GRICE E MORDENTE

 Scholars and historians of science have considered Giordano Bruno and Fabrizio Mordente's ideas on infinitesimals and commensurability in the context of the historical development of the concept, which  eventually led to Leibniz's infinitesimal calculus. The link is generally explored in the context of the historical evolution of mathematical and philosophical thought on infinity, atomism, and the continuum, rather than a direct personal or philosophical connection between the individuals themselves across different centuries.    Key points regarding the connections made by scholars: Aristotelian problem: Aristotle denied the existence of an actual infinite (both large and small) and maintained the infinite divisibility of the continuum in potentia, a standard view that Bruno explicitly challenged. The issue of commensurability was central to Euclidean geometry and Aristotelian philosophy, where quantities were generally considered commensurable or incommensurable in a specific mathematical sense. Bruno and Mordente: Bruno initially disregarded the Aristotelian distinction between mathematical and physical quantities. Influenced by his controversy with Mordente regarding the latter's proportional compass, Bruno began to argue for the existence of a physical and a mathematical minimum (atomism), making geometric objects (and thus infinitesimals) potentially determinable and commensurable, contrary to the standard Aristotelian view of continuous magnitudes. This represented a significant shift in his mathematical thinking, attempting a reform of mathematics to accommodate the infinitely small. Leibniz and infinitesimals: Leibniz, developing calculus independently of Newton in the 17th century, used infinitesimals (or "incomparably small" magnitudes) as a central component of his notation and method. The philosophical status of these infinitesimals was debated, with Leibniz often describing them as "useful fictions" or ideal entities, without objective physical existence in the strictest sense, but essential for mathematical operations. Scholarly connections: Scholars connect Bruno's radical ideas on the actual infinite and the minimum (atom) to the broader historical trajectory that made the concept of the infinitesimal a viable, albeit controversial, subject of mathematical and philosophical inquiry in the 17th century. While Leibniz did not directly reference Bruno's specific arguments with Mordente, both were grappling with the limits of Aristotelian physics and mathematics regarding the continuum and the infinite, a conceptual shift that paved the way for calculus.  In summary, the connection is typically drawn by historians tracing the conceptual lineage of the infinitesimal and the infinite, identifying Bruno and Mordente's debate as an early, significant challenge to the Aristotelian framework that dominated scientific thought before the era of Newton and Leibniz