Change. The third set of necessary truths entailed by spatiomaterialism has to do with change, and it is by far the largest set, since it includes all of science. Science is the explanation of change by efficient causes, and the range of kinds of changes found in the world means that science includes not only all the branches of natural science (physics, chemistry, biology, and physiology), but also all the social sciences (psychology, sociology, economics, political science, anthropology, and history).

What changes in the natural world are properties and relations of substances, not the basic substances themselves, since substances, as substances, simply endure through time. Properties and relations are aspects of substances constituting the world, and given the essential natures of the basic substances and the basic relationship by which they exist together as a world, there are aspects that can change. That means that some of those changes can be given genuine ontological explanations., And such ontological explanations are important, because they can explain the nature of the necessity about efficient causation..

Some changes in contingent properties can be explained ontologically, because they are simply changes in certain aspects of basic substances as they endure through time. Such ontological explanations can be given only when the possibility of change is entailed by the essential properties of matter and space and how they exist together as a world. For example, the possibility of changes in spatial relations can be explained ontologically.

As we shall see, change in spatial relations is possible, because bits of matter can have different relations at different times without compromising the essential nature of either space or matter and compatibly with their basic relationship as parts of the same world. It can occur by motion, and those same ontological causes entail, as we shall see, that spatial relations can change only by motion.

Efficient cause explanations depend on regularities about change, that is, on so-called "laws of nature." But insofar as such regularities about change are given genuine ontological explanations, the connections they describe between efficient causes and their effects are shown to be ontologically necessary (because they follow from the endurance of the substances through time with the same essential natures). That explains the necessary connection between efficient causes and what they make happen in the world.

Ontological explanation is genuinely explanatory only when substances work together in some way to constitute something more that what is assumed about them. Or to put it negatively, insofar as change has to do with regular changes in the contingent properties that are used to define the essential natures of substances (that is, insofar as the substances have temporally complex, or dispositional, essential properties), there is no genuine ontological explanation of the change, for the change is simply what is assumed by the ontology. Hence, there is no ontological necessity.

Traditional epistemological philosophy, by contrast, does not treat change as an aspect of the substances constituting the world, but rather as an object of knowledge. Science tries to explain what happens in the world by finding efficient causes, and since such efficient-cause explanations presuppose laws of nature, epistemological philosophy takes the goal of science to be the discovery of laws of nature. But that approach to the philosophy of science has encountered problems that remain unsolved.

One main problem of epistemological philosophy of science has been the explanation of the nature of efficient causation itself. Efficient causes are supposed to produce their effects, that is, make it necessary that they occur. But the laws of nature on which science bases such efficient-cause explanations seem to be just descriptions of regularities about how properties and relations that have been observed to change over time. But if they are merely descriptions of observable regularities, there is no explanation of the source of the necessary connection that is supposed to hold between the efficient cause and what it explains. This is basically the problem about causation that Hume discovered.

Since epistemological philosophy of science takes the goal of science to be the discovery of the laws of nature on which efficient-cause explanations are based, it has also encountered a major problem concerning the relationship between the laws discovered by different branches of science. It now seems that the laws (and, thus, the efficient-cause explanations) of the less general sciences cannot be reduced to the laws of more general branches of science and ultimately to the basic laws of physics. That complicates the problem about the nature of efficient causation, because the causal connections described by less general branches of science cannot be explained by physics. But it also makes the relationships among the branches of science problematic.

Though epistemological philosophy of science has not found an adequate solution to either of these problems, we will see how ontological philosophy solves them when we return to the issue of efficient causation after explaining change as an aspect of substances.

Another project of philosophy of science has been to show that what science claims to know about change is genuine knowledge. Since it takes an epistemological approach to philosophy, that is the project of defending realism in some form, and it leads, once again, to anti-realism, or skepticism about science. But we will see how this problem is solved when we trace the course of evolution at the end of this chapter. Indeed, we will see why the problem arises. (See Change: Evolutionary stage 10, the Career of epistemological philosophy.)

Change as an aspect of substances. Existence is one of the two most basic aspects of substance as substance, and as we have seen, there are two aspects to the existential aspect of substance, particularity and temporality. Temporality was not relevant in explaining the truth of mathematics, since spatial relations exist completely at each moment. (Particularity was required to explain the relations among basic substances, since relations depend on how substances exist together as a world). The temporal aspect of the existential aspect of a substance is how substance endures through time, and its consequences are considered in this chapter.

Though we assume that substances have essential natures that do not change as time passes, change is possible, as we have seen, because space and matter have opposite natures and each bit of matter coincides with some part(s) of space or other. But since spatiomaterialism leaves it open which parts of space each bit of matter coincides with, it is ontologically possible for bits of matter to have different locations at different times. Moreover, it is possible for bits of matter to change their locations as time passes, because bits of matter can move. Motion is possible, as we have seen, because the parts of space are connected continuously, just as moments in time. Furthermore, motion makes it possible, as we have also seen, for bits of matter to change by interacting with one another, because if bits of matter can move, the three dimensional geometrical structure of space makes it possible for more than one bit to move to the same (or adjacent) parts of space. When bits of matter have the same or adjacent locations, they can act on one another, thereby changing properties or relations of the bits of matter and parts of space involved.

Their ways of moving and interacting are extrinsic properties of bits of matter. Their intrinsic properties may also change as their extrinsic properties change, though changes in intrinsic aspects of their essential natures do not affect how bits of matter move and interact.

What makes it possible to explain change ontologically, rather than merely assume it, is the essential nature of space, that is, its structure or wholeness. The parts of space are all necessarily connected in three dimensions according to Euclidean geometry (entailing that space is whole), and since space contains all the bits of matter, its nature makes it possible for bits of matter to move and interact with one another. And we will see how space and matter work together to constitute the regularities described by the basic laws of physics. But not only does the basic nature of a spatiomaterial world make change possible and afford an ontological explanation of the laws of physics, it also makes certain kinds of changes impossible and other kinds ontologically necessary. They are the ontologically necessary truths about how change takes place. Unless those regularities hold, the world cannot be constituted by matter and space enduring through time with all the matter contained by space.

There are, however, two basically different kinds of regularities entailed by spatiomaterialism, because space not only constrains how each bit of matter can move and interact in relation to other bits of matter in its neighborhood, but it also connects all the changes they undergo in any region of space.

The ontological constraint on how bits of matter can move and interact in relation to one another entail necessary principles about the kinds of local regularities that can hold. Within those ontologically necessary limits, there are further regularities about change that are contingent. More specific aspects of local regularities depend on the specific kind of matter and space making up the actual world, and thus, they can be known only by further experience of the world. They are the regularities described by the basic laws discovered by physics, and as we shall see, there ways of explaining ontologically why those laws are true.

The way that space connects the changes that happen to different bits of matter in any region imposes global regularities on change. The changes that occur to all the bits of matter in any region must “add up” in a certain way as time passes, because they all coincide with parts of space in the same region and space also endures through time as a substance with a wholeness that connects all of them to one another. Their motion and interaction “add up” in any closed or isolated region of space to global regularities about change, though most of the specific global regularities also depend on the laws of physics that hold only in spatiomaterial worlds like ours.

The wholeness of space can be distinguished from the geometrical structure of space, because the fact that all the parts of space fit together as a whole is just one consequence of its parts having geometrical relations to one another. Thus, we can say that, whereas the local regularities depend on the structure of space as an ontological cause, the global regularities also depend specifically on the wholeness of space as an ontological cause.

Local regularities about change. Regularities about change are local when they are about how each bit of matter moves and acts relative to other bits of matter. This aspect of the world is singled out when we focus on a particular bit(s) of matter and consider how it moves in relation to other bits of matter in its neighborhood or how it interacts with them. There is, however, a difference between necessary principles and contingent laws about local regularities.

There are certain aspects of such changes that hold, regardless of anything further that physics may discover empirically about the essential natures of the matter or space involved, because they are entailed by spatiomaterialism (or the basic nature of matter and space and how space contains matter). They are what I will call “ontologically necessary principles” about local regularities.

Many possible ways of changing are left open by the limits imposed by the necessary principles about local regularities. And bits of matter (and space) can change only in some determinate way, for they are just substances with some specific essential nature or other, entailing that such change is regular in some way. But how they change depends on the specific kind of matter and space of which the actual world is constituted. The regularities about change that depend on the specific nature of matter and space will be called “contingent laws” about local regularities. These contingent laws include all the basic laws of physics.

In what follows, we will see how it is possible to explain the basic laws of physics ontologically. It must be possible to explain them by the specific essential natures of matter and space, if spatiomaterialism is true. The possibility of such an ontological explanation is not very surprising in the case of classical physics (though it has some surprising implications, for example, about the nature of kinetic energy). But the possibility of such an explanation is precisely what is put in doubt by contemporary physics. Showing how relativity theory can be explained ontologically by spatiomaterialism is one of the mortgages that remains to be paid in order to use that ontology as the foundation for this argument demonstrating necessary truths, and as we shall see, quantum mechanics can also be explained ontologically by spatiomaterialism.

Necessary principles about local regularities. Necessary principles about local regularities follow from the basic natures of space and matter as substances enduring through time assuming that each bit of matter coincides with some part of space or other. We have already seen how their essential natures explain the possibility of change by motion and interaction ontologically. The same ontological causes imply that they can change only by local motion and local action.

The principle of local motion. The principle of local motion holds that bits of matter can change their locations as time passes only by moving continuously across the space that separates the starting points and the ending points. That is what I will call “local motion.” What it denies is that bits of matter can ever change their locations by simply disappearing from one location at one moment and appearing somewhere at a distance at the next moment. That is, it denies that bits of matter can “flit about” discontinuously in space from moment to moment. 

The reason that “flitting about” is impossible is that it could occur only if one of the three basic assumptions of spatiomaterialism were false, that is, only if space were not a substance, matter were not a substance, or bits of matter did not coincide with parts of space.

Given that the bit of matter is a substance enduring through time, how could it have one location at one moment and another location at a distance from it the very next moment, that is, without moving to the second location? It might be possible if space were not a substance, but a mere relation between bits of matter, for spatial relations could simply be defined as kinds of relations that change discontinuously. That is a possibility for a materialist ontology, which reduces space to relations among bits of matter. But if space is a substance with the essential nature we have assumed and it gives bits of matter spatial relations by how they coincide with different parts of space, then the spatial relation between the first location and the second location depends on the existence of all the other parts of space enduring as substances through time, including all those parts of space in between the two locations. Thus, the only way that the bit of matter could come to have the new spatial relations is by coinciding with a continuous series of parts of space separating the two locations as time passes. That is the only way that bits of matter can change their spatial relations in space, if they get their spatial relations from the relations among the parts of space with which they coincide and the parts of space are all related according to a geometrical structure.

Given, therefore, that space is a substance, how is it possible for bits of matter to flit about discontinuously? It might be possible, if the bit of matter could simply drop out of existence at one moment and come back into existence at the distant location the next. But that would be to deny that the bit of matter is a substance in our sense, for it would not be enduring through time. Its existence would not be continuous, if it dropped out of existence and then came back into existence, even if it came back into existence the very next moment.

Nor can we suppose that the bit of matter simply slipped out of space altogether at one location and slipped back into space at another location, because that would contradict the assumption that bits of matter are contained by space. The basic relationship assumed by spatiomaterialism is that, at the present moment, each bit of matter coincides with some part of space or another. This is what give bits of matter their spatial relations to one another. And since it holds at the present moment, it must have held at all moments in the past and it must hold at all moments in the future, for there is no other way for bits of matter to acquire spatial relations to one another

In a spatiomaterial world, therefore, the only way that bits of matter can change their spatial relations is by local motion, that is, by moving continuously across space. Nothing else is compatible with the assumption that space and matter are substances enduring through time, with all the bits of matter coinciding with parts of space.

And that means that bits of matter move with a finite velocity, since infinite velocity would be equivalent to “flitting about” in space.

The principle of local action. Once again, the same factors that explain the possibility of change by interaction also imply that such change can occur only by local action. Motion makes it possible for bits of matter to come to occupy the same or adjacent locations, and if motion does so, that puts them in a position to act on one another, assuming that matter has a more specific essential nature that includes such powers. On the other hand, if bits of matter are not in the same (or adjacent) locations in space, they coincide with distinct parts of space that are separated by other parts of space, and they cannot affect one another without something traveling across the space between them, for space is the only connection the bits of matter have to one another.

They are also related by being parts of the same world, but we are using “parts of the same world” to mean only that they exist or are a part of everything that exists, and bare existence does not entail any other relations between them.

In order for bits of matter located at a distance from one another to interact, another bit of matter must travel across the space separating the one bit of matter from the other as time passes. The bit of matter may be just the exertion of a force (in which case it is an inter-action, with an opposite force also being exerted, according Newton’s third law of motion). But even if such a force were just a “modification” of relevant parts of space, it would still be a bit of matter, that is, a material substance, and as such, it cannot get from one location to the other without something moving across space as time passes time, or else it would violate the principle of motion.

The principle of local action is not as simple as it sounds, for as we shall see, there are various forms of matter, and some of them coincide with more than one part of space at any given moment. Indeed, one form of matter (forces with infinite range) can, in principle, coincide with all parts of space (albeit not all equally). Such forms of matter can interact with other bits of matter wherever they are located.

There are, however, other forms that are completely outside one another in space (including, as we shall see, some of the rest mass of the material objects that exert forces with infinite range), and the principle of local action does constrain their interactions. These complications will be taken up as we explain the various forms of matter and how they move and interact.

The principle of local action has to do with how bits of matter that are localized in space can act on one another when they are located at a distance from one another, and such “actions” will be defined more fully in explaining how quantum mechanics is true in a spatiomaterial world. But there is another kind of very limited effects that certain forms of matter can have on one another, in addition to such inter-actions, and space is an ontological cause of the same kind of limitation on them. That is, the principle of local action is really just part of a more basic principle, which might be called the “principle of local action or effect.”

These peculiar effects that bits of matter of certain kind can have on one another without the mediation of other bits of matter are possible in a spatiomaterial world, because if space and matter are both substances, then not only can space and matter affect one another, but parts of space can affect one another. Though a bit of matter can affect only those parts of space with which it coincides (but not any distant parts of space), it is possible for a bit of matter to have effects on space itself that affect other parts of space and, thereby, the bits of matter that coincide with distant parts of space. However, if there were such effects (and, as we shall see, there are, though they are severely limited), the ontological causes of the principle of local action would impose the same constraint on them. One bit of matter cannot have effects on other bits of matter at a distance by way its effects on space without some change in space traveling across space as time passes from the location of the one bit of matter to the location of the other.

There is no reason to doubt that it is possible for parts of space to affect one another. Parts of space are particular substances, even though they all have necessary geometrical relations to one another. Each part of space, as a substance, endures through time, and spatiomaterialism leaves open the possibility that parts of space have properties that can change under certain circumstances (though that would be a temporally complex aspect of the essential nature of space, since there is no deeper ontological explanation of it). However, spatiomaterialism does imply that, if a property of one part of space can change a property of other parts of space, it can affect only neighboring parts of space, so that in order to affect parts of space at a distance, the effect would have to propagate across space as time passes. Such a further causal connection among the parts of space could mediate the effect of one bit of matter on bits of matter at a distance from it, but it would depend on some change traveling across space as time passes. And it would have to be at a finite velocity, for effects with an infinite velocity would be effects at a distance.

What is relevant here is the general principle that what happens to the bits of matter in one location cannot affect (either interact with or have an effect on) what happens to bits of matter located elsewhere without something traveling across the space separating them. What moves across space may be another bit of matter, or it may a change in space itself. But those are the only ways for one to change the other, because bits of matter have no connection with one another except for how they coincide with parts of space.

If a bit of matter were to get from one location to the other without moving across space in time, it would violate the principle of motion. And its velocity must be finite, or else the bit of matter would be flitting about.

If a modification in one location of space were to affect other locations in space immediately, it would mean that space is not made up of parts of space that endure through time as distinct substances. Though the geometrical relations among parts of space are aspects of their essential natures, they are distinct substances related geometrically, that is, by way of the parts of space between them, and any change in one part of space must first produce real changes to the parts in between before it can affect more distant parts of space. And it must propagate at a finite velocity, or it would not be propagating at all.

In either case, whether the action is mediated by a bit of matter or by space itself, something must move across space as time passes, or there can be no effect of one on the other.

The principle of local action (and effects) denies that there is any action (or effect) at a distance. Though action at a distance is ontologically impossible in a spatiomaterial world, it is conceivable, because if space were not a substance, but merely a kind of relation that holds among bits of matter (or an aspect of how they exist together as a world), the relations postulated might include bits of matter acting on one another at a distance. Such a spatial relationism would be a kind of materialism. But substantivalism about space makes action at a distance impossible, because bits of matter at a distance from one another are separated (and connected) by all the other spatial substances that exist between (and around) them. Space is the ontological cause that limits interaction to local actions.

Empirical science explains events and conditions by efficient causes, but if those causal connections have ontological explanations at all (and those connections are not merely assumed as part of the specific nature of matter or space), they must be mediated by the motion and interaction of bits of matter in space (or effects in space) as time passes, because nothing else is permitted by the necessary principles of local motion and local action. We shall see that spatiomaterialism can go quite a way in explaining efficient causes ontologically, but it may be possible to go even farther than what is sketched here.