This article stems from the statement that dialogical approaches to a study of the self face a double challenge: that of developing a conception of the self that both avoids social reductionism and accounts for the stability of the self. In discussing this double challenge, we identify three much debated issues: (a) To what does the notion of "Alter" exactly refer? (b) How could we conceptualize the fact that Subject-Alter interactions are not only interpersonal but entail larger social entities, in particular institutions? (c)What importance should we attach to the materiality of objects? We discuss these three questions from two standpoints - that of linguistics and that of psychology - and illustrate our theoretical proposals with an analysis of an excerpt taken from a focus-group discussion. In conclusion, we argue that the dialogism of discourse provides us with some clues about the dialogicality of the mind, whereas the latter invites us to develop a theory showing the importance of interactions in the construction of the self, to pay more attention to the transpersonal dimension of the social, and to consider that the material world contributes to the construction of the self.