Ted Sider is a leading metaphysician who defends four-dimensionalism, the idea that objects persist over time as distinct "temporal parts." Here is his definition

According to ‘four‐dimensionalism’, temporally extended things are composed of temporal parts. Most four‐dimensionalists identify ordinary continuants—the persisting objects ordinary language quantifies over and names—with aggregates of temporal parts (‘space‐time worms’), but an attractive alternate version of four‐dimensionalism identifies ordinary continuants with instantaneous temporal slices and accounts for temporal predication using temporal counterpart theory. Arguments for four‐dimensionalism include the following: (1) Either substantivalism or relationalism about space‐time is true, but given substantivalism one might as well identify continuants with regions of space‐time, which have temporal parts, or with instantaneous slices of space‐time, whereas relationalism about space‐time cannot be made to work without temporal parts. (2) It can never be vague how many objects exist; if temporal parts do not exist, then a restrictive account of which filled regions of space‐time contain objects must be given, but no such account can be given that is plausible and non‐vague. (3) Four‐dimensionalism—especially the alternate, counterpart‐theoretic version—provides the most satisfying overall account of the ‘paradoxes of material constitution’, in which numerically distinct material objects (e.g. statues and lumps of clay) apparently share exactly the same parts. Objections to four‐dimensionalism (involving, e.g., motion in homogeneous substances and de re modal properties) may be answered. While logically independent of the question of four‐dimensionalism, the book also defends related theses, including (1) a robust meta‐ontology according to which unrestricted existence‐statements are non‐vague, non‐analytic, and uninfected by human convention; (2) the B‐theory of time (the opposite of presentism); (3) unrestricted composition; and (4) counterpart theory (both modal and temporal).

(Four-Dimensionalism: An Ontology of Persistence and Time , abstract)

Four-dimensionalism is a variation of the Academic Skeptic argument about growth, that even the smallest material change destroys an entity and another entity appears. In this case, a change in the instant of time also destroys every material object, followed instantaneously by the creation of an "identical" object.

Willard van Orman Quine proposed a similar idea that he called object "stages." The great Anglo-American philosopher Alfred North Whitehead attributed the continued existence of objects from moment to moment to the intervention of God. Without a kind of continuous creation of every entity, things would fall apart. This notion can also be traced back to the American theologian Jonathan Edwards, for whom God intervened in all human actions.

David Lewis's theory of temporal parts argues that at every instant of time, every individual disappears, ceases to exist, to be replaced by a very similar new entity, with its own properties that he calls "temporary intrinsics."

Lewis proposed temporal parts as a solution to the problem of persistence. He calls his solution "perdurance," which he distinguishes from "endurance," in which the whole entity exists at all times. Lewis says:

Our question of overlap of worlds parallels the this-worldly problem of identity through time; and our problem of accidental intrinsics parallels a problem of temporary intrinsics, which is the traditional problem of change. Let us say that something persists iff, somehow or other, it exists at various times; this is the neutral word.

The road parts do not exactly persist. They are intrinsically different parts. The enduring entity does persist simpliciter. There is no evidence of a discontinuous process that suggests a disappearance and reappearance, which would violate the conservation laws of physics.

Something perdures iff it persists by having different temporal parts, or stages, at different times. though no one part of it is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time. Perdurance corresponds to the way a road persists through space; part of it is here and part of it is there, and no part is wholly present at two different places. Endurance corresponds to the way a universal, if there are such things, would be wholly present wherever and whenever it is instantiated. Endurance involves overlap: the content of two different times has the enduring thing as a common part. Perdurance does not.

(On the Plurality of Worlds, p. 202)

In his thinking about persistence, Sider has been inspired (as have many metaphysicians) by Einstein's theory of special relativity. The idea of a four-dimensional manifold of space and time supports the idea that the "temporal parts" of an object are as distinct from one another as its spatial parts. This raises questions about the continued identity of an object as it moves in space and time.

There is no physical basis for the wild assumptions of past metaphysicians and theologians that the contents of the universe cease to exist and then reappear de novo at the next instant. This notion violates one of the most fundamental of physical laws, the conservation of matter and energy.

More metaphysically significant, neither temporal nor spatial "slices" carve nature at the joints. They are arbitrary mental constructions imposed on the world by philosophers that have little to do with "natural" objects and their "integral" component parts. Ironically, Sider's most recent work claims to pay a great deal of attention to carving nature.

In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts ‐ including the right logical concepts. One must use concepts that "carve at the joints’’, that give the world’s *structure*. There is an objectively correct way to “write the book of the world”. Metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, metaphysics is about the world’s structure. Metametaphysics ‐ inquiry into the status of metaphysical questions ‐ turns on structure. The question of whether ontological, causal, or modal questions are “substantive” is in large part a question of whether the world has ontological, causal, and modal structure ‐ whether quantifiers, causal relations, and modal operators carve at the joints.

Although philosophical doubts can be raised about structure, it is sensible to follow David Armstrong and David Lewis in taking the idea at face value. As will be seen in the rest of the book, the idea illuminates metametaphysics. Some critics think that certain questions of metaphysics are “insubstantial” (or merely verbal), in something like the way in which the question of whether the pope is a bachelor is insubstantial. Whether they are right depends on whether the key notions in the questions carve at the joints.

(abstract for Writing the Book of the World. Oxford University Press.

Sider's book begins with a number of powerful terms that are not precisely defined, but are used in ways that suggest they are getting to some deep truths about fundamental reality. They include fundamentality, substantivity, genuine, ideology, and most of all, structure. Let's try to unpack some of the "primitive expressions" from his "ideology." He says in his preface

The central theme of this book is: realism about structure. The world has a distinguished structure, a privileged description. For a representation to be fully successful, truth is not enough; the representation must also use the right concepts, so that its conceptual structure matches reality’s structure. There is an objectively correct way to “write the book of the world”...

I connect structure to fundamentality. The joint-carving notions are the fun­damental notions; a fact is fundamental when it is stated in joint-carving terms. A central task of metaphysics has always been to discern the ultimate or fundamental reality underlying the appearances. I think of this task as the investigation of reality’s structure.

Questions about which expressions carve at the joints are questions about how much structure reality contains...reality lacks a certain sort of structure...A subsidiary theme is: ideology matters...A fundamental theory’s ideology is as much a part of its representational content as its ontology, for it represents the world as having structure corresponding to its primitive expressions. And the world according to an ideologically bloated theory has a vastly more complex structure than the world according to an ideologically leaner theory; such complexity is not to be posited lightly.

Sider suggests that the metaphysical structure he is after underlies linguistic theory and discourse

A final theme is a “pure” conception of metaphysics...Here too, there is a growing consensus: that it is not so important for metaphysical and linguistic theory to neatly mesh. The funda­mental metaphysics underlying a discourse might have a structure quite unlike that suggested by the discourse. Whereas a good linguistic theory must fit the suggested structure, good metaphysics must fit the underlying structure.

(Writing the Book of the World , p.vii)

And from his chapter 1, we have more insights into Sider's notion of "structure."

Metaphysics, at bottom, is about the fundamental structure of reality. Not about what’s necessarily true. Not about what properties are essential. Not about conceptual analysis. Not about what there is. Structure.

Again, concepts help, but we need to get beyond logic and language to how the world is, not our ways of talking about it. For this, we need to discern patterns - the abstract information in structures

Inquiry into necessity, essence, concepts, or ontology might help to illuminate reality’s structure. But the ultimate goal is insight into this structure itself—insight into what the world is like, at the most fundamental level.

Discerning “structure” means discerning patterns. It means figuring out the right categories for describing the world. It means “carving reality at its joints”, to paraphrase Plato. It means inquiring into how the world fundamentally is, as opposed to how we ordinarily speak or think of it.

(Writing the Book of the World , p.1)

Sider raises questions about his terminology or ideology. In chapter 7, he introduces some new jargon terms or "concepts?" - complete, pure, subpropositional, absolute, determinate, and with virtuous circularity?, fundamental itself, which is expanded to "fundamental notion," "fundamental truth," and "fundamental fact."

Friends of fundamentality face some abstract questions about its nature. My way of thinking about fundamentality—in terms of structure—is distinctive in large part because of how I answer the questions. My answers: the fundamental is complete, pure, subpropositional, absolute, determinate, and fundamental.

(Writing the Book of the World , p.105)

Completeness and determinate seem to be the materialistic and deterministic view that the subatomic particles are the "bottom-up" causes for everything else. Sider uses the terms "truth" and "fact" almost interchangeably, when it seems very important to distinguish them.

Truths are logical, necessary, perhaps by linguistic definition. They are analytic and a priori. Facts are empirical, contingent, and a posteriori.

A fundamental truth (or fact), intuitively, is a metaphysically basic or rock-bottom truth (fact). Facts about the positions of subatomic particles would be, on most views, fundamental facts, whereas the fact that some people smile when they eat candy would presumably not be. ‘In virtue of, intuitively, stands for the relationship whereby the fundamental facts underwrite or give rise to all other facts...

There is a second assumption about structure that I think we ought to make—what I call “purity”: fundamental truths involve only fundamental notions. When God was creating the world, she was not required to think in terms of nonfundamental notions like city, smile, or candy.

As with completeness, there are subtleties about how exactly to understand purity in my preferred terms. “Fundamental notion” is easy (it means “carves at the joints”) but “fundamental truth” remains to be explained...

Here is a truth: there exists a city. Since the notion of a city is not fundamental, purity says that this truth is not fundamental. No surprises so far. Completeness then says that this truth holds in virtue of some fundamental truth T—perhaps some truth of microphysics. So we have:

(1) There is a city in virtue of the fact that T...

(ibid. pp.105-107)

Surely "all cities are cities" needs only the fundamental (logical) axiom that all As are As"?

But given purity, it cannot be that all modal truths are fundamental. The modal truth that it is necessary that all cities are cities, for example, must be nonfundamental given purity, since it involves the nonfundamental notion of cityhood.

(ibid. p.107)

Let us end on a concrete note. What might a comprehensive “worldview” look like, given realism about structure?

Think of a worldview as consisting of i) an ideology; ii) a fundamental theory phrased in terms of the ideology, specifying laws of metaphysics and perhaps other principles; and iii) a sketch of a metaphysical semantics for nonfundamental discourse in terms of the ideology. I will put forward a worldview according to which fundamental reality contains nothing but physics, logic, and set theory. While I believe that this worldview may well be true, I won t say much in its defense; the point is to illustrate.

First, ideology. My primitive notions are those of first-order quantification theory (with identity), plus a predicate ∈ for set-membership, plus predicates adequate for fundamental physics, plus the notion of structure.

Next, the fundamental theory. Since my ideology includes the first-order quantifiers, one part of giving the laws of metaphysics will be the statement of an ontology—a statement, in general terms, of what there is. My worldview's ontology contains only points of spacetime and sets, both pure and impure. Thus it contains no composite objects. This is not to say, however, that ‘There are no composite objects’ or even ‘Everything is a set or a point of spacetime’ is a law of metaphysics. For ‘composite’, ‘set’, and ‘point’ are not in my fundamental ideology...

Since there are no composite entities in its ontology, my worldview is a version of mereological nihilism..Since there are no aesthetic, moral, or supernatural notions in its ideology, it is a version of naturalism. Since there are no causal, nomic, or modal notions in its ideology, it is a version of Humeanism...

Let's begin with talk about ordinary physical objects. Although my ontology contains no physical objects per se, it does contain entities with which they may naturally be identified: the sets of spacetime points that they occupy. I, for example, can be identified with a set whose earliest points are around 1967, whose temporal cross-sections are person-shaped, and which continues on into the future for an unknown duration.

A metaphysical semantics based on this identification would construe talk of ordinary physical objects as being about sets of spacetime points. It would interpret names of physical objects as referring to the sets with which the objects are identified, predicates as applying to'tuples of sets of spacetime points, and quantifiers as ranging over sets of spacetime points...

The identifications I have proposed—of physical objects with sets of occupied points, linguistic atoms with sets of production points, linguistic complexes with set-theoretic constructions from linguistic atoms—are somewhat arbitrary. They’re not wholly arbitrary; it's not as if I’ve simply observed that the pure set-theoretic hierarchy has enough entities with which to identify everything, and left it at that. But there's no denying that there are multiple alternates to my sketch of a metaphysical semantics. Fortunately, this multiplicity is harmless. What we want out of a metaphysical semantics for L is a good explanation of the linguistic behavior of speakers of L, and there is often an element of arbitrariness when explaining higher-level phenomena. What we're after in linguistics (and psychology, and economics, and …) is a good model, not a unique model.

I have imagined one way the book of the world might be. It is not a tale of common sense. But we can, I think, recognize it as our own.

(ibid. pp.292-296)

Information philosophy offers a unique model. Close to Sider's notion of "structure" as fundamental reality, we maintain that the world consists of information structures, bits of matter arranged with an abstract form that can be quantified over. Some of these information structures have internal integrity that depends on the way they were formed. For example, astronomical and geological objects were formed by gravitation and chemical forces that give them their forms..

Artifacts, by contrast, are created for a purpose. Some of their "proper parts" may be essential (though not logically necessary) to that purpose, in which case they are parts that are essential to the whole and can be called "integral parts,"since they perform a function and contribute to the holistic integrity of the entity.

Sider says that he is a mereological nihilist, like Peter van Inwagen, whereas David Lewis, Sider's source of naturalness (carving nature at the joints), favors mereological sums or unrestricted composition. The Statue of Liberty and Eiffel Tower as a composite object is an example of arbitrary unrestricted composition. Considering Theon (Dion missing his left leg) or Tibbles minus one hair are arbitrary disjunctions. Such arbitrariness hardly carves nature at the joints.

Between the two absurd extremes of mereological nihilism and universalism, information philosophy provides strong reasons for why some things are composite objects. Moreover, some things include "proper parts" that are composite objects, which we can call "integral" parts as they serve a function in the integrated object.

These same reasons show that artifacts are composite objects.

Artifacts and living things have a purpose which Aristotle called final cause or "telos." They are "teleonomic." For example, "simples arranged tablewise" have been arranged by a carpenter, whose "telos" was to make a table. This telos carves the artifact at the joints (legs, top). The arrangement or organization is pure abstract information.

Living things were described by Aristotle as "entelechy, "having their telos within themselves." They are more than just matter and static form like an artifact. They have internal messaging between their integral parts that helps to achieve the teleonomic end of maintaining themselves against degradation by the second law of thermodynamics. Many such integral parts are themselves wholes, from vital organs down to the individual cells. The boundaries of integral parts "carve nature at the joints."

Living things also contain many "biological machines" that include "biological computers" or information processors that respond to those messages, which are written in meaningful biological codes that are analogous to and the precursor of human languages.

Now the "time slices" that are the "temporal parts" of Sider's four-dimensionalism do not "carve nature at the joints," any more than his putatively analogous slices in any spatial dimension. Indeed, any two-dimensional spatial slice perpendicular to the third spatial dimension would normally destroy a physical object and kill any living thing.

An actual temporal slice, cutting the continuity between an object and its future existence, would also destroy the object, which was the ancient view of the Greek philosophers and the commonsense view today.

Perhaps Sider thinks of his arbitrary slicing as not "real" but merely as an analytic tool, like the CAT scan of the human brain that gives us the information in the slice without harming the patient? But David Lewis insisted that his extravagant proliferation of infinite possible worlds was real and probably meant his temporal parts with their "temporary intrinsic" properties to be numerically distinct real objects?

In his 2005 article “Bare Particulars,” Sider contrasts the "substratum theory," which says that particulars are, in a certain sense, separate from their universals, with the "bundle theory," according to which particulars are just bundles of universals.

In his Metaphysics, Aristotle said the material substrate (ὕλη ) is that of which attributes can be predicated. For information philosophy, this most fundamental distinction can be best understood as the difference between matter and its form (μορφή), the information we have about the matter.

It is impossible to separate matter completely from its form, except to claim that it is, for all practical purposes, inchoate, amorphous, or formless, which just means we do not see any meaningful form. Sider is correct that there are no "bare particulars" because we can always predicate that they are propertyless, a metaphysician's quibble of course.

It is also impossible to say that any visible information is not embodied in matter, except that we think or speak of a universal, circularity, for example, as being abstracted from any particular embodiment of a circle. When we say "there is a circle," or "circles exist," we are using the abstract entity of circularity, which is immaterial and independent of any particular embodiment. In this case, universals are "bundles of properties" with no particular matter associated.

So information-based metaphysics sees the substance and bundle theories as verbal quibbles that emphasize one or the other of matter and form, or try to separate the two as numerically distinct coinciding objects in the ancient puzzles and paradoxes about Dion and Theon, The Growing Argument, The Ship of Theseus, The Sorites Puzzle, and The Statue and the Clay.

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