Personal reference, one of the simplest functions of human language, presents linguistic theory with one of its most basic problems: what is the range of possible person systems, and why? Impossible Persons offers an innovative and parsimonious solution to this problem and, in the process, formulates a fresh understanding of what features are in linguistic theory. Shifting the empirical focus away from syncretism towards more abstract partitions, the book shows that person and spatial deixis alike exploit the same small number of partitions, with a much greater number unattested in both domains. The challenge posed by this new empirical insight is met by positing just two features, which generate all and only the attested partitions without recourse to extrinsic constraints. To create this exact generative capacity, Impossible Persons refutes the standard view that features denote first order predicate. Instead, they and their values denote actions by sets on sets. This change in perspective yields a wide range of robust consequences, including a well saturated typology of morphological compositionality for different persons, a straightforward but novel view of how person and number interact in the syntax and semantics, a basis for the nexus between person and spatial deixis, and an understanding of the primitives of thought that ramifies beyond linguistics into more general cognitive scientific concerns.