Two years into the project, i2’s first results shed new light on the history of logic, epistemology, metaphysics, and mathematical thought from the late 14th to the 16th century.
Our first Objective (O1) is to reassess mid-14th century “nominalist” semantics—i.e. theories on the relation between words, thoughts, and things by authors like John Buridan, Albert of Saxony, and Marsilius of Inghen. Unlike Buridan, and contrary to what one might expect from a “nominalist,” Marsilius considers chimeras and absolute impossibilities imaginable, understandable, and even proper referents. But how can we grasp such impossible concepts? If knowledge arises from reality, how can we form a concept of a chimera? While Marsilius omits these issues in his logic, he addresses them in some of his commentaries on Aristotle—e.g. Questions on Metaphysics and Questions on De Anima. Using provisional editions we prepared, we are answering these questions by examining Marsilius’ logic alongside his metaphysics. We found that this new semantics of necessarily empty terms is neither meaningless nor a mere technical tool divorced from our understanding—as shown in specialized communications and forthcoming publications.
O2 aims to reconstruct the “via Marsiliana” in the 15th–16th centuries, supporting our historical hypothesis of a tradition linking Marsilius’ semantics to Cardano’s early thoughts on complex numbers. We are mapping Marsilius’ influence, particularly at the University of Pavia, through texts later familiar to Cardano as a student and young master. As demonstrated in specialist communications and forthcoming works, we identified Giovanni Apollinare Offredi as a key figure in the reception and transmission of Marsilius’ views at the intersection of logic and natural philosophy. We are preparing a critical edition of Offredi’s Treatise on the First and Last Instant, a pivotal yet overlooked link in this chain of ideas.
O3 investigates three seemingly distinct senses of “imagination”: (a) a cognitive step elaborating sense perception; (b) a form of abstraction in mathematical construction; and (c) by the 14th century, the conceiving of things that are more or less—even absolutely—impossible. After two years, we found these senses less distinct than they appear, often merging in late medieval debates. This is exemplified by John Dorp of Leiden, an influential late-14th-century nominalist logician influenced by Buridan and Marsilius. As shown in scientific communications, Dorp connects impossible, perceptual, and mathematical imaginations.
