There is a long and rich tradition of thinking about relations, stemming from ancient Greek philosophy and running through the Middle Ages, which has been guided by the intuition that relations reduce to the monadic properties of related things. Despite the prominence of this tradition in the history of philosophy, and despite the stature of philosophers whose support it claims, reductive approaches to relations are now widely rejected on the basis of advances in twentieth-century logic. This di…
Read moreThere is a long and rich tradition of thinking about relations, stemming from ancient Greek philosophy and running through the Middle Ages, which has been guided by the intuition that relations reduce to the monadic properties of related things. Despite the prominence of this tradition in the history of philosophy, and despite the stature of philosophers whose support it claims, reductive approaches to relations are now widely rejected on the basis of advances in twentieth-century logic. This dissertation challenges the reigning consensus by examining some of the theories that comprise the older tradition. It argues that these theories are far more subtle and sophisticated than contemporary philosophers have recognized, and that properly understood, avoid all the standard 'logical' objections. ;The dissertation focuses on the texts of three medieval philosophers writing before Aquinas: Boethius , Abelard , and Albert the Great . These texts are commentaries on Aristotle's short treatise, the Categories. In the Categories Aristotle identifies relations as one of the ten irreducible kinds of beings, and devotes the entire seventh chapter to analyzing their nature and ontological status. Although this study takes Categories 7 as a starting point for its discussion, it focuses on the commentary tradition that grew up around the Categories during the years 510-1250 A.D. ;By examining theories developed within the Categories commentary tradition, this study attempts to show that medieval philosophers have a contribution to make to our contemporary understanding of relations. It reveals that there is an important distinction to be drawn between the ontological reduction of relations and their logical or conceptual reducibility . The way in which medieval philosophers relied on this distinction demonstrates the compatibility of at least some reductive approaches to relations with the advances made by twentieth-century logicians. ;The dissertation includes English translations of Boethius's Latin translation of Categories 7, chapter 7 of the early medieval composite edition of the Categories , and all the relevant portions of Boethius's, Abelard's, and Albert's Categories commentaries
