An important feature of the transition from ancient to modern views of matter is the recognition of the distinction between substance and phase, and the realisation that a substance like water is not necessarily liquid, as Aristotle thought, but the same substance might be solid or gas too. This chapter reviews just how surprisingly tenacious the older view was, noting that even Lavoiser had difficulty abandoning it completely although he prepared the ground for doing so. The distinction was clear enough throughout most of the nineteenth century, but received its definitive formulation in Gibbs’ phase rule, which he presented in connection with his formulation of chemical thermodynamics in the late 1870s. The import of this fundamental principle of chemistry is discussed and illustrated in the final sections by way of preparing the ground for discussion of the mereological import of substance and phase predicates in the next chapter.