Anat Schechtman

The dissertation offers a new reading of Descartes’ causal proof for the existence of God in the “Meditations.” Descartes argues that insofar as we grasp the infinite, an infinite being must exist. Yet, do we really grasp the infinite? The dissertation shows that Descartes defends this position by an appeal to the dependence of the idea of the finite on the idea of the infinite. It is then suggested that this method of invoking dependence foreshadows Kant’s transcendental method. In addition, an examination of proofs in Descartes’ “Geometry” suggests that they, too, invoke dependence, between the “construction” of a geometrical problem and its solution. What emerges from this investigation, then, is a unified account of this method of Descartes’ which both illuminates and connects his philosophy, theology, and mathematics.

Contemporary mathematics and philosophy are dominated by a quantitative conception of infinity, which regards infinity as a number or magnitude. In contrast, prominent thinkers in the seventeenth century held a qualitative conception of infinity as linked to the non-quantitative notions of perfection or reality. This project is the first book-length study of this important, yet relatively unfamiliar, conception of infinity in modern thought. Its main aim is to provide a systematic treatment of this conception through an examination of works by Descartes, Spinoza, and Leibniz. A further aim is to indicate the significance of this conception for contemporary philosophy, which by and large subscribes to the post-Cantorian paradigm of conceptualizing infinity within the parameters of set theory.