The concept of diachronic identity contains a serious puzzle. Irving Copi once described the puzzle of diachronic identity by observing that these two statements both seem true but appear inconsistent:

(a) if a changing thing really changes, there can’t literally be one and the same thing before and after the change;

(b) if a changing thing remains one and the same thing throughout the change, then it can not really have changed.
Stuart A. Burns