In chapter 3 of Individuals, entitled ‘Persons’, Strawson argues against dualism and the no-ownership theory, and proposes instead that our concept of a person is a primitive concept. In this paper, it is argued that the basic questions that frame Strawson’s discussion, and some of his main arguments and claims, are dubious. A general diagnosis of the source of these problems is proposed. It is argued that despite these problems Strawson gives an accurate and very insightful description of the way we think about ourselves, which should form the starting point for more speculative accounts of ourselves.