Meeting 27


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DATE: Tuesday, March 2

TIME: 1:30 PM Princeton time (EST) / 8:30 PM Bucharest time (GMT+2)

PANEL: Parallel Influences: Ancient Greek Geometry in the Port-Royal Logic and Spinoza’s Ethics

SPEAKERS: Laura Kotevska (University of Sydney) and Raffi Krut-Landau (University of Pennsylvania)


In this session, we describe some of the underappreciated consequences of early moderns’ examination of ancient Greek geometry. Focusing on Arnauld and Nicole’s Logic, and Spinoza’s Ethics, we show that Euclid inspired insights beyond mathematics that encompassed reflections on reasoning well and the nature of eternity. 

Geometry and the Art of Thinking

Laura Kotevska

Dismayed by “encounter[ing] nothing but faulty minds who have practically no ability to discern the truth”, Arnauld and Nicole penned the Logique, ou l’art de penser. Their principal goal was to cultivate their readers’ good sense, mental accuracy, and capacity for self-understanding. The Elements of Euclid, I argue, played a significant role in Arnauld and Nicole’s prescriptions for thinking well. The Port-Royalists looked to the Elements as the standard of demonstrative certainty and to geometry as the science, par excellence, for accustoming the mind to sound demonstrations and arriving at the truth. A discussion of what this meant for the seventeenth-century reader of the Logique concludes the talk.

Hidden Figures: Spinoza on Geometrical Construction and Potentiality

Raphael Krut-Landau

Spinoza famously believes that everything that can exist, must. Nevertheless, he sneaks into his metaphysics certain things that could exist, but don’t. Or so I will argue. I make my case by discussing two unnoticed sources of Spinoza’s metaphysics. The first is Aristotle’s theory of geometrical construction, the influence of which shows in Ethics 2p8s. The second is Proclus’s commentary on the first book of Euclid’s Elements, the influence of which can be seen in 5p31s, where Spinoza says he will fictionally describe the eternal mind “as if it were now beginning to be.”

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