The two aspects of Descartes split apart in his intellectual heritage. His Geometry instructed Newton and Leibniz, and is forever integrated into the living body of mathematics. Mathematicians remember him with the name “Cartesian product” for ordered pairs in set theory and geometry.
In theology, the story is more complex. It would be unfair to suppose Descartes’ bows to the Church were insincere. He really was a devout Catholic. His commitment to philosophy and science originated in a dream-vision of the Blessed Virgin.
Descartes was very considerate of the Church’s worries. Still some denounced him as a skeptic or crypto-skeptic. His First Meditation raises profound doubt. Does the Third Meditation really dispel it? Will his “clear and distinct idea” really revive faith, once his doubt has shaken it? In 1663 he was put on the Index (Vrooman, p. 252). In 1679 Leibniz wrote of Descartes’s philosophy, “I do not hesitate to say absolutely that it leads to atheism” (Leibniz, p. 1).
In the following century, nevertheless, Cartesianism became popular among Church apologists. But Descartes’s follower, the “God-intoxicated” Spinoza, was denounced as an atheist, and “Spinozism” became a synonym for atheism. Cartesians were prominent denouncers of Spinoza (Balz, pp. 218–41).
