Global regularities about change. Global regularities are regularities about change in a spatiomaterial world that hold of whole regions of space.

Change, as an aspect of the substances constituting the world, involves something more than just properties and relations. It also depends on the temporal aspect of (the existential aspect of) the nature of substance as substance. Having explained (in the first two chapters of the Necessary Truths of ontological philosophy about What is) how properties and relations are aspects of a world constituted by space and matter (given how they exist together), we have already found in Change how the endurance of space and matter through time as substances explains local regularities about change. In the remainder of this ontological explanation of change, we shall see how the same ontological causes also explain global regularities about change. There are four kinds of global regularities, explaining, respectively, the truth of the first law of thermodynamics, the second law of thermodynamics, the principles of mechanics, and two unrecognized laws about evolutionary change.

There is, besides local regularities, another kind of effect that space has as an ontological cause. The two principles about local regularities describe limits that the structure of space imposes on how bits of matter change locations relative to one another and act on one another because they coincide with parts of space. The reason that there are also necessary principles about global regularities is that the parts of space all fit together as a whole. Bits of matter must move and interact (if they can move and interact act all) in some part of the same space that contains all the bits of matter in the world, and that means that the changes they undergo are all interconnected in a regular way.

The changes that occur in one place must affect bits of matter that are located nearby before they affect what happens farther away. That is a consequence of the principles of local motion and local action. But such effects do spread out in space as time passes, affecting more and more of the world. And it is a reciprocal relationship, because what happens elsewhere in space also has effects that spread back in space towards it. The structure of space with which they coincide helps determine how each event affects what happens elsewhere. But since that structure entails a wholeness about space, the motion and interaction of the bits of matter in any region of space must all add up in space as time passes. And insofar as the bits of matter are located in a region of space that is closed or isolated from the rest of the world, the way that all their local changes add up over time in the whole region may be regular. Since such regularities would hold of whole regions of space, I will call them “global regularities.”

Space is an ontological cause of regularities about change, because space and matter together constitute the world, and change is just an aspect that those substances have because they endure through time. We have seen how space is an ontological cause of local regularities. It causes global regularities in the same way. But global regularities are different, because they depend on a further aspect of the nature of space, the wholeness that is entailed by the geometrical structure of space.

Local regularities about change in bits of matter are caused ontologically by space, because the bits of matter all coincide with parts of space and change is just an aspect of substances enduring though time. It follows from this explanation of change, as we have seen, that two principles hold necessarily about how bits of matter change, namely, the principles of local motion and local action. They hold in every possible spatiomaterial world. But space also helps cause ontologically contingent laws about how bits of matter change, as we have seen by showing that space and matter can explain ontologically the truth of the basic laws of physics (classical and contemporary).

Global regularities about change are caused ontologically by space (and matter) in the same way, by constituting the world in which the regularities are aspects of substances enduring through time. They must be caused the same way, because space and matter constitute everything in the world and everything about the world. But global regularities are a different aspect of the change that takes place, because they depend specifically on the wholeness of space.

Local regularities are aspects of change that are picked out by referring to particular bits of matter and describing how they move relative to one another and how they interact with one another. But global regularities are aspects of change that are picked out by referring to space itself and describing how all the bits of matter in some region of space move and interact relative to it. Because of the wholeness of space, the local changes must all “add up” in the region of space as time passes, and what they add up to are global regularities about change over time.

It may not seem possible to describe motion and interaction relative to space itself, because velocity relative to space (absolute velocity) is not measurable. But that aspect of the relationship of bits of matter to space is not relevant in causing global regularities. What is relevant is that space connects what happens to all the bits of matter so that what happens to each must affect all the others. This comes from a property of space, namely, its wholeness, and it is not affected by absolute motion.

Physics does not necessarily ignore regularities as a result of failing to recognize that space is a substance. It can studies global regularities in practice by taking some more stable material object (such as the box containing a gas of molecules) as its frame of reference (and arguing from what happens in such closed regions to what would happen everywhere or anywhere in the world).

Wholeness is an aspect of the structure of space, because it is a consequence of the essential natures of the parts of space, that is, how they are related to one another geometrically in three dimensions. The wholeness is the fact that all the parts of space fit together in a uniquely simple way.

The aspect of the nature of space that is relevant in causing local regularities, both necessary and contingent, is the geometrical structure itself, that is, the relations among parts that are described by the various theorems of geometry (and trigonometry). That aspect of the space that contains the bits of matter determines, for example, where the inertial motion of a material object takes it, how fast, and which other bits of matter it will interact with as a result. It might be called the “local aspect of space.”

The global aspect of space is its wholeness, or the fact that all the parts of space fit together in the uniform, simple way they do. It means that parts of space in different regions fit together as parts of their more limited wholes in the same way. And the property of wholeness is a cause of global regularities, because it implies that the changes that occur to the bits of matter that coincide with different parts of space must all add up as time passes. How they add up in space also depends on the local regularities and basic laws of physics (which are explained ontologically by the nature of matter and the local aspect of space). But that they all add up as time passes depends on its wholeness. And we shall see how local changes add up in space over time to global regularities.

Space is, therefore, together with matter, the ontological cause of another kind of regularity about change, besides local regularities. That means that there is an ontological necessity about global regularities, because ontological philosophy takes every proposition that follows from its ontological foundation to be a necessary truth. But unlike the two principles about local regularities, the following global regularities (except for the simplest) have only a conditional ontological necessity, because they also depend on matter and space having the specific natures they have in our spatiomaterial world, that is, on the basic laws discovered by physics.  Hence, global regularities are only conditionally necessary truths. Their truth is ontologically necessary only in a spatiomaterial world like our own.

In a spatiomaterial world with different physical laws, there might not be any interesting global regularities, because bits of matter do not move and interact at all or they move and interact in different ways. However, as we shall see, the physical laws in the actual world seem to be of just the right kinds to make the most of the wholeness of space in generating global regularities. Many regularities that are not even currently recognized to hold turn of our world out to be ontologically necessary in spatiomaterial worlds like our own.

To be sure, in order to use spatiomaterialism as an ontological foundation for proving necessary truths about the world we had to take out several mortgages. But they are being paid off, and in any case, global regularities do not involve any of the extreme phenomena on which Einsteinian relativity is based.

Two of these mortgages have been paid off. We kept our promise to explain the nature of consciousness in Properties. And the debt that arose from the apparent incompatibility of spatiomaterialism with Einsteinian relativity was paid off by explaining ontologically why Einstein’s theories are true. Indeed, we have seen that all of the basic laws of classical and contemporary physics can be explained as regularities that hold of substances that endure through time as a spatiomaterial world. (See Contingent laws).

Having just completed those explanations, it is relevant to mention, furthermore, that far from casting doubt on spatiomaterialism, contemporary physics provides additional empirical evidence that spatiomaterialism is true. The recognition of space as a substance would solve several mysteries that currently puzzle physics, such as the nature of spacetime, curved spacetime, the relationship between gravitation and quantum mechanics, and even the Bell Inequality entailed by quantum mechanics. And science has further reason to accept  this ontological explanation of physics, because it offers a new approach to cosmology which may help solve the prevailing mysteries about the origin of the large scale structure of the universe.

In fact, given our interpretation of contemporary physics, the existence of space as a substance can even be shown by an inference to the best efficient-cause explanation, because substantival space is the efficient cause of the Lorentz distortions (which explain the phenomena of special relativity) and its interaction with centers of mass is the efficient cause of the acceleration of the ether (which explains gravitation). That is, scientific realists about contemporary physics would have to admit that space is a substance, if they believed that nothing exists but the present moment, for the existence of space would be known by its effects on the behavior of matter.

Global regularities are not very sensitive to the extreme phenomena that divide contemporary from classical physics. They are basically unaffected by Einsteinian relativity, as long was we can take gravitation for granted and can assume that the universe has a large scale structure that includes planetary systems like ours. Most global regularities do depend on matter being of the kind found in our spatiomaterial world and, thus, on quantum mechanics. But none of the puzzling phenomena of quantum mechanics are particularly relevant. Global regularities depend mainly on the wholeness of space, that is, how, by containing all the bits of matter, space gives the world itself (as well is regions within it) a determinate wholeness.

There are four kinds of global regularities. Each is recognized in a way by empirical science, as a principle, law or “mechanism” of some kind. But since empirical science does not recognize the validity of ontological explanations, it does not recognize space as an ontological cause of them, and thus, it does not have an explanation of why these regularities hold. Nor does it always fully recognize what the regularities involve. Furthermore, although global regularities depend on the basic laws of physics, they do not follow from those laws alone, and thus, empirical science does not recognize that they are necessary, even when the basic laws of physics are assumed.

The crucial role in explaining each of the kinds of global regularities ontologically is played by space, and more specifically, by the wholeness of space (or, if you will, the “global aspect” of space). Though the wholeness of space makes the world itself whole, it also makes every region of space whole. Thus, global regularities can be seen in regions of space that are somehow closed or isolated from the effects of what happens outside. Since the global regularities are ontological effects of the wholeness of space (and what coincides with it), they arise from inside the region.

The reason there are four different kinds of global regularities is that different aspects of what exists according to spatiomaterialism can be combined with the wholeness of space to generate regularities about the change that occurs in whole regions of space as time passes.

Spatial global regularities. The first kind of global regularity has a single instance, namely, the conservation of matter. It will be called the “spatial global regularity,” because it makes no assumptions at all about the nature of matter except that it is many different substances that each coincide with some part of space or other. Thus, the spatial global regularity can be said to be generated by “spatial causation,” for it is how the wholeness of space makes any kind of matter add up over time. When we take into account the various forms of matter that we distinguished in order to explain the truth of the basic laws of physics ontologically, spatial causation will also explain ontologically the truth of the first law of thermodynamics, the principle of the conservation of energy.

Material global regularities. The second kind of global regularities will be called “material global regularities,” because in addition to the wholeness of space, these regularities depend on matter obeying the basic laws of physics. Alternatively, material global regularities will be said to be generated ontologically by “material causation,” for they are simply how the wholeness of space requires motion and interaction to add up over time when the bits of matter obey the basic laws of physics. That will explain ontologically why the second law of thermodynamics is true.

Structural global regularities. The third kind of global regularities will be called “structural global regularities,” because in addition to the wholeness of space and material causation, these regularities depend on the unchanging geometrical structures of the material  objects contained in the region of space, or what will be called “material structures” or “structural causes.” Structural global regularities will be said to be generated ontologically by “structural causation,” because these regularities are how the wholeness of space requires motion and interaction to add up over time when the bits of matter include material structures (or particular structural causes). This explains ontologically the truth of the principles of mechanics (such as the principle of the lever), and when combined with the other ontological effects of material causation, it will explain the sense in which machines can “do work” and certain dispositional properties. 

Reproductive global regularities. The fourth kind of global regularities will be called “reproductive global regularities,” because in addition to the wholeness of space, material causation, and structural causation, these regularities depend on how complex material structures go through reproductive cycles, that is, how they go through cycles of structural global regularities that include the reproduction of the structural cause itself as well as non-reproductive work. Thus, reproductive global regularities will be said to be generated ontologically by “reproductive causation,” because these regularities are simply how the wholeness of space requires motion and interaction to add up over time when the bits of matter include complex material structures going through cycles of reproduction. This will explain ontologically the truth of Darwin’s mechanism of evolution, or what might be called the principles of evolution, which includes much more than is currently recognized.

The order of these kinds of global regularities is necessary, because each adds a new ontological cause that works together with ontological causes of all the previous global regularities. That is, we start by assuming that the world is constituted by space and matter (with all the bits of matter coinciding with some part of space or other), and we consider how the wholeness of space constrains what happens to the bits of matter. When no further assumptions are made about the nature of matter, these assumption entail the simplest global regularity (spatial causation). The second global regularity adds that matter with the specific nature described by the basic laws of physics, including the forms of matter that were distinguished. The third adds material structures to the region. And the fourth adds the temporal structure of complex material structures going through reproductive cycles.

The first global regularity is entailed by the basic assumptions of spatiomaterialism themselves, and each of the other three is the result of adding an ontological cause, that is, assuming something further about the nature of what coincides with space in the region: about the specific nature of matter, about its spatial structure, and about its temporal structure.

Thus, considering the ontological causes added to the basic assumptions of spatiomaterialism, material global regularities may be said to be due to “material causation,” structural global regularities may be said to be due to “structuro-material causation,” and reproductive global regularities may be said to be a result of “temporo-structuro-material causation.” Those names bring out the necessary order of the global regularities in a spatiomaterial world.

In the following four sections, these kinds of global regularities will be shown to follow from spatiomaterialism and the kind of matter that explains the truth of classical and contemporary physics ontologically. If nature had a different essential nature, some of the global regularities might not hold. (For example, there would be no structural causes unless matter could make up material objects with geometrical structures that do not change as they move and interact.) But given that matter takes the various forms we used to explain the basic laws of physics, the global regularities are simply how the wholeness of space makes the change in what coincides with space add up as time passes. The ontological effect of spatial causation includes the first law of thermodynamics, or the principle of the conservation of energy. When material causation is added to spatial causation, the ontological effect is the second law of thermodynamics, or the law of entropy. When structural causation is combined with spatial and material causation, we have an explanation of how machines do work. Finally, when reproductive causation is added to spatial, material and structural causation, the ontological effect is evolutionary change.

The ontological explanation of evolution as a global regularity has, as we shall see, implications about what is to be found in nature that goes far beyond what is recognized by evolutionary biology and contemporary Darwinists. But it depends on all the other global regularities, and so we will begin with the simplest and work our way up.