This article offers solutions to two historically unresolved subject matter problems in psychology: (a) What is a “person”? And, (b) what is the “self”? Part 1 of the article presents Peter Ossorio’s (2006) Descriptive Psychologically based answer to the first of these questions, an answer that comprises a paradigm case formulation of the concept “person” itself, as well as a parametric analysis for describing individual persons. Part 2 of the article presents a new solution to the second question. The solution is a disarmingly simple one in which “self” or “I,” consistent with actual usage, means simply and essentially “this person”—this holistically considered, embodied, conscious, deliberate actor that I intend when I use the terms “I” or “me” or “myself”—as opposed to “that person,” the specific individual I intend when I say “he” or “she” or “herself.” The ways in which this formulation (a) uniquely possesses an empirical grounding, (b) avoids many historical problems that have arisen in trying to delineate the nature of the self, and (c) integrates the field of self psychology, are all demonstrated. The article provides logical and empirical arguments in support of both of its formulations, as well as for the importance of the science of psychology possessing such formulations of its core subject matter.