Petau was a Jesuit, poet, classical scholar, controversialist, professor of philosophy, and theologian. This polymath humanist was admired by the much younger Pierre-Daniel Huet, who greatly resembled him. He was also much admired by Jacques-Benigne Bossuet, who defended him against the charges of Socinianism made by Pierre Jurieu. He practiced a form of “positive” theology, with careful attention to tradition and ancient sources. He had a bitter, extended debate over free will and grace with Libertus Fromondus (pseudonym Vincent LeDoux) and then with Amable de Bourgeis. He also attacked Arnauld's De la fréquente communion, in what was an early round in the battle between the Jansenists and the Jesuits. His De libero arbitrio was an offprint from a later work, perhaps rushed into print as a Jesuit response to Jansenius's Augustinus (1640). Despite all this, he was accused of Jansenism himself, an interpretive issue of relevance to his significance for Descartes.
He appears only twice, it would seem, in the Cartesian corpus. First, he is mentioned explicitly by name in a letter, probably written from Leiden to Mesland on May 2, 1644. Descartes says there that he has not read what Petau has written but that, given how Mesland has explained himself on the free will, probably advancing Petau's views, there is not wide disagreement among them on the topic. A second text is taken by Adam and Tannery (AT IV 172) to be perhaps a letter to Mesland of February 9, wherein Descartes says, at the outset, that he fully agrees with the “Reverend Father.” It is possible that the referent is Guillaume Gibieuf, as Adrien Baillet thinks (1691, 2:516), or Mesland, as others have thought, or someone else, but the rest of the paragraph, on indifference of the will, seems best to support the Petau hypothesis proposed by Étienne Gilson. In particular, the two notions of indifference deployed by Petau enable Descartes to agree with him that indifference in one sense is essential to the will, while maintaining that in his own, other sense, it is the lowest grade of freedom.
See also Arnauld, Antoine; Free Will; Huet, Pierre-Daniel; Jansenism; Jesuit; Mesland, Denis