In the Categories Aristotle claims that substances may be the subjects of true predications, but that a substance may never be truly predicated of a subject. Yet in the Metaphysics substance is identified with form, although form may be predicated of a subject. The questions posed by these two claims about substance remain no matter how the puzzle in Aristotelian interpretation is solved. Frege, and most contemporary philosophers, hold that individuals are not predicable of anything. This is reflected in the standard formal semantics of first order logic. The identity of substance and essence, on the other hand, has won little sympathy in the analytic tradition. On close examination, however, it is found that there is little reason to hold that the differences between subjects, or individual terms, and predicates reflects an ontological difference. An adequate language may be formulated in which the distinction between individual terms and monadic predicates is eliminated altogether. Once the claim that substances cannot be predicated is abandoned, the question of how to distinguish substances from other predicables takes on renewed urgency. A critical examination of recent work on the persistence of objects provides support for the view that material substances are necessarily members of a hierarchy of kinds, from genus to infima species. Substances may be distinguished from a wide variety of material predicables, and may be identified with the remainder. A formal system of quantified modal logic with identity provides a tool for understanding the identity of substance and essence. In this system, predication is interpreted by means of set inclusion, rather than by means of set membership. This is in keeping with some of the traditional views of predication expressed by Aristotle, Porphyry, and the Port-Royal logicians, and it provides a framework for the examination of related problems in philosophical logic.