 These two theses describe elements in different ways. In the first, elements are explicitly identified by a procedure. Elements are simply the ingredients in a mixture that can be separated no further. The second conception is more theoretical, positing elements as constituents of composite bodies. In the pre-modern Aristotelian system, the end of analysis thesis was the favored option. Aristotle believed that elements were the building blocks of chemical substances, only potentially present in these substances. The modern conception of elements asserts that they are actual components, although, as we will see, aspects of the end of analysis thesis linger. This section will explain the conceptual background behind chemistry’s progression from one conception to the other. Along the way, we will discuss the persistence of elements in chemical combination, the connection between element individuation and classification, and criteria for determining pure substances.