<p>Can formal logic make pure chance intelligible? This paper examines how pure chance, understood as what lies beyond probability and determination, both disrupts and extends formal reasoning. Drawing on Jean Ladrière, we explore how logic, despite its reliance on determinate structures, must engage with an irreducible indeterminacy that conditions its very operation. Pure chance serves as both the origin of logical structures-providing the space for determinations-and their unattainable horizon, toward which reason asymptotically moves. Through Ladrière’s concept of reducing purification, we analyze how logic progressively abstracts from determinations to approach pure existence. Examining five modes of abstraction, from individual objects to logic as a discipline, we show that this movement is inherently eschatological: logic strives toward totalization while never achieving full closure. Parallels with Gödel’s incompleteness theorems and Kant’s self-expanding reason reinforce that logic’s engagement with chance reflects a deeper structure of intelligibility, not a failure of formalization. Ultimately, we argue that hope (espérance) is inscribed in the structure of reason itself. Rather than resolving indeterminacy, logic participates in an intelligibility that always exceeds its grasp, revealing that reason’s fulfillment is always beyond reach, yet always already at work.</p>