What Is It to Be Real? Numbers as Real Species of a Category in the Late Medieval Debate about the Ontological Status of Numbers

Abstract The article deals with one of the facets of a hitherto almost completely unexplored subject: the late medieval debate about the ontological status of numbers. It focuses on one of the most popular arguments in favor of a realist view of number. The realist view holds that a number adds a new form over and above the things that it numbers. The argument for the view is based on the thesis that since the categories are a classification of extramental reality, and number belongs to the category of Quantity, it, together with its form, must have extramental existence. The second part of the paper is devoted to an exposition and analysis of various rebuttals of this argument advanced by critics of realism about numbers. Throughout the whole discussion, the paper also gives an evaluation of the dialectical moves made by the participants in the debate.