A circularity in psychological theories of personal identity

On psychological theories of personal identity, the diachronic identity of a person is defined in terms of psychological properties. But for any human person x who possesses a psychological property ψ at time t, x’s possession of ψ at t grounded both in how x is at t and how x was at times other than t (typically, at least times shortly before t). Thus, x’s possession of ψ presupposes x’s diachronic identity. I expect this is somewhere in the literature, but in any case it seems to me to be a serious problem.