Gibbs's phase rule treats mixtures by relating the number of independent variables governing their state to the numbers of phases and independent substances. For the case of a single substance, it provides a criterion of purity. But where more substances are involved, the notion of independent substance is less readily understood. Textbook writers sometimes use algebraic terminology in ways that are suggestive but cannot be taken as literally accurate. I suggest that a mereological interpretation applies to these cases, as it captures more concisely the insights underlying the use of algebraic terminology and illuminates the general notion of substance.