This dissertation examines the way the Pythagorean conception of the incommensurable structures the assertions of subjective agency in Blaise Pascal’s Pensées (1670), Søren Kierkegaard’s Concluding Unscientific Postscript (1846), and Alain Badiou’s Being and Event (1988). The Pythagoreans coined the term “incommensurable,” alogos, to describe magnitudes that cannot emerge within a specific system of signification. Across three chapters, I extend the Pythagorean understanding of the incommensurable into the areas of philosophy, religious studies, and mathematics in order to posit the fundamental instability at the core of subjective agency. Moving from Thomas S. Kuhn’s failure to define the incommensurable logically in his Structures of Scientific Revolutions, I argue that such a conception of the incommensurable must be understood as fundamentally faith-based.
Given the fact that the incommensurable cannot emerge into signification, its existence must be posited on faith. Pascal, Kierkegaard, and Badiou each move from a faith-based assertion of the incommensurable to offer a conception of subjective agency within a specific system of signification. Thus, against the work of Bonaventura Cavalieri and Evangelista Torricelli, Pascal refigures the incommensurably infinite to establish a heterodox subjective agency within Augustinian faith-by-grace; Kierkegaard manages to navigate the incommensurability of direct communication and personal faith by effacing his pseudonym Johannes Climacus; and Alain Badiou relies on the incommensurable “event” to imagine the possibility the subject’s calling into being of the new. In each of these three texts, the incommensurable functions to guarantee the possibility of subject agency within a specific system of signification.