Cognitive scientists have become increasingly interested in understanding how natural minds represent and reason about possible ways the world may be. However, there is currently little agreement on how to understand this remarkable capacity for ‘modal thought’. Drawing on formal frameworks for reasoning about possibilities from logic, philosophy, computer science, and linguistics, we argue that this capacity is built from a set of relatively simple component parts, centrally involving a basic ability to consider possible extensions of a piece of the actual world. Natural minds can productively combine this basic ability with a range of other capacities, eventually allowing for the observed suite of increasingly more sophisticated ways of reasoning about what is possible. We demonstrate how this (de)compositional account can accurately predict both what has been observed in the trajectory of children’s developing capacity to reason about possibilities and what has been observed in how modal thought is expressed within and across natural languages. Our hope is that this framework will provide cognitive scientists with a more systematic way of understanding variation in actuality-directed modal thought and talk, which will serve as the beginnings of a common language that allows researchers across disciplines to better understand each other.