Western metaphysics has long been obsessed with describing reality as
an assembly of static individuals whose dynamic features are either
taken to be mere appearances or ontologically secondary and
This attitude of static essentialist metaphysics derives some paradoxes when change and transformation is to be accounted.
Change is so pervasive in our lives that it almost defeats description
and analysis. One can think of it in a very general way as alteration.
But alteration in a thing raises subtle problems. One of the most
perplexing is the problem of the consistency of change: how can one
thing have incompatible properties and yet remain the same thing?
Change and Inconsistency
Among them is the ship of Theseus.
An approach to tackle this issue is the following: what relates some object A, with an object B at a later instant is a unique (similarity) relation between A and B, A ~ B, which uniquely relates B as the evolution or transformation of A. In this sense, this relation is what persists and not strict identity.
In the above sense, one can talk about A changing (to B), since B is uniquely related back to to A, as its evolution or transformation, but without B having to be identical to A, thus without introducing any paradox or inconsistency.
For any time interval dt between ta and tb (ta is the time instant where A is and tb is the time instant where B, an evolution of A, is) same reasoning can be applied (if dt=ta then B=A, else B~A, for some evolution relation ~ between A and B).
For example, when we see an old friend after many years of being apart what we implicitly do is the following: we recognize this person as the unique historical evolution of the person we knew years ago, not as the identical person that was years ago. In this sense, even though the person is not literally the same, we still recognize them and consider them to be the continuation of our friend back then.
The subtlety is that during a chain of evolution/transformation of A, ie A -> A1 -> A2 -> .. -> Ak, there is no need for this similarity relation to be the same. For example A ~ A1 need not be the same relation as Ak-1 ~ Ak. In the case that some definitive change, like a destruction, took place one then cannot say that Ak is similar, all the way back, to A, in this sense.
Process philosophy instead focuses on processes, and A would not be a static instance, but a process itself. So this identity during change paradox is not present.
Processes may have a start and termination time, need not be eternal, going on forever (ie they may have a finite "lifetime"). Furthermore, processes may exhibit stable features throughout their lifetime.
Taking A as a dynamic process in time is also compatible with previous reasoning based on similarity, in that, different time slices of the process A (eg A1, A2,..) are related to some similarity between them which stems from being the same process A.