Diagrammatic Immanence: Category Theory and Philosophy

by Rocco Gangle

Overview

Spinoza, Peirce and Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation.
Gangle integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuze’s philosophy of difference in conjunction with the formal operations of category theory. He introduces the methods of category theory from a philosophical and diagrammatic perspective in a way that will allow philosophers with little or no mathematical training to come to grips with this important field.

Product Details

ISBN-13:	9781474474580
Publisher:	Edinburgh University Press
Publication date:	06/04/2020
Pages:	264
Product dimensions:	6.14(w) x 9.21(h) x (d)

About the Author

Rocco Gangle is Associate Professor of Humanities/Philosophy at Endicott College, USA. His work on contemporary French thought, Spinoza, Peirce and diagrammatic logic has appeared in Philosophy Today, SubStance, Political Theology and other journals and edited collections. He is the translator of François Laruelle’s Philosophies of Difference (Continuum Press, 2010).

Table of Contents

Acknowledgements; Introduction; 1 Spinoza and Relational Immanence; 2 Diagrams of Structure: Categories and Functors; 3 Peirce and Semiotic Immanence; 4 Diagrams of Variation: Functor Categories and Presheaves; 5 Deleuze and Expressive Immanence; 6 Diagrams of Difference: Adjunctions and Topoi; Conclusion; Bibliography.

What People are Saying About This

This exceptionally useful text explores the rich and complex contours of the relation between category theory and philosophy with admirable clarity. In the process it develops a diagrammatic philosophy of immanence as an exemplar of this relation, and demonstrates the value and remarkable potential of category theory for philosophy.

Simon B. Duffy, Yale-NUS College, Singapore

Fernando Zalamea

The Philosophy of Category Theory comes of age with Spinoza, Peirce and Deleuze, understood through functors, presheaves, and adjunctions. A compelling use of nearly 50 diagrams supports a deep understanding of structure, variation, and difference. Gangle introduces a new, needed voice for the provocative "visual turn" of the 21st Century.

Editorial Reviews

Do I believe that category theory and diagrams can be useful to philosophy? Certainly. Does Gangle's book provide an illustration and a useful entry point for philosophers who might want to learn how to use category theory in their own research and thinking? It will depend on their sensitivity to the philosophical issues chosen by Gangle. His presentation of category theory and categorical notational systems are clear and instructive. That will certainly be useful and could be a starting point to non-mathematicians. As to whether, in the end, philosophers will be convinced and will find ways of using these concepts and notational systems in their own philosophical work, I will leave that to readers to decide.

Notre Dame Philosophical Reviews - Jean-Pierre Marquis

This exceptionally useful text explores the rich and complex contours of the relation between category theory and philosophy with admirable clarity. In the process it develops a diagrammatic philosophy of immanence as an exemplar of this relation, and demonstrates the value and remarkable potential of category theory for philosophy.Simon B. Duffy, Yale-NUS College, Singapore

Fernando Zalamea

This is a philosophical essay whose intended public is composed by philosophers. Nevertheless, for a mathematician it may be of interest because it provides a different, alternative and in some ways provocative view of category theory. In turn, this view hints toward an immanent foundation of mathematics, although the text does not elaborate this line specifically. It is a stimulating way of thinking out of the usual tracks of mathematics, and it could bring new ideas and insights or, perhaps, just provide a critical, non-standard point of view based on a solid philosophical tradition.

Zentralblatt MATH - Marco Benini

"Do I believe that category theory and diagrams can be useful to philosophy? Certainly. Does Gangle's book provide an illustration and a useful entry point for philosophers who might want to learn how to use category theory in their own research and thinking? It will depend on their sensitivity to the philosophical issues chosen by Gangle. His presentation of category theory and categorical notational systems are clear and instructive. That will certainly be useful and could be a starting point to non-mathematicians. As to whether, in the end, philosophers will be convinced and will find ways of using these concepts and notational systems in their own philosophical work, I will leave that to readers to decide."— Jean-Pierre Marquis, Université de Montréal, Notre Dame Philosophical Reviews

"This is a philosophical essay whose intended public is composed by philosophers. Nevertheless, for a mathematician it may be of interest because it provides a different, alternative and in some ways provocative view of category theory. In turn, this view hints toward an immanent foundation of mathematics, although the text does not elaborate this line specifically. It is a stimulating way of thinking out of the usual tracks of mathematics, and it could bring new ideas and insights or, perhaps, just provide a critical, non-standard point of view based on a solid philosophical tradition." —Marco Benini, Università degli Studi dell'Insubria

From the Publisher