Iconicity and Abduction

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This book consolidates the authors’ exploration of the relationship between iconicity and abductive inference, emphasizing a pragmatic, experimental, and fallibilist perspective on knowledge while maintaining formal rigor. It particularly examines scientific knowledge and the role of mathematics within it. To address the question of what constitutes the scientific use of mathematics, the book delves into the challenges of formalizing abductive cognition, employing the concept of iconicity and modeling it mathematically through category theory and topoi. A thorough analysis of Peirce's iconic signs is provided, highlighting how his diagrammatic logical notation, Existential Graphs, utilizes iconicity and its representable features in category theory. The work integrates Alain Badiou’s set-theoretical model of truth procedures and his relational sheaf-based theory of phenomenology within a Peircean logical framework. Ultimately, it paves the way for a more naturalist interpretation of the abductive models developed by Peirce and Badiou, particularly through an examination of recent efforts to reformulate quantum mechanics using categorical methods. Overall, the book presents a comprehensive overview of iconic semiotics and abduction, along with innovative extensions toward a naturalist interpretation of abductive reasoning.