"PHILOSOPHICALLY SPEAKING...":

The classic philosophical thought experiment of identity, the Ship of Theseus, asks thinkers to consider what constitutes identity over time. This article, from Philosophy Now (UK), expands on this idea.

"In many ways I have different properties now than those I had last week. But if I am different, how then can I be the same? ... [L]et me introduce two key terms, the first of which is concrete particular. A concrete particular is an entity which comes into existence at a certain time, passes out of existence at some later time, and exists at all the times in between. Its career is ‘temporally bounded’. Examples include human beings, animals, plants, chairs, and hamburgers – as opposed, for instance, to abstract ideas, such as 1+1=2. A concrete particular is what we usually mean by a ‘thing’ or ‘object’. The second term is diachronic sameness, which literally means ‘the same thing at two times’. If I say something has diachronic sameness, I am saying that 'an individual existing at one time is the same object as an individual existing at some other time' (Metaphysics: A Contemporary Introduction, Michael J. Loux & Thomas M. Crisp, 2017, p.224). Having diachronic sameness means I can accurately describe myself as being the same concrete particular that I was last year, two minutes ago, or when I started typing this sentence.

"Like the notion of time itself, on the face of things, all this seems to be common sense. All of our pre-philosophical intuitions tell us this story, and it is a widely accepted one. In these terms, one answer to the question of what it means to persist through time is that throughout its career a concrete particular is wholly present at each of the different times at which it exists: that is, for any one time that X exists, all of the parts that X has are present at that time. This is the account given by endurantists. Endurantists maintain a steadfast hold on the notion of diachronic sameness, claiming that at any one time in its career, object X is identical with X at any other time it exists. So expressions like ‘the Jack of today’ and ‘the Jack of yesterday’ are referring to one numerically identical concrete particular whose spatial parts are wholly present at any given time throughout Jack’s existence. The endurantist will claim that an object’s spatial parts are the only genuine parts of it.

"By contrast, the account of persistence through time known as perdurantism claims that along with a thing’s spatial parts, it also has temporal parts. Perdurantists argue that over and above the three dimensions of space, there exists a fourth dimension in which an object’s temporal parts exist; so that Jill yesterday, Jill today, and Jill tomorrow, are different parts of Jill. These expressions do not pick out one numerically single object, rather they refer to numerically different parts of a single thing. Its persistence through time consists in its being an aggregate of different temporal parts present at different times. For the perdurantist, these temporal parts are just as real as spatial parts: temporal parts have properties just like spatial parts – such as the property of ‘being Jill last week’. So, along with having spatial extension – for example, fingers and toes – the perdurantist will claim that a concrete particular also has temporal extension – for example, Jill yesterday, Jill today and Jill tomorrow. There are also temporal parts of temporal parts. An example of this could be that Jack this morning is a temporal part of Jack today."
philosophynow.org/issues/141/To_Be_Is_To_Persist