Four-dimensionalist theorists 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.56
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",7 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".
Exdurantism, like perdurantism, presumes the temporal ontology of eternalism. With this alternative four-dimensionalist persistence theory, however, ordinary objects are no longer perduring worms but, rather, are wholly present instantaneous stages. Moreover, things also do not gain or lose properties/parts because each distinct stage has all these properties/parts in their entirety from one counterpart stage to the next.
It has been argued that stage theory should be favored over worm theory as more accurately accounting for the contents of our experience. Worm theory seems to require that we currently experience more than a single moment of our lives; that we actually find ourselves experiencing only one instant of time is argued to be more in line with the stage view. Contemporary perdurantists disagree, arguing that the "worm" is a fusion of all the perdurant’s instantaneous time slices compiled and blended into a mereological whole. Perdurantism, then, does not require that you experience more than one time slice at any given time, but instead argues that all those moments are a part of reality, and comprise you as a whole.
Recently, it has been argued that perdurantism is superior to exdurantism because exdurantism is too extravagant in counting ordinary objects in the world. That is, if each momentary stage of a persisting object's existence is to be counted as a unique object, the practically interminable number of these stages would make counting objects in the world an unreasonable task. An exdurantist claims a continuant to hold the same identity simply from this stage’s being similar to a subsequent stage, which is what makes the two stages temporal counterparts. Resemblance amongst momentary counterpart stages is insufficient to escape vagueness because similarity itself is vague. Similar in what way? By noting when there is a similarity amongst sortals and that there are adequate causal relations held between them, exdurantists avoid vagueness the best they can. Counterpart theorists follow the identity of a continuant from following the relationship among stages. The problem still lies that there is no clear cutoff point concerning what was and what was not a counterpart of the object and whether we can really attribute a causal relationship between the distinct momentary counterpart object-stages.
For an exdurantist, there are as many objects as there are moments in a continuant’s spacetime career, i.e., there are as many objects as there are stages of a continuant’s existence; e.g., with a continuant like an apple, there are as many distinct objects as there are stages in the span of the apple’s spacetime career, which is an enormous number. Perdurantists and endurantists both think there is only one object—one continuant—that persists, while exdurantists think that there is one continuant but a multiplicity of object-stages that exdure. 8910 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.
Temporal parts – Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/temporal-parts/ ↩
Hawley, Katherine (2004-09-30). How Things Persist. Oxford University Press. p. 12. ISBN 978-0-19-927543-4. 978-0-19-927543-4 ↩
See also: McKinnon (2002) and Merricks (1999) ↩
Brian Garrett (2011). What Is This Thing Called Metaphysics?. Taylor & Francis. pp. 54–55. ISBN 978-1-136-79269-4. 978-1-136-79269-4 ↩
Douglas Ehring (25 August 2011). Tropes: Properties, Objects, and Mental Causation. Oxford University Press. p. 100. ISBN 978-0-19-960853-9. 978-0-19-960853-9 ↩
Timothy D. Miller (2007). Continuous Creation, Persistence, and Secondary Causation: An Essay in the Metaphysics of Theism. pp. 75–77. ISBN 978-0-549-39708-3. 978-0-549-39708-3 ↩
Sider, Theodore (1996-09-01). "All the world's a stage". Australasian Journal of Philosophy. 74 (3): 433–453. doi:10.1080/00048409612347421. ISSN 0004-8402. /wiki/Doi_(identifier) ↩
Balashov, Y. (2015). Experiencing the Present. Epistemology & Philosophy of Science, 44(2), 61-73. ↩
Skow, B. (2011). Experience and the Passage of Time. Philosophical Perspectives, 25(1), 359-387. https://dspace.mit.edu/openaccess-disseminate/1721.1/73471 ↩
Parsons, J. (2015). A phenomenological argument for stage theory. Analysis, 75(2), 237-242 https://academic.oup.com/analysis/article-abstract/75/2/237/165507 ↩