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.
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My current blood pressure is not the product of just my current heartbeat, but is instead a product of many prior heartbeats, which pressurize the system in a way that allows my current heartbeat to maintain. Does this make blood pressure diachronic? If it does, then there is certainly a first heartbeat, as the heart forms in the embryo, and the blood pressure is not present with the first heartbeat but with later heartbeats, as the the circulatory system becomes more fully formed and pressurized.
How does this relate to personal identity? I expect that among those psychological theorists that hold the position that identity is based on prior identity, it is not controversial that an early embryo has no personal identity (psychologically speaking, I mean: it has personal identity in other ways, including epigenetic and genetic identity). It would also not be controversial that in many cases a toddler has a personal identity of the sort that requires a prior personal identity.
Logically, there must be a point in time in the lifespan where the former embryo has an identity where it did not before. That identity is only diachronic because it is a basis for a later identity. Because of this, it would be logical that the initial moment of identity in the child is not diatronic with regard to such personal identity. It may well be diachronic with regard to prior memory.
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