This chapter develops a phenomenological account of what it is to encounter someone as a person, an achievement that many discussions of intersubjectivity presuppose rather than address. I take, as a starting point, Sartre's view in Being and Nothingness that our sense of others is pre-conceptual, bodily and involves a distinctive way of experiencing possibilities. I concede that Sartre's emphasis on the loss of possibilities is too restrictive, but defend this more general view. In so doing, I consider some alterations in the structure of interpersonal experience that can occur in psychiatric illness. I propose that they are best interpreted as changes in a felt sense of possibility that is constitutive of our sense of others as persons.