Temporaryism—the view that not always everything always exists— comes in two main versions: presentism and expansionism (aka the growing block theory of time). Both versions of the view are commonly formulated using the notion of being present, which we, among others, find problematic. Expansionism is also sometimes accused of requiring extraordinary conceptual tools for its formulation. In this paper, we put forward systematic characterisations of presentism and expansionism which involve neither the notion of being present nor unfamiliar conceptual tools. These characterisations are full blown logics, each logic comprising an axiomatic proof system and an intuitive semantics with respect to which the system is both sound and complete.