Structural global regularities. Spatial and material causation are the most direct ways that space and matter impose regularities on change in whole regions over time. But they are not the only ways, because the forms of matter that explain the truth of the basic laws of physics are not the only kinds of substances that can coincide with space. The nature of matter also makes non-basic, or derivative substances possible, and they can work together with space as ontological causes to generate global regularities.

Though everything that coincides with space is made of matter, matter is capable of being organized into more complex material substances that move around in space and interact as units with other bits of matter, and the wholeness of space also requires their motion and interaction to add up in space over time. They are more complex ontological causes, and they add up in space over time to more complex regularities about the change that takes place in entire regions.

These more complex ontological causes are “derivative substances” (or “derivative ontological causes”) because they are constituted by the basic ontological causes, matter and space. Though they can endure through time like basic substances, they can also come into existence and go out of existence as time passes.

These more complex kinds of substances include not only material objects with unchanging geometrical structures, such as ordinary composite objects, from cups to automobiles, but also a more complex, temporally structured kind of process that is based on such material structures. The first is discussed in this chapter, and the second will be taken up in Reproductive global regularities.

In both cases, however, the derivative substances are ontological causes of global regularities, because they work together with space to cause change to be regular in entire regions by their continuous existence through time as (derivative) substances that coincide with some part of space or other in the region. Though the wholeness of space is what requires motion and interaction to add up in space over time, how their motion and interaction adds up in space over time depends on their natures as (derivative) substances as well as the structure of space. And as we shall see, they add up to complex global regularities about change.

Material Structures. Since material structures are just material objects with relatively stable geometrical structures, most ordinary objects are examples of them. They have geometrical structures that do not change in relatively wide ranges of interactions because they are byproduct of certain cases of the tendency of potential energy to become kinetic (one of the two material global regularities). Thus, they continue to exist in the region even when entropy is maximum. Though as we shall see, material structures can be constructed by machines using free energy to do work, that is just a more complex example of the structural global regularities to be explained. And the existence of material structures does not depend on such machines, because there are material structures that form naturally.

The best examples of such naturally forming structures involve the electromagnetic forces described by quantum field theory. It account for the formation of atoms (from nuclei and electrons), molecules (from atoms), and crystals, rocks and other natural material objects (from molecules). But similar explanations hold for the formation of the nuclei of atoms.

Material structures come to exist naturally because of the attractive forces that simpler material objects exert on one another. The exertion of attractive forces across space is a form of potential energy that can draw material objects together and bind them into relationships with one another that are stable and do not change. The stability of such composite objects comes from the parts giving up potential energy as kinetic energy (or radiation) when they form themselves into a unit, because, once united, their bonds to one another cannot be broken, unless subsequent interactions supply enough energy in the right form to make up for the energy that was lost forming the bonds. The improbability of that happening is, as we have seen, what causes the tendency to kinetic energy. (Kinetic matter and photons lack the inherent geometrical structure of potential energy, and thus, almost anything that happens to such matter will make it impossible for it to regain its initial geometrical structure as potential energy). But the quantum nature of the interactions helps account for their stability, because that means the objects can be freed from their embrace with one another only when enough energy is supplied by a single interaction (as illustrated by the photo-electric effect). Thus, such composite objects have geometrical structures that do not change even though they are interacting with other objects (as long as the energy of those interactions is not too great).

Thought material structures may seem to override the tendency to randomness, they are just byproducts of the tendency toward kinetic energy, the other global regularity involved in the second law of thermodynamics.

Material structures may seem to override the tendency toward randomness in two ways. Instead of interacting by elastic collision, the parts of composite objects exert forces that bind them to one another, and thus, instead of being spread out evenly in space, material objects are clustered together in the same local area. And instead of winding up with momentums in every which direction, the parts of such structures all have much the same direction, like a wind with fixed parts. In other words, instead of being a gas or liquid, they are a solid state of matter, which moves and interacts as a whole.^[1]

But instead of overriding the tendency to randomness, they exemplify the other material global regularity that is covered by the second law of thermodynamics. The existence of material structures is part of the price that is paid to have kinetic energy that can become randomized as evenly distributed heat. It is the loss of potential energy (which is actually a loss of rest mass) that binds the parts into stable geometrical structures. Their formation is part of the process of free energy becoming entropy.

Composite material objects with unchanging geometrical structures are the derivative ontological causes that will be called “material structures” or “structural causes”. But it should be noted that not all objects that form naturally as byproducts of the tendency of potential energy to become kinetic energy are material structures, and the main exceptions, not surprisingly, result from gravitation.

Stars form as a result of gravitation, but these “composite objects” do not have unchanging geometrical structures in this sense. Gravitation concentrates material objects in certain locations, and though this is a deviation from the tendency of rest masses to be distributed evenly throughout space, the forces are so great, when enough matter is concentrated at some location, that material objects continue to move and interact randomly with one another, as a plasma of nuclei and electrons (a fourth state of matter, besides solids, liquids and gases). This gives stars only the minimal geometrical structure required to speak of them as composite objects at all. They approximate a sphere, but since there are no unchanging spatial relations among particular parts that would give the whole a geometrical structure that remains stable as it interacts with other objects in space, they are not structural ontological causes. Though planets and smaller astronomical bodies do acquire unchanging geometrical structures from gravitational attraction, they also depend on the parts forming bonds based on electromagnetic forces.

If gravitational acceleration is explained by the acceleration of the ether, then the nature of the gravitational force would explain why stars are different from objects that depend on other forces. Material objects that are clustered simply because of the ether (by which they coincide with space) accelerating them towards one another do not necessarily form bonds with one another. By contrast, the interactions on which other kinds of composite objects are based involve either opposite forces of attraction and repulsion canceling one another out (as in electromagnetism) or are short range forces (as in the weak and strong forces), and they all have a quantum nature which helps makes the structures they constitute stable.

It should be noticed, however, that even some composite objects formed by forces with a quantum nature lack unchanging geometrical structures. For example, water molecules interact by weak electromagnetic forces, called “hydrogen bonds”, but when water forms into a drop, the molecules continue to move relative to one another as they interact, resembling to some extent star-like gravitational objects on a small scale.

Reversible processes. The existence of material structures depends on the specific nature of the matter that helps constitute the actual world, and when they exist, the wholeness of the space containing them causes their motion and interaction in any region to add up over time as regularities about entire regions of space. But since they have a geometrical structure, how they add up also depends on the structure of space. Though the new global regularity is rather simple by itself, it makes all the difference in the world, as we shall see, when combined with material global regularities, that is, free energy, for that is what constitutes irreversible processes.

What is regular in the case of reversible processes is not just that the geometrical structure of the material object does not change. That is a property of the composite object, rather than a property of region as a whole. But since its geometrical structure does not change over time, there is a geometrical structure about the dynamic processes in the region that does not change, and that is a global regularity. In other words, material structures contribute to the geometrical structure of the region in much the same way that potential energy does, by its inherent geometrical structure. The difference, of course, is that the material structures do not lose their geometrical structure as potential energy tends to do as it becomes kinetic.

As long as the composite object’s geometrical structure does not go out of existence, it is like a new kind of material substance, which is not mentioned by the basic laws of physics. Indeed, the reason material structures are ontological causes is that, like space and more elementary forms of matter, they exist continuously over time like substances. And since change is just an aspect of substances enduring through time, material structures cause change to be regular by helping constitute the process. As in all ontological explanations, that is how the essential natures of substances help determine the nature of what is found in the natural world. Material structures are unchanging aspects of the substances making up the region as time passes.

Material structures cause a global regularity, because as they move and interact as particular substances in space, their geometrical structures help determine, along with the structure of space and the other bits of matter in the region, how change occurs as time passes. Though everything happens by efficient causation, the motion and interaction of material structures with other bits of matter must add up over time in space. The kind of global regularity that material structures add up to is simple. It is just the existence of the material structures in the region moving and interacting with other bits of matter. And material structures with different geometrical structure impose different regularities on how geometrical structures of whole regions change over time.

Though the wholeness of the space containing all the bits of matter is what makes their motion and interaction add up over time, how the motion and interaction of material structures adds up over time depends on the structure of the space containing them.

In the first place, the uniform structure of space makes it possible for composite objects to move without changing the spatial relations among their parts. Every local area in space has a geometrical structure that can contain any specific kind of geometrical structure that composite material objects may have.

Second, when such objects do interact, space allows what happens to depend not only on the forces that the objects exert on each other (by way of the forces exerted by the parts of such geometrical structures), but also on how their geometrical structures fit together. This is a geometrical aspect about how material objects in the region interact with one another that cannot even be simulated by forces.

Material structures can, therefore, be said to structure dynamic processes. Thus, structural global regularities of are “structured dynamic processes”.

Even though structural global regularities may be little more than the existence of material structures in the region, there is no doubt that the existence of such geometrical structures in the region imposes a regularity on change in the region. It can be seen in how round pegs, but not square pegs, fit into the round holes in a board, how rings linked with one another act like a chain, or how molecules can be confined in a box.

Consider, for example, a box of gas that is part of a larger (closed) region of space. Although the molecules are not bound to the box and move around independently of it, those on the inside never get outside, while the molecules on the outside never get inside. This is because the box has a geometrical structure that, together with the structure of space, leaves no route for molecules to move from one region to the other. The gas molecules are not equally likely to be located in every part of the region, and as the box moves around in the region, the structure about the distribution of matter in the region changes in a regular way, because the otherwise randomly moving molecules always move around inside the box. The dynamic process taking place in that region has, therefore, a geometrical structure that does not change over time.

The part-whole relationship in the box-of-gas example suggests a more general point about material structures and the global regularities they and space generate: the unchanging geometrical structure of a composite object as a whole constrains the motion and interactions of its parts, and that generates (regular) behavior in the object as a whole. This is, perhaps, obvious in complex machinery, but consider a simple example, two rings linked together. The rings can move and interact independently of one another to some extent, but their locations are not random, because they can move only within limits which are imposed by the geometrical structure of the object as a whole. This further geometrical structure about what happens to the rings is a kind of global regularity about change over time that might well be called the “behavior” of the object as a whole. The behavior of chains of many such linked rings is quite useful in communicating forces from one place to another. The notion that the whole controls the part is sometimes thought to entail a holism that is incompatible with materialistic reductionism, but when we recognize that the substances constituting such objects include space as well as matter, a regular behavior on the part of the whole is just what is expected.

Structural causation introduces a complication into the ontological explanations of spatiomaterialism, because material structures are derivative ontological causes. In order to be ontological causes of the global regularity about change, they must endure through the whole period. But over longer periods of time, material structures do come into existence and go out of existence. In speaking of them as ontological causes, we are treating them like substances, which have essential natures, that is, properties that hold at each moment of their existence and help determine how contingent properties come and go over time. But since they are derivative ontological causes, we must take into account their “generation” and “corruption”, much as Aristotle did in explaining his very different kinds of substances with essential forms. They are analogous to the various, interconvertible forms of matter we distinguished in order to explain the basic laws of physics ontologically, except that we can explain the generation and corruption of material structures from simpler substances by their motion and interaction in space according to the basic laws of physics. However, the advantages of introducing this complication far outweigh the disadvantages.

Many puzzles are cleared up by recognizing that material structures are ontological causes.

It settles, for example, a question about the criterion for the identity of ordinary objects over time that arises for epistemological philosophers. Material objects are commonly classified by their geometrical structures, and some epistemological philosophers (Hirsh 1982, p. 134) rely on it so heavily that they are tempted to believe that simply having the same kind of geometrical structure at a later moment would be sufficient for its identity—even if the object were to vanish from one location at one moment and were to appear somewhere else the next. That is not a case we need to worry about, since it is not even possible according to our ontology. But the recognition of material structures as ontological causes can solve puzzles about identity posed by epistemologists who pit having the same geometrical structure against spatio-temporal continuity.

Nozick (1981, p. 29ff), for example, considers the case of Theseus’ ship, which is rebuilt, plank by plank, over a period of time. One would ordinarily claim that what results from the rebuilding is the same ship, although none of the parts is the same. But Nozick poses a further question by supposing that each of the parts of the original ship is saved and later used to reassemble the original ship. He asks, which later ship is identical to the original ship. Nozick’s answer is the “closest continuer theory”, which has intuition deciding in each case (and for each person) which is closest. But if we recognize how global regularities depend on ontological causes, it is clear which ship is identical to the original ship, because only one of them has an unchanging geometrical structure that can cause change to be regular by existing continuously over all that time as a substance. Its role as an ontological cause determines its identity over time.

The recognition of global regularities solves various problems about the irreducibility of less general laws in science to the laws of physics, as we shall see in Epistemological philosophy of causation. The general form of the problem can be seen in the case of structural global regularities. Science tends to overlook this explanatory role of material structures, because it its looking for efficient causes, not ontological causes. The only relevant factors involved in efficient-cause explanations, besides the laws of physics (and mathematical theorems), are initial and boundary conditions. A structural cause is not just an initial condition (although it can be inferred from initial conditions together with the relevant laws of physics), because it causes by its continuous existence over the whole period of time that the global regularly occurs. To be sure, boundary conditions also cause by persisting through the period of the regularity. But structural ontological causes are not boundary conditions, for they are not just a condition about the system’s limits in space (how it is related to or isolated from the rest of the world). Thus, structural ontological causes tend to fall through the cracks. That is not to say that they are ignored. It is rather they are implicit in efficient causes that are recognized. The familiar deductive-nomological model of explanation has no way to acknowledge the distinctive kind of role that material structures play as ontological causes of global regularities.