Abstract

This dissertation argues that a number of the technical quandaries that bedevil the geometry of Rene Descartes, the vacuum experiments of Blaise Pascal, and the early quadratures of Gottfried Leibniz stem in part from their constitution as spiritual exercises, or modes of cultivation with different religious and secular ends. Each thinker despaired about the disorder of knowledge and society but distrusted available epistemic and institutional solutions. Drawing from different sets of resources---respectively, rhetoric, conversational culture and techniques of perspectival deceptions---Descartes, Pascal and Leibniz each set forth a set of technical exercises intended to perfect the faculties making up the subject. Mathematics and natural philosophy offered at once empirical evidence for humanity's faults and abilities and, if correctly tuned, remedies for its faults. This conviction about the moralizing capacity of knowledge motivated and framed the seeking after new forms of mathematical and natural philosophical knowledge production and the perfection of new means to express and transmit those new epistemic practices. The innovative uses and defenses of algebra in Descartes, experimental narrative in Pascal and infinite series in Leibniz, all new written forms designed to help overcome the insufficiencies of postlapsarian language and thought, were defended as ways simultaneously to gain knowledge and to cultivate the self