In a non-Everettian context (Hugh Everett) identity may be understood in different ways. Consider David Wallace’s example of the ancient pot (P2). An antiquities specialist informs you that your P2 is the same as P1, a famous pot owned by Emperor Tiberius in ad 30. There is a four-dimensional tube P in spacetime extending from P1 toP2—a spacetime worm. The matter of the tube has certain structural and dynamical connections running along it. If we write P(t) for the contents of P indexed at time t, the specialist’s claim is underwritten by the existence of some structural-dynamical relation R holding, for each t, between P(t) and P(t + δt), with δ signifying a difference or change in time. Each indexed moment along P(t) would simply be a stage of the pot’s existence.
There are two basic philosophical conclusions about the identity of the pot being the same pot. The first is called the Worm View as I’ve previously alluded to. Under this view, P is the pot and P1 and P2 are just different names for the pot (literally, P1 = P2). The second view that the P1 and P2 are the same is the Stage View. The pot appears as an instantaneous three-dimensional object: P1 = P(AD 30); P2 = P(AD 2016). Thus, to say that P1 and P2 is the same pot, it means: P2 is linked to P1 by a continuous chain of R-related pots.