Breaking the lines is the on-going research project that I am carrying out at KU Leuven as a FWO Junior Postdoc (2021-2024).
It is centered on one fundamental issue in the history of philosophy and science, namely, the debate about atomism. Regarding this debate, late medieval thinkers made a remarkable contribution with long-lasting influences on Modern thought. The aim of the project is to shed new light on the mathematical approach by which the medievals questioned a central problem in natural philosophy, i.e., the nature of continuum.
This medieval debate was marked by two opposing stances on the nature of geometrical extension: ‘divisibilism’ (which claims that everything which is in a space – be it a geometric figure or a body – is indefinitely divisible) and ‘indivisibilism’ (which maintains that extended spaces are grounded on elements – atoms – that cannot be divided). These positions were held by Aristotelians and atomists, respectively. 13th- and 14th-century discussions on indivisibles were grounded in the reading of Aristotle’s works on natural philosophy – especially the Physics – but Islamicate sources, such as Avicenna’s and Averroes’s works, enriched this debate substantively.
A distinctive feature of the debate over the continuum in natural bodies between Aristotelians and atomists consists in the mathematical arguments raised to defend the one tenet or the other. More precisely, geometrical reasoning enlivened these discussions, making use of techniques of parallel or radial projection. In geometry, the assumption of the existence of indivisibles (i.e. points or indivisible lines) leads to absurd conclusions, such as that even the diagonal and the side of a square, whose ratio is impossible with respect to Euclidean geometry, can have a common measure, i.e., the indivisible itself. Arguments of this sort were more and more recalled in the field of natural philosophy: a renewed, deeper, and indissoluble bond between mathematics and physics was constituted.
From today’s perspective, one can rightly hold that Aristotelian philosophy contributed only indirectly to the medieval debate on atomism by providing geometrical explanations, as the genuine core of the Aristotelian writings did not contemplate mathematics. However, medieval thinkers engaging with atomism could refer to one ‘Aristotelian’ mathematical work, the De lineis indivisibilibus. Translated into Latin in the 13th century and possibly a genuine work of Theophrastus, this brief but fundamental text was ascribed to Aristotle throughout the Middle Ages. The author of the De lineis indivisibilibus argues against the theory of the indivisible lines – hence the name of my project. Tracing back to Senocrates, this theory postulates the existence of a primary and indivisible unit of linear measurement, by which even the immeasurable magnitudes can be related. So this pseudo-Aristotelian text criticized the theory of indivisible lines by showing its incongruous consequences within both the geometric and logical realm.
Who translated the De lineis indivisibilibus into Latin? Scholarship credited Robert Grosseteste (ca. 1170 – 1253), 13th-century polymath, to be responsible for the first Latin translation of the text. Although this claim needs further verification, Grosseteste’s acquaintance with De lineis indivisbilibus is corroborated by some of his philosophical tenets, especially in his De luce, in which he develops his original theory of atomism, combining the metaphysics of light and hylomorphism.
This pseudo-Aristotelian text did not allow a univocal reading. Did it contribute to setting a clear boundary between atomists and Aristotelians? Or did it contribute to developing special forms of atomism? How were its geometric reasonings received and exploited? Only a careful consideration of the reception of this fundamental source can unequivocally define the earliest medieval roots of Renaissance and Modern atomism and shed new light on this crucial moment in the history of philosophy and science.
What is sure is that the De lineis indivisibilibus had a remarkable success in the late Middle Ages. As a consequence, it is still preserved in more than seventy codices disseminated in libraries across Europe!
To sum up
Breaking the lines takes its name from an ancient theory on indivisible lines as constituting every three-dimensional object. This research path will lead to a thorough knowledge of the geometrical arguments used by late medieval philosophers, retracing the medieval roots of the philosophical discussion of the geometric space. The first critical edition of De lineis insecabilibus will be produced and its impact on Latin atomism evaluated, and further evidence in support of the attribution of its Latin translation to the 13th-century polymath Robert Grosseteste will be provided.