Powered properties, modal continuity, and the patchwork principle

The principle of modal continuity has become an increasingly popular bit of modal epistemology, featuring prominently in debates about mereology, value, causation, and theism. It claims, roughly, that degreed properties are modally unified. So, if the property of being three inches tall is exemplifiable, so is the property of being four inches tall, and five inches tall, etc. Despite its plausibility, in this paper I show that there is a class of counterexamples to modal continuity: what I call ‘powered properties.’ More surprisingly, I show that an instance of these powered properties is entailed by another widely popular family of modal principles: the Lewisian patchwork principles, also known as cut-and-paste, or recombination, principles. Thus, despite appearing to be similar, and motivated by plenitudinous intuitions about the nature of modality, it turns out that the continuity and recombination approaches to modality rely on crucially different pictures of plenitude.