In Mathematics of the Transcendental, Alain Badiou presents category theory, elucidating its internal logic and distinct derivation from set theory. This work is essential for comprehending his broader philosophical system, particularly the transcendental logic outlined in his seminal Logics of Worlds. Badiou’s exploration showcases category theory as not merely an alternative but a complement to set theory, reinforcing his ontological assertions with logical phenomenology.
This book fully articulates Badiou’s use and understanding of category theory and offers profound insights into the mathematical and logical underpinnings of his theory of appearing, making it indispensable for followers of his philosophical trajectory. The text is valuable not only for philosophers seeking to grasp the basics of category and topos theory but also for mathematicians interested in their philosophical implications.
Badiou, who teaches at the École Normale Supérieure and the Collège International de Philosophie in Paris, has a prolific career spanning novels, plays, political essays, and major philosophical treatises. In Mathematics of the Transcendental he continues his tradition of blending rigorous mathematical knowledge with philosophical inquiry, thereby reorganizing and expanding the horizons of contemporary thought.
The translators emphasize the significance of this work, comparing Badiou’s philosophical endeavor to the tradition of Plato, Descartes, Leibniz, and Hegel, all of whom sought to unify mathematical rigor with philosophical depth. The dual focus of Badiou’s engagement with category theory—initially as an ontological rival to set theory and later as a complementary logical phenomenology—reveals his evolving appreciation for its conceptual power.
Mathematics of the Transcendental stands as a testament to Badiou’s commitment to formalization, reflecting his lifelong dedication to intertwining mathematical principles with philosophical exploration. This book not only documents Badiou’s intellectual journey but also invites readers to participate in the rigorous, imaginative, and transformative process of philosophical thought conditioned by mathematics.
Simon Gros 
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