Authors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Studies in Applied Philosophy, Epistemology and Rational Ethics (SAPERE, volume 29)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
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.
Keywords
- 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
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Department of Mathematics, Endicott College Department of Mathematics, Beverly, USA
Gianluca Caterina
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Department of Humanities/Philosophy, Endicott College Department of Humanities/Philosophy, Beverly, USA
Rocco Gangle
Bibliographic Information
Book Title: Iconicity and Abduction
Authors: Gianluca Caterina, Rocco Gangle
Series Title: Studies in Applied Philosophy, Epistemology and Rational Ethics
DOI: https://doi.org/10.1007/978-3-319-44245-7
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: Springer International Publishing AG 2016
Hardcover ISBN: 978-3-319-44244-0Published: 27 September 2016
Softcover ISBN: 978-3-319-83019-3Published: 15 June 2018
eBook ISBN: 978-3-319-44245-7Published: 13 September 2016
Series ISSN: 2192-6255
Series E-ISSN: 2192-6263
Edition Number: 1
Number of Pages: XIII, 180
Topics: Logic, Category Theory, Homological Algebra, Epistemology, Cognitive Psychology, Semiotics