Work in Progress Spring 2025 - Infinities out of the ratios of motion, time, and space: Thomas Harriot as a reader of Proclus' "De motu"

Robert Goulding (University of Notre Dame): Infinities out of the ratios of motion, time, and space: Thomas Harriot as a reader of Proclus' De motu 

Thomas Harriot's papers De infinitis, written in the early seventeenth century, have been an object of speculation for decades. Scattered as they are through multiple volumes of the British Library volumes of Harriot's papers, it has been difficult to discern the overall argument or even intent of Harriot's work on "infinities." In the past, they have been taken to provide strong evidence for the influence of Giordano Bruno's ideas in England. Recently, a group of historians (including myself, Matthias Schemmel, and Stephen Clucas) have reassembled Harriot's papers into what is plausibly their original form. They consist of two main groups: one develops a mathematical argument on the infinite, building upon a theorem of Viète's; and the other explores the philosophical consequence of Harriot's mathematical conclusions, particularly with respect to the continuum. There is no evidence that Harriot engages here with Bruno; in fact, his conclusions are often contrary to Bruno's. His focus is mainly on the sixth book of Aristotle's Physics, which he knows both directly, and through its presentation more geometrico in Proclus's De motu or Elements of Physics. The latter text foregrounds the place of the infinite and the infinitesimal in Aristotle's argument; in this paper, I will show how Harriot's creative disagreement with Proclus allows him to consider differently sized infinites and infinitesimals.

Robert Goulding received his PhD from the Warburg Institute, under the direction of Jill Kraye. After a postdoctoral fellowship at Princeton University, he has been teaching since then in the Program of Liberal Studies at the University of Notre Dame. He is the author of Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History. As well as his ongoing projects on the Harriot manuscripts, he is completing a book on Plotinus's natural philosophy.

IMAGE: Thomas Harriot's papers, British Library: BL Add. MS 6784, fol. 429