Abstract

This study examines Pascal's collected works, up to and including his Pensees, from the perspective of geometry. Pascal's geometry is seen not exclusively as a model for clear demonstration or for demonstrable certainty but primarily as a means of discovery. As a consequence, the initial focus of this study is on Pascal's practice of geometry from the projective geometry of the 'Essay on Conics' and the use of the 'Arithmetic Triangle' in the development of a theory of probable outcomes to the application of both of these methodologies in the solution of the 'Cycloid' problems near the end of his life. The apparent eclecticism of these works hides a common basic concern with the problem of invention, or a creative use of data or pre-existing materials in the establishment of new ideas. The problem of invention is at once tied to the rhetorical tradition inherited from antiquity and medieval culture and to 'method,' the focus of the European intellectual in the mold of Ramus, Bacon, and Descartes. Pascal's inventive practice likewise reflects the aims of these two discursive programs: finding new ways of persuasion and finding ways to new knowledge. The key to Pascalian invention is the combinatoire, a systemization of inventive approaches issuing from medieval meditative and dialectical practices. Identified in the late Renaissance with the occult sciences, the combinatoire becomes for Pascal a tool for his scientific investigations and for his construction of an initiatory passage to faith and to a search for knowledge of the divine. In much the same way, the fragmentary nature of the Pensees is a sign both of the combinatory invention used in the composition of the text and of the initiatory aim of its rhetoric. The Cartesian itinerary, essentially a path of successive conclusions leading to a full knowledge and mastery of the world, is rewritten by Pascal in the figure of this frightening, inconclusive initiation pieced together from experience, reason, and intuition