Aristotle is the first in the history of Western Philosophy to provide a list of categories. His list includes the following: substance [e.g., man] or quantity [e.g., four-foot] or qualification [e.g., white] or a relative [e.g., double] or where [e.g., in the Lyceum] or when [e.g., yesterday] or being-in-a-position [e.g., is-lying] or having [e.g., has-shoes-on] or doing [cutting] being-affected [e.g., being-cut]. Since then, other philosophers have provided their own unique list of categories. For example, E.J. Lowe lists kinds, attributes, objects, and modes as the fundamental categories. Given this diversity, three questions are pertinent: (1) Is there a way of definitively establishing a list of categories? (2) How are particular categories established? (3) What is the justification for such a procedure? These questions were addressed and debated by many medieval authors. Thomas Aquinas and Duns Scotus addressed them and their views substantially influenced subsequent attempts to answer these questions. Aquinas proposed and implemented a logical technique for establishing the number and identity of the categories and Duns Scotus argued that Aquinas's technique fails and that no technique as that used by Aquinas can be used to establish the list. This debate is the subject of my dissertation. First, I offer a philosophical interpretation of Aquinas's so-called derivation of the categories. Aquinas says that the list of categories can be established by reflecting on the ways that a predicate of a proposition is related to its subject. This approach aims to distinguish propositions from each other that signify different categories according to their logical structure. In opposition to contemporary interpretations of this view, I argue that the beginning point for Aquinas is a reflection on the ways in which the predicates of per se propositions are related to their subjects. I point out that, according to Aquinas, a predicate can be per se related to its subject in three ways (namely, primo modo, secundo modo, and quarto modo). I then show that the only kind of per se propositions that can signify substance are primo modo propositions; the only kind of per se propositions that signify quantity and quality are secundo modo propositions; and the only kind of per se propositions that signify the remaining seven categories are quarto modo propositions. In this way, Aquinas distinguishes the categories strictly according to the logical structure of propositions. Next, I discuss Duns Scotus's criticism of Aquinas's logical technique for establishing the list of categories. Although he acknowledged that there are only ten categories of being, Scotus argued both that Aquinas's specific attempt at establishing the categories fails and also that the very possibility of establishing the list of categories through a logical technique is impossible. The latter criticism is at the heart of Scotus's attack on Aquinas's position. Scotus states that categories are distinguished from each other according to real essences and can only be determined through metaphysics. Logic, since it is indifferent to the distinction between that which exists in the extra-mental world and that which exists only in the mind, presupposes an understanding of the categories and cannot be used to determine or distinguish them in any way. There is a radical distinction between how metaphysics and logic approach essences. The metaphysician considers essences as they are in themselves, whereas the logician deals only with these essences insofar as they are produced or mediated by the intellect. Thus, the logician can only consider the essence of categories insofar as they are understood according to the "second intention" of "highest genus." According to this understanding, there is no distinction among the categories; although quality and quantity are understood as distinct from each other metaphysically, logically they are both understood exactly in the same way, namely, as "highest genus." According to Scotus, an understanding of essences at the level of second intentions does not offer an understanding of how essences are in themselves. Categories are about the most basic kinds of real being and not about the most general kinds of predicates. Therefore, a logical justification of them from logic is not possible. Finally, I argue that Scotus's criticisms of Aquinas can be deflected when a fuller understanding of Aquinas's position is propounded. Finally, in the conclusion of the dissertation, I reflect on how this debate impacts contemporary metaphysical discussions of determining the nature, order and number of ontological categories. I focus mainly on the position of E.J. Lowe in The Four-Category Ontology. I discuss his criteria for establishing ontological categories and for establishing a certain order of priority among them. I show that all four of Lowe's categories (objects, tropes, universal kinds and universal properties) can be established through Aquinas's logical approach. (Abstract shortened by UMI.).