In 1640, Bourdin, a Jesuit and mathematics professor at Clermont College in Paris, challenges in public disputation several theses of Descartes’ Dioptrics. Descartes reacts angrily. First, he is outraged that the objections were not sent to him before being publicized. Second, because he was hoping that the Jesuits would support and disseminate his views, Descartes perceives Bourdin's challenge as a flat rejection and the sign of a coming offensive by the whole order. Indeed, Descartes is persuaded that the discipline within the Society of Jesus is such that none of its members speaks without expressing the opinion of the whole body. Thus, in order to avoid having to fight one Jesuit after another, Descartes writes to the rector of Clermont College to demand that any Jesuit criticizing him be officially commissioned. He also suggests that the society choose another champion in place of Bourdin, whom he regards as incompetent and on whom he repeatedly pours scorn. Otherwise, Descartes threatens, he will write a systematic refutation of Scholastic philosophy and science taught in Jesuit colleges, presented alongside his own to the advantage of the latter (this project would eventually lead to the Principles of Philosophy, after Descartes gave up the critical part).

The response is not as Descartes expects. In 1641, Bourdin, uninvited by Descartes or by Mersenne, raises objections against the recently released first edition of the Meditations. This time, the criticisms are conveyed privately to Descartes. But Bourdin also proposes a nonaggression pact: he will not publish his objections if Descartes refrains from writing against the Jesuits. Again, Descartes takes Bourdin's piece as the reaction of the whole society and, indignant, does not waver. He adds Bourdin's objections (known as the Seventh Objections, which are the longest set), along with his scathing replies, to the second edition of the Meditations (1642). He also appends an open letter to the head of the French Jesuits, Dinet, in which he attacks both Bourdin and the Dutch Calvinist theologian Voetius (AT VII 449–603, CSM II 303–97).

By the end of 1642, Descartes is more or less reconciled with Bourdin and the Jesuits. Still, Bourdin's objections might indeed reflect the society's negative judgment on Descartes’ thought. Notably, Bourdin does not engage with particular theses but aims at the Meditations’method.