This paper examines the ethical and religious dimensions of mathematical practice in the early modern era by offering an interpretation of Antoine Arnauld and Pierre Nicole’s Nouveaux éléments de géométrie. According to these important figures of seventeenth-century French philosophy and theology, mathematics could achieve extra-mathematical or non-mathematical goals; that is, mathematics could foster practices of moral self-improvement, deepen the mathematician’s piety and cultivate epistemic virtues. The Nouveaux éléments de géométrie, which I contend offers the most robust account of the virtues (...) cultivated by mathematics in the period, was envisaged by its authors to cultivate moral, Christian and epistemic virtues that could serve in the fulfilment of moral and Christian obligations. In this paper, I set out the goals of mathematical inquiry for the Port-Royalists and describe the specific virtues they believed a revised edition of the Elements of Euclid could foster. I show that Arnauld and Nicole believed that an acquaintance with mathematics could render a student of Euclid more just, truth-loving, attentive and humble, and better able to discern truth from falsity. (shrink)

In the Port‐Royal Logic, Arnauld and Nicole argue that eloquence plays a crucial role in the cultivation of the art of thinking. In this essay, we demonstrate that Arnauld and Nicole's reflections on eloquence exemplify the need to reconceive the larger framework in which Cartesian theories of ideas operate. Instead of understanding epistemic agents as solitary thinkers who pursue their intellectual goals without the influence of others, our analysis shows that for Arnauld and Nicole thinking well was an intersubjective discursive (...) activity that unfolds between complexly organized persons. Central to this activity is the ability to gauge the affective and associative tendencies of interlocutors and to communicate accordingly. This ability is required to enable speakers to deal constructively with problems arising from the context sensitivity of language, the influences of the passions, and the audience's capacity to decipher meaning in the communication of ideas that facilitate understanding and knowledge. By drawing attention to communication, affect, and association in the Port‐Royal Logic, we show that there is a significant connection between thinking and expressing oneself well in the early modern period. (shrink)

In the Port-Royal Logic, Arnauld and Nicole argue that eloquence plays a crucial role in the cultivation of the art of thinking. In this essay, we demonstrate that Arnauld and Nicole's reflections on eloquence exemplify the need to reconceive the larger framework in which Cartesian theories of ideas operate. Instead of understanding epistemic agents as solitary thinkers who pursue their intellectual goals without the influence of others, our analysis shows that for Arnauld and Nicole thinking well was an intersubjective discursive (...) activity that unfolds between complexly organized persons. Central to this activity is the ability to gauge the affective and associative tendencies of interlocutors and to communicate accordingly. This ability is required to enable speakers to deal constructively with problems arising from the context sensitivity of language, the influences of the passions, and the audience's capacity to decipher meaning in the communication of ideas that facilitate understanding and knowledge. By drawing attention to communication, affect, and association in the Port-Royal Logic, we show that there is a significant connection between thinking and expressing oneself well in the early modern period. (shrink)