Four-dimensionalism

This article is about the metaphysical doctrine. For four-dimensional space, see Four-dimensional space.

In philosophy, four-dimensionalism (sometimes called the doctrine of temporal parts) is a family of views about the ontology of time and persistence. Roughly, four-dimensionalists hold that persisting objects are extended in time in a way analogous to their extension in space, and that they are composed of distinct temporal parts located at different times, in addition to their spatial parts.^[1][2][3]

The label four-dimensionalism is used in more than one way in the literature. In a narrow sense it refers to theories of persistence—most prominently perdurantism and the closely related stage theory or exdurantism—according to which ordinary objects persist by having temporal parts.^[4][5] In a broader sense, the term is sometimes used for any view on which past, present and future times—and the objects located at them—are all equally real, in opposition to presentism. On this usage, "four-dimensionalism" functions as a label for non-presentist eternalist views of time rather than for a specific account of persistence.^[6][7]

Four-dimensionalist views play a central role in contemporary debates about identity over time, the nature of temporal reality and the interpretation of modern physics. They are typically contrasted with three-dimensionalism or endurantism, according to which persisting objects are wholly present at each time at which they exist and do not have temporal parts.^[2][3]

Terminology and definitions

Four-dimensionalists commonly appeal to the notion of a temporal part. A temporal part of an object is, roughly, a part that exists at some but not all of the times at which the object exists, and that stands to the whole as an ordinary spatial part stands to a spatially extended object.^[2][8] Some writers take temporal parts to be instantaneous, while others allow them to occupy short temporal intervals.^[9]

The dispute between three- and four-dimensionalists is often framed in terms of how objects are located in spacetime. On one influential formulation, four-dimensionalism is the thesis that whenever an object exists across an extended stretch of time, there are distinct temporal parts of it corresponding to each sub-interval of that stretch; three-dimensionalism denies this and maintains that persisting objects are wholly present whenever they exist.^[1][2]

Because the label "four-dimensionalism" is used in different ways, authors sometimes adopt terminological stipulations. Sider uses four-dimensionalism for the doctrine that objects persist by having temporal parts—that is, for perdurantism in his sense.^[1][4] By contrast, Rea reserves the term "four-dimensionalism" for the denial of presentism, and uses perdurantism for the claim that persisting objects are not wholly present at every time at which they exist.^[6]

Four-dimensionalism about material objects

On one common understanding, four-dimensionalism is primarily a thesis about the nature of material objects. According to this view, material objects do not merely extend across regions of space but also extend across regions of time: they have both spatial and temporal parts and occupy four-dimensional regions of spacetime.^[10][4][5] Persisting objects are sometimes described metaphorically as "space–time worms" whose temporal dimension corresponds to their career over time.

In this material-object sense, four-dimensionalism is compatible with different views about which times and objects exist. A theorist may hold that material objects have temporal parts while remaining neutral on whether only present objects exist, or whether past and future objects exist as well. In practice, however, four-dimensional views of material objects are usually combined with non-presentist ontologies of time.^[3][11]

Four-dimensionalism and theories of time

Four-dimensionalism is closely connected to debates in the philosophy of time about which times and events exist.

Eternalism, growing block, and presentism

Eternalists hold that past, present and future times, and the objects and events located at them, are all equally real. On this view, there is no ontologically privileged present, although there may still be objective relations of earlier-than and later-than.^[12] Eternalism is often combined with four-dimensionalism about material objects, yielding a "block universe" picture in which reality consists of a four-dimensional spacetime filled with four-dimensional objects.^[4][3]

By contrast, presentists claim that only present objects and events exist, in the most fundamental sense; past and future things are said not to exist at all, or to exist only in a derivative or abstract way.^[13] On Rea's usage, four-dimensionalism is simply the denial of presentism, and thus includes both eternalism and views such as the growing block universe theory, on which the past and present exist but the future does not.^[6]

Although eternalism and four-dimensionalism are conceptually distinct, many arguments for four-dimensionalism appeal to features of relativistic spacetime that are also taken to support eternalism, such as the lack of an absolute, theory-independent notion of the present and the geometrical treatment of time in modern physics.^[7][11]

Four-dimensionalism and persistence

Four-dimensionalism, in the narrower, persistence-theoretic sense, concerns how objects persist through time and bear properties at different times.

Perdurantism (the "worm view")

Perdurantism (or perdurance theory) claims that persisting objects are four-dimensional aggregates, or fusions, of temporal parts.^[14][5][3] On this view, an ordinary object persists by having different temporal parts at different times, and facts about change are explained by the differing properties of those temporal parts rather than by a single wholly present thing having incompatible properties at different times. Because of this, perdurantism is sometimes called the "worm view": a persisting object is identified with the entire spacetime "worm" composed of its temporal parts.^[2][10]

Perdurantism is usually taken to be a paradigmatic four-dimensionalist position about persistence. Many four-dimensionalists understand four-dimensionalism simply as perdurantism, together with the claim that all material objects persist in this manner.^[1][4]

Stage theory (exdurantism)

Stage theory or exdurantism is a closely related four-dimensionalist theory that also posits temporal parts, but differs in how it identifies ordinary objects.^[15][16] According to stage theory, the object ordinarily referred to at a time is an instantaneous (or short-lived) temporal stage, not the entire spacetime worm. Other stages at different times are related to the current stage by a suitable "temporal counterpart" relation, analogous to the counterpart relation used in some modal metaphysics.^[15] Statements about an object's past and future are analysed in terms of these temporally related counterparts.

Stage theory thus offers a four-dimensionalist account of persistence and change, but denies that persisting objects are identical with extended spacetime worms. Many authors therefore treat perdurantism and exdurantism as distinct four-dimensionalist options.^[3][9]

Endurantism and three-dimensionalism

Endurantism (or three-dimensionalism) is the main rival to four-dimensionalist theories of persistence. Endurantists hold that ordinary objects are wholly present at each time at which they exist and do not have distinct temporal parts.^[2][3] A persisting object is numerically the same entity at each moment of its existence, even though it may have different properties at different times.

The dispute between endurantism and four-dimensionalist theories such as perdurantism and stage theory concerns how to understand the relation between objects, time and change. It also has implications for questions about material constitution (for example, statue–lump cases), identity, and the semantics of tensed discourse.^[2][9]

A-series, B-series and four-dimensionalism

Main articles: A-series and B-series and B-theory of time

The contemporary debate about four-dimensionalism is often framed using J. M. E. McTaggart's distinction between the A-series and B-series of temporal positions.^[17] The A-series orders events as future, present and past, and treats these tensed properties as changing with time. The B-series orders events only by the tenseless relations earlier than, later than and simultaneous with, which do not themselves change.^[17][12]

Four-dimensionalist views are typically associated with B-theoretic or tenseless approaches to time. Eternalists and other non-presentists often claim that the B-series structure of spacetime, especially as it appears in modern physics, supports a four-dimensionalist picture of reality in which past, present and future events all belong to a single four-dimensional block.^[7][11] By contrast, many A-theorists and presentists reject four-dimensionalism, arguing that an objective distinction between past, present and future is incompatible with the idea that objects are merely temporal worms or stages spread across time.^[13]

Arguments for four-dimensionalism

A number of influential arguments have been advanced in support of four-dimensionalist views.

Puzzles of change and material coincidence

One set of motivations arises from puzzles about change and material constitution. Classic examples include the Ship of Theseus and cases of coinciding objects such as a statue and the lump of clay from which it is made.^[2][8][3] If the statue and the lump share all their parts while the statue exists, they seem to occupy exactly the same region of spacetime yet differ in properties such as age and modal profile. Similar puzzles involve amoebas that divide, cats and their tail-complements, and other cases of apparent temporary or permanent coincidence.^[18]

Perdurantists and other four-dimensionalists claim that these puzzles are best resolved by treating persisting objects as four-dimensional entities with temporal parts. They can say, for example, that the statue and the lump partially overlap by sharing some temporal parts, or that one is a temporal part of the other, thereby explaining both our intuition that there is only one object in a given place at a time and the differences between the coinciding objects over their longer careers.^[2][10][9]

Temporary intrinsics and intrinsic change

Another line of argument appeals to the problem of temporary intrinsics—properties that an object appears to have independently of its relations to other things, but that can vary over time.^[14][19] A familiar example is shape: a single object may seem to be first spherical and later cubical. On an endurantist view, this raises the question of how one and the same wholly present object can possess incompatible intrinsic properties.

David Lewis and other four-dimensionalists argue that the best response is to treat the apparently incompatible properties as belonging to different temporal parts of a four-dimensional object, much as spatially separated parts of an object can have different shapes.^[14][20][16] On this view, the persisting object has temporal parts that are spherical and cubical, and there is no single thing that must be both at once.

Spacetime and relativity

Four-dimensionalist views are also motivated by considerations from special and general relativity, which treat space and time together as a four-dimensional spacetime manifold. The relativistic account of simultaneity makes it difficult to identify a unique, global present shared by all observers, and the geometry of spacetime is naturally represented using four-dimensional structures.^[11][7] Many authors therefore argue that the physics of spacetime supports some combination of (i) a four-dimensional spacetime ontology, (ii) a B-theoretic or tenseless view of time, and (iii) a four-dimensionalist account of persistence such as perdurantism.^[4][3]

Gilmore, Costa and Calosi (2016) distinguish several different "four-dimensional" theses suggested by relativity—about spacetime itself, about the ontology of time, and about persistence—and analyse how strongly the physics supports each.^[11]

Criticisms and alternatives

Four-dimensionalism has been widely discussed and also widely criticised. Some critics argue that the notion of a temporal part is obscure or metaphysically extravagant, and that the puzzles used to motivate four-dimensionalism can be solved without positing such entities.^[21][9] Others contend that four-dimensionalism conflicts with common-sense intuitions about identity over time or with certain religious or ethical views about persons.

Endurantist accounts of persistence have been developed to meet many of the same puzzles that motivate four-dimensionalism, sometimes by appealing to constitution relations between coinciding objects, sometimes by revising principles about identity and parthood, and sometimes by adopting restricted ontologies that recognise fewer composite objects.^[2][19][6] Some presentists argue that a dynamic, tensed conception of time is more fundamental than any four-dimensionalist picture inspired by physics, and that presentism can be reconciled with modern spacetime theories.^[13][7]

Within four-dimensionalist camps, there are also disagreements. Stage theorists criticise the worm view for mislocating ordinary objects in spacetime, while worm theorists question whether stage theory can account adequately for our ordinary talk about persistence.^[15][3] Some philosophers develop hybrid or alternative views—for example, "multi-location" or "transcendentist" theories—aimed at combining advantages of both three- and four-dimensional approaches while avoiding their respective problems.^[3][11]

See also

• A-series and B-series
• B-theory of time
• Endurantism
• Eternalism
• Growing block universe
• Light cone
• Material constitution
• Perdurantism
• Presentism
• Spacetime
• Stage theory (perdurance)
• World line