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Diagrammatic Immanence

Category Theory and Philosophy

Rocco Gangle

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A renewal of immanent metaphysics through diagrammatic methods and the tools of category theory

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. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuze’s philosophy of difference in conjunction with the formal operations of category theory.

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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

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).


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.
- Fernando Zalamea, author of "Synthetic Philosophy of Contemporary Mathematics"

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, author of "Synthetic Philosophy of Contemporary Mathematics"

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, Zentralblatt MATH

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