© 2016

Iconicity and Abduction


  • Analyzes the role of iconic signs in scientific hypothesis-formation

  • Uses category theory to explore the connection between iconicity and abduction

  • Provides an explanatory framework for model-based reasoning in science

  • Integrates formal diagrammatic and mathematical methods in Peirce and Badiou


Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 29)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gianluca Caterina, Rocco Gangle
    Pages 1-25
  3. Gianluca Caterina, Rocco Gangle
    Pages 27-56
  4. Gianluca Caterina, Rocco Gangle
    Pages 57-92
  5. Gianluca Caterina, Rocco Gangle
    Pages 93-110
  6. Gianluca Caterina, Rocco Gangle
    Pages 111-132
  7. Gianluca Caterina, Rocco Gangle
    Pages 133-152
  8. Back Matter
    Pages 153-180

About this book


This book consolidates and extends the authors’ work on the connection between iconicity and abductive inference. It emphasizes a pragmatic, experimental and fallibilist view of knowledge without sacrificing formal rigor. Within this context, the book focuses particularly on scientific knowledge and its prevalent use of mathematics. To find an answer to the question “What kind of experimental activity is the scientific employment of mathematics?” the book addresses the problems involved in formalizing abductive cognition. For this, it implements the concept and method of iconicity, modeling this theoretical framework mathematically through category theory and topoi. Peirce's concept of iconic signs is treated in depth, and it is shown how Peirce's diagrammatic logical notation of Existential Graphs makes use of iconicity and how important features of this iconicity are representable within category theory. Alain Badiou’s set-theoretical model of truth procedures and his relational sheaf-based theory of phenomenology are then integrated within the Peircean logical context. Finally, the book opens the path towards a more naturalist interpretation of the abductive models developed in Peirce and Badiou through an analysis of several recent attempts to reformulate quantum mechanics with categorical methods. Overall, the book offers a comprehensive and rigorous overview of past approaches to iconic semiotics and abduction, and it encompasses new extensions of these methods towards an innovative naturalist interpretation of abductive reasoning.


Semiotics of Iconicity Logic of Abductive Inference Mathematical Abduction in Science Model-Based Reasoning Pierce’s Existential Graphs Logic of Sheaves Categorical Duality Functorial Semantics Sheet of Indication Diagrammatic Reasoning Partial Orders Formal Phenomenology Set-Theoretical Ontology Category Theory Topos Quantum Theory Peter Galison Cayley's Theorem Yoneda’s Lemma Abductive Reasoning in Badiou

Authors and affiliations

  1. 1.Department of MathematicsEndicott College Department of MathematicsBeverlyUSA
  2. 2.Department of Humanities/PhilosophyEndicott College Department of Humanities/PhilosophyBeverlyUSA

Bibliographic information