarks: Shoelaces, Knots, and the Intuition of Space
Exploring and Visualizing 3-manifols and the Importance of Topology
Introduction
Topological Visualisation, or How to Apprehend the Invisible
Feynman Diagrams: A New Way Forward in Theoretical Physics
Diagrammatics and Invariants in Knot and Braid Theory
Philosophical and Scientific Implications
Diagrammatics and Category Theory
A French Singularity in Epistemological Field: Gilles Châtelet
Phenomenology of Space (and Time) and Diagrammatic Epistemology
Towards a "Diagrammatic Critique of Aesthetics"
Acknowledgments
Contents
Part I Logic, Forms and Diagrams
The Semiotics of Laws of Form
Introduction
Finding Distinction
Finding Primary Arithmetic
Finding Logic
Finding Mathematics
The Arctic Essay
Epilogue
References
Can We "Show" the Correctness of Reasoning? On the Role of Diagrammatic Spatialization in Logical Justification
Introduction
The Eulerian Thesis: The Logical Correctness of the Diagrams "Jumps to the Eyes"
Determining the Logical Framework of Our Research
The Late Emergence of "Analytical" Logic Diagrams in a Pedagogical Context
First Section: The Cognitive Advantages of the Diagrammatic Method
Second Section: Can Diagrams Be Given the Task of Validating Reasoning?
Third Section: Can a Diagram Show ("donner à voir") the Nature of a Proposition or the Correctness of a Reasoning?
Back to Euler
Showing the Nature of a Proposition
Showing the Correctness of a Reasoning
Some Remarks on the Relationship Between the Principles of Logic and Spatiality in Syllogistic (From Aristotle to Hamilton)
Conclusion: Summary and Discussion
References
Articles and Monographs
Proceedings of International Colloquia
Catégorification et méthode
Le polynôme de Jones
Sterographic Projections in Dimension 1 and 2 (Figs. 4 and 5)
Origins of Birational Geometry and Classification
Cremona Transformations (Fig. 6)
de Jonquiéres Transformations (Fig. 8)
Classical Problems and Rational Parametrizations: Curves and Surfaces
Classical Problems and Rational Parametrizations: Cubics
The Classical Turn in Algebraic Geometry
References
Knots, Diagrams and Kids' Shoelaces. On Space and their Forms
Introductive Remarks: Shoelaces, Knots, and the Intuition of Space
Exploring and Visualizing 3-manifols and the Importance of Topology