Perdurantism

Perdurantism or perdurance theory is a philosophical theory of persistence and identity. The perdurantist view is that an individual has distinct temporal parts throughout its existence. Perdurantism is usually presented as the antipode to endurantism, the view that an individual is wholly present at every moment of its existence.
The use of "endure" and "perdure" to distinguish two ways in which an object can be thought to persist can be traced to David Kellogg Lewis (1986). However, contemporary debate has demonstrated the difficulties in defining perdurantism (and also endurantism). For instance, the work of Ted Sider (2001) has suggested that even enduring objects can have temporal parts, and it is more accurate to define perdurantism as being the claim that objects have a temporal part at every instant that they exist. Currently there is no universally acknowledged definition of perdurantism. Others argue that this problem is avoided by creating time as a continuous function, rather than a discrete one.
Perdurantism is also referred to as "four-dimensionalism" (by Ted Sider, in particular) but perdurantism also applies if one believes there are temporal but non-spatial abstract entities (like immaterial souls or universals of the sort accepted by David Malet Armstrong).
Worm theorists and stage theorists.
Perdurantists break into two distinct sub-groups: worm theorists and stage theorists.
Worm theorists believe that a persisting object is composed of the various temporal parts that it has. It can be said that objects that persist are extended through the time dimension of the block universe much as physical objects are extended in space. Thus, they believe that all persisting objects are four-dimensional "worms" that stretch across space-time, and that you are mistaken in believing that chairs, mountains, and people are simply three-dimensional.
Stage theorists take discussion of persisting objects to be talk of a particular temporal part, or stage, of an object at any given time. So, in a manner of speaking, a subject only exists for an instantaneous period of time. However, there are other temporal parts at other times which that subject is related to in a certain way (Sider talks of "modal counterpart relations", whilst Hawley talks of "non-Humean relations") such that when someone says that they were a child, or that they will be an elderly person, these things are true, because they bear a special "identity-like" relation to a temporal part that is a child (that exists in the past) or a temporal part that is an elderly person (that exists in the future). Stage theorists are sometimes called "exdurantists".
It has been argued that stage theory, unlike the worm theory, should be favored as it accurately accounts for the contents of our experience. The latter requires that we currently experience more than a single moment of our lives while we actually find ourselves experiencing only one instant of time, in line with the stage view. However, on the other hand, as Stuchlik (2003) states, the stage theory will not work under the possibility of gunky time, which states that for every interval of time, there is a sub-interval, and according to Zimmerman (1996), there have been many self-professed perdurantists who believe that time is gunky or contains no instants. Some perdurantists think the idea of gunk means there are no instants, since they define these as intervals of time with no subintervals.