Diagrammatic Immanence

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 *
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"
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"