Properties. Among the necessary truths about what is that follow from spatiomaterialism, the first set has to do with the nature of properties. Its main significance for issues in traditional philosophy is how it offers naturalists a solution to the problem of mind. By "consciousness," I mean the the fact that experience has an appearance to the subject, or that it is like something to be the subject. It cannot be explained without substances having phenomenal properties as well as physical properties, and ontological philosophy offers an explanation of phenomenal properties which entails that they have a necessary relationship to physical properties.

This implication of our ontology does not depend on recognizing the existence of space, but would follow from any form of materialism that took ontology to be explanatory and used the concept of substance introduced in Ontology: Substances. That makes it unique among the implications of ontological philosophy concerning the issues raised by traditional philosophical issues, for the rest depend on substantivalism about space.

In the case of phenomenal properties, the implications depend on our definition of the nature of substance, and the reason contemporary naturalists have overlooked this explanation is that materialism (or physicalism) is understood as realism about the theories of contemporary physics. Materialists posit the existence of whatever is required for the truth of the theories they believe, but they do not think much further about the nature of substances and properties. Thus, they take properties to be as ontologically basic as material substances, and that makes the relationship between physical and phenomenal properties seem puzzling.

Let us consider first what ontological philosophy implies about the nature of basic properties and their kinds before we take up the problem that follow from taking properties as just objects of knowledge.

Properties as aspects of substances. We have already seen how properties are related to the substances postulated by an explanatory ontology. They are aspects of substances, or part of what is assumed by postulating them which reason can pick out. We leave open questions about how rational beings like us are able to distinguish one aspect from another (until we discuss how reason comes to exist in a spatiomaterialist world like ours and see how reason depends on spatial imagination).

The basic properties of substances. We have already seen that substances, as substances, have two basic aspects, existence and essence. That is, they have the property of existence as well as an essential aspect to their nature. (See Ontology: Nature of substance.) But at this point, we must recognize two further aspects that may be involved in the essential aspect of the nature of substance as substance.

Existence. We have already seen how the existential aspect of substance as substance (or its property of existing) includes two properties, particularity and temporality. In other words, to say that a substance exists is to say that it has an existence that is distinct from other substances in the world (particularity) and that it endures through time temporality). (We take the temporal aspect to be endurance, because we have seen that endurance is the best ontological explanation of the nature of time, including both change and what makes the present different from past and future than perdurance. See Spatiomaterialism: Best explanation of time.)

Essence. Each substance must have an essential aspect in addition to its existential aspect, because in order to exist at all, it must exist in some determinate way. This was our reason for holding that substances have two basic aspects to their natures as substances, not only existence, but also an essence. It makes no sense to hold that something exists and to deny that it has any further aspect to its nature. But there may be two aspects to the essential aspect of the nature of substance as substance.

Intrinsic nature. This most basic aspect of its essential nature will be called its "intrinsic" essential property, for it is the kind of essential property that a substance has in virtue of existing as something distinct from all the other substances in the world. It is what the substance is in itself, or its way of existing on its own.

Extrinsic nature. But its intrinsic essential nature is not all there is to the essential nature of a substance, if the substance is part of the same world as other substances (and the existence of other substances is not entailed by its essential nature, as in the case of parts of space). Insofar as the world is made up of substances that exist independently of one another, and insofar as those substances are related to one another in some way other than simply being parts of the same world, each substance must also have extrinsic essential properties relative to those other substances. It may have different extrinsic essential properties relative to each kind of substance to which it is related, but its essential nature must have some such aspects.

Thus, the essential aspect of the nature of substance as substance includes two kinds of essential properties: an intrinsic essential property and extrinsic essential properties. In other words, each substance must exist some way in itself and it must also exist some way for other substances that exist independently of it as part of the same world.

The intrinsic and extrinsic aspects of the essential natures of substance can certainly be distinguished by reason. The world is made up of substances, and we can think about each distinct substance as it is in itself, whatever that may turn out to be, because in order to exist at all, it must exist in some determinate way. And if there are other substances whose existence does not depend on what it is in itself, we can also think about what it is for other substances, assuming that it is related to other substances in some determinate way in addition to merely being part of the same world with them (and that relation is not part of its intrinsic essential nature, as in the case of parts of space relative to one another).

What a substance is in itself cannot be reduced to what it is for other, independent substances, because if its extrinsic essential nature were all there is to its essential nature, there would be nothing to be related to other substances. Relations need relata, or something that already exists. The relata are substances, and since every substance has an essential aspect to its nature as well as an existential aspect, each relatum has an intrinsic essential aspect. Since substances already have intrinsic essential natures, their relationships to other, independent substances must be a further aspect of the essential aspects of their natures as substances. Thus, each substance must have properties of both kinds, though different kinds of substances making up the same world may have different kinds of intrinsic and extrinsic essential natures.

The basic properties of the two basic substances. Spatiomaterialism postulates the existence of two basic substances, matter and space, and it assumes that each bit of matter coincides with some part of space or other. But as we have seen, matter and space have opposite natures as parts of the world. Though in both cases, it makes sense to think of the substances as consisting of many particular substances, their parts are related to one another in opposite ways. Bits of matter can exist independently of one another, but no part of space can exist without all the other parts of space. That is, space has a unique kind of wholeness about it, which matter lacks. The parts of space are dependent on one another, whereas the parts of matter are independent of one another. Being opposite in this way is crucial to their roles in making up the natural world, for nearly every new necessary truth that is supported by ontological philosophy comes from how space contains all the bits of matter.

Matter and space are, however, different basic substances. The existence of one does not entail the existence of the other. We do not know what bits of matter would be like, if they did not coincide with space, or even if that is possible. But each has an existence that is distinct from the other. That is the basic assumption of spatiomaterialism. That is, there would be a difference between parts of space with which bits of matter coincide and parts with which no bits of matter coincide, even if that never actually happens, given what physics implies about the nature of matter. (As we will see, however, space can be empty.)

Both space and matter must, therefore, have all the basic properties that entities must have to be substances at all, including both kinds of existential properties and both kinds of essential properties. Space and matter have existential properties in the same way. But since each basic substance is made up of parts in opposite ways, each has intrinsic and extrinsic essential properties in different ways. To make this clear, let us generate a catalogue of all their basic properties, starting with matter.

Basic properties of matter. Matter is a basic kind of substance, and since it is related to every other substance (of both basic kinds) in a determinate way, it must have both an intrinsic and extrinsic aspect to the essential aspect to its nature as substance.

Intrinsic nature of matter. Matter must have an intrinsic nature, even if matter cannot actually exist without being contained by space, because it must exist in itself in a determinate way in order to have an existence that is distinct from space. (That intrinsic nature may, therefore, be what matter is in itself as it coincides with space, but it is nevertheless different from the aspect of matter by which it is related to space.) What is more, however, matter comes in particular substances that exist independently of one another, and thus, each material substance must have an intrinsic property independently of all the other bits of matter.

The intrinsic property of each bit of matter is simply whatever it is in itself, that is, as something that has an existence distinct from every other substances. This could be anything a substance might be in itself (though as we shall see, it is the aspect of the essential nature of matter that makes it possible to explain phenomenal properties.) Since there may be different forms of matter, with different essential natures, the intrinsic properties of matter may be various.

Extrinsic nature of matter. Each bit of matter must also have an extrinsic aspect to its essential nature, because it is related to other substances which exist independently of it as parts of a single world. But according to spatiomaterialism, the substances that exist independently of each bit of matter include both space and other bits of matter, and thus, each bit of matter can have two fundamentally different kinds of extrinsic essential properties: one by which it is related to space, and aspect, which presumably depends on the former, by which it is related to other bits of matter.

Extrinsic nature of matter relative to space. One kind of extrinsic essential property of matter is how it is related to space. Every bit of matter must be capable of coinciding with some part of space or other, since that is what spatiomaterialism assumes the basic relationship between matter and space to be. Given the essential nature of space, as we have seen, that gives each bit of matter certain spatial relations (in three dimensions) to every other part of space. And since every other bit of matter coincides with some part(s) of space or other, coinciding with space also gives each bit of matter certain spatial relations to every other bit of matter in space. They are all contained by space.

Each bit of matter coincides with a part or parts of space. No assumption has been made about how much space bits of matter can coincide with. There may be different forms of matter contained by space, and different forms of matter may coincide with larger or smaller areas of space. Bits of matter may even be spread out in space unevenly. It depends on further aspects of the extrinsic essential nature of matter relative to space which will be discussed later (in Change: Contingent laws of physics), when we take up the ontological explanation of physics and how space and matter endure through time. All we assume here is that each bit of matter has, at the moment of its existence, a unity about it, so that it exists as a whole distinct from all other bits of matter.

Furthermore, since both matter and space endure through time, there may also be a temporal aspect to the extrinsic essential nature of matter relative to space. For example, it is possible that part of the extrinsic essential nature of bits of matter relative to space is that they move across space in some determinate way.

Extrinsic nature of matter relative to matter. Simply being contained by space gives each bit of matter determinate spatial relations to every other bit of matter, but that is not a basic part of its extrinsic essential nature, because it is entailed by its extrinsic nature relative to space, being contained by space, and the nature of space. But since other bits of matter in space exist independently of it, there can be a basic extrinsic aspect to its essential nature that is relative to other bits of matter is space. For example, if one bit of matter coincides with a particular part(s) of space, it may not be possible for other bits of matter to be located there, or not possible for bits of matter of certain other kinds to be contained by that part of space. Furthermore, if motion is an aspect of the extrinsic essential nature of bits of matter relative to space, their spatial relations may change over time, and there may be regularities about how their motions affect one another (that is, they may exert forces by which they change one anothers motion). Indeed, if there are different forms of matter, there may be ways that bits of matter, because of their relative locations and motion, affect one another’s forms.

This is how physical properties are explained ontologically. The basic laws of physics describe regularities in the motion and interaction of basic particles, and the properties they must mention in order to predict or control what happens are called "physical properties." Hence, the truth of the basic laws of physics can be explained ontologically by the extrinsic essential natures of bits of matter relative to space and relative to other bits of matter, since their extrinsic properties include how the bits of matter move and interact with one another. Indeed, that is how spatiomaterialism will explain the basic laws of physics. In other words, physical properties will turn out to be extrinsic aspects of the essential nature of matter with respect to space, with respect to matter, or with respect to both.

It should be noticed, however, that this way of explaining physical laws makes a distinction between two different aspects of the extrinsic essential aspect of matter, implying that there is a difference between two kinds of physical properties. The physical properties having to do with spatial relations and motion are different from those having to do with interactions, because the extrinsic essential natures of matter relative to space is different from their extrinsic essential natures relative to other bits of matter. Indeed, this is, as shall see, the beginning of a deeper (that is, ontological) explanation of the truth of the basic laws of physics.

Basic properties of space. Space is also a substance enduring through time, and since, as a substance, it exists independently of matter, it must also have two aspects to its essential nature: an intrinsic and an extrinsic essential aspect to its nature as a substance. That distinction arises for space because of its relationship to matter, and unlike bits of matter, no such distinction between intrinsic and extrinsic properties can be made in the case of parts of space.

Space has an opposite nature from matter. It has a unique wholeness, because its parts cannot exist at all unless they are all related to one another geometrically in three dimensions. They are not independent substances. Since their relations to one another are part of the essential nature of each part of space, they do not need any further aspect of their essential natures by which to account for the relations to one another. Their essential natures include their relations to one another, and thus, there is no way to distinguish between an intrinsic and extrinsic aspect to their essential natures.

The reason for distinguishing an extrinsic from the intrinsic aspect of the essential nature of a substance was that when a substance exists together with other substances as parts of the same world, it needs some way of being related to them (beyond merely being parts of the same world). But since that was to assume that the substances exist independently of one another, we excluded substances whose essential natures entailed the existence of other substances, for they must already have relations to those other substances as part of their essential nature. That holds in the case of the parts of space.

To be sure, each part of space has an existence that is distinct from every other part of space. But they all have the same kind of essential nature, for they each have the same kind of relations to all the other parts of space. What makes the parts of space different from one another is the particular parts of space to which they have those relations. And since their relations to one another are part of their essential nature, they need only their essential natures to be related to all the other parts of space. That is why the existence of any part of space entails the existence of all the other parts of space.

It is possible to put this point paradoxically. Since the intrinsic nature of a substance is what it is in itself and its extrinsic nature is what it is for other substances, one might say that the intrinsic nature of each part of space relative to other parts of space entails its extrinsic nature, because what it for other parts of space is just what it is in itself as a part of space. But the paradox just emphasizes that no distinction can be made between the intrinsic and extrinsic natures of parts of space relative to one another.

In the case of space, therefore, the essential nature of each part of space as a part of space includes all its relations to other parts of space. That is the wholeness of space, and though it means that there is no distinction between the intrinsic and extrinsic aspects of the essential nature of each part of space relative to other parts of space, it also has implications for both the intrinsic and extrinsic essential nature of space relative to matter.

Intrinsic essential nature of space relative to matter. To exist independently of matter as its container, space must be something in itself. It must exist in a determinate way apart from space. That is the intrinsic essential nature of space relative to matter. But it is a nature that space can have only as a whole.

The essential aspect of the nature of space as a whole includes its being made up of parts with geometrical relations to one another in three dimensions, that is, being made up of all the locations in three dimensional space. This interdependence of the parts of space means that the essential nature of each part of space includes having geometrical relations to every other part of space. In both cases, the essential nature is the aspect the substances have in virtue of how they exist, and since the parts of space necessarily make up the whole of space, it is the same aspect of these substances that characterizes the essential nature of both part and whole. That aspect of the essential nature of space is the intrinsic nature of space.

There is, however, a part-whole relation involved in the essential nature of space. That is, the part is not identical to the whole, because it is only part of the whole. The whole is identical to all the parts. Thus, the existence of space as a whole entails the existence of each of its parts. But since all the parts must exist, if any one of them exists, the existence existence of any part of space also entails the existence of the whole. (Though there is a necessary relationship between them, it is, at this point, true because of what we mean by the terms used, that is, an analytic truth, not an ontologically necessary truth. It is an ontologically necessary truth about the world only if spatiomaterialism is the best possible ontological explanation of the world.)

Neither part nor whole is prior to the other. Space cannot be explained ontologically as a collection of parts of space, because no part of space can exist without the whole. Likewise the parts of space cannot be explained ontologically by the whole, because the whole of space is just all the parts of space.

What makes the parts of space different from one another is not their essential natures, but the particular parts of space to which each part has the geometrical relations entailed by its essential nature. This is to assume that all the parts of space have the same kind of essential nature, and that is the assumption we are making, since it is the simplest assumption we can make about the nature of space. But it does imply that space is infinite, both in its divisibility and its extent, and thus, the essential nature of space (or its intrinsic essential nature relative to matter) is an aspect of something that is infinite. (Of course, if it were to turn out that space is finite, as contemporary cosmology assumes, a much more complex assumption would have to be made about space, because if space has edges, the parts of space would have to have different essential natures. But space would presumably still have an essential nature that characterizes both part and whole equally, since they would still entail one another, and that would be its intrinsic nature relative to matter..)

The part-whole relation that holds for space is the unique wholeness of space, and since it is an assumption of spatiomaterialism, there is no genuine ontological explanation of it. But it is a remarkable essential nature, and since it is so basic to the spatiomaterialist explanation of the world (including its explanation of many further part-whole relations, as we shall see), a few comment might make it easier to grasp what is involved in taking space to be a substance.

The parts of space are puzzling. Mathematicians call them points because the simplest parts of space have no spatial dimensions. But since they make up space as a whole, there are infinitely many of them in any finite distance. That is called the "continuousness" of space, or its infinite divisibility. But since it has been assumed as part of the essential nature of space, there is no ontological explanation of it in spatiomaterialism. It is just another aspect of the wholeness of space.

As explained above, the wholeness of space implies that parts of space do not have extrinsic essential natures relative to one another. This is because what forces us to recognize that any substance has an extrinsic nature is that it can exist independently of other substances and is nevertheless related to them in some more determinate way than simply being parts of the same world with them. An extrinsic essential property characterizes what the substance is for the other substance, or what it contributes to how they are related. But since parts of space cannot exist independently of one another, they lack extrinsic essential natures as parts relative to other parts of space. Their relations to one another are part of their essential natures. The existence of one part of space entails the existence of all the others.

To say that the parts of space lack extrinsic essential natures relative to other parts of space makes it seem that they do have intrinsic essential natures relative to other parts of space. After all, since each part of space does have an existence that is distinct from every other part of space, it must have something in itself. But since what it is in itself includes it geometrical relations to every other part of space, its intrinsic nature seems to be just its essential nature as a part of space. Thus, it is less misleading to say that no distinction can be made between extrinsic and intrinsic natures of parts of space relative to other parts of space. That is just the unique part-whole relation about space.

It is the unique wholeness of space that makes it odd to think of space as a substance. Space does not seem to be a substance because it is everywhere. That makes it seem like nothing to us, because we are, as rational beings, parts of the world (that is, located in space), and we use the structure of space as a way of thinking about the world. We think of material objects as what is substantial about the world, and we take for granted that such substances have have spatial relations to one another, because that is also a most basic aspect of our way of thinking about the world. (That is, spatial imagination is built into every perception). But the appearance that space is nothing is just the essential nature of space (both part and whole). That is just its intrinsic nature relative to matter. And it is because the parts of space exist in such a way that they make up a three dimensional whole that the bits of matter that coincide with parts of space are related to one another. Thus, to see as nothing is, in effect, to grasp its intrinsic nature relative to matter. That is how it appears from "inside space," so to speak.

On the other hand, to think of space as a substance is, in effect, to see space from the outside, rather than from the inside. It gives us the same angle on space that space itself gives us on material objects, because it provides a context in which we can see how space is related to other things, most relevantly, how it is related to bits of matter.

It may help, therefore, to step back a bit and think about what we are doing in taking space to be a substance. We are recognizing that space is an ontological cause of the things that are found in the natural world that is different from matter, that is, as a separate principle, along with matter, in explaining everything. Space is something self-subsistent that helps constitute the world. It may not be possible to have a deeper understanding of the intrinsic essential nature of space relative to matter than what we know by its role, along with matter, in explaining the world ontologically. That is the step that is required, as I have suggested, to see the world from the outside. But "from the outside" is itself a spatial metaphor. You cannot see space from the outside, for taken literally, the outside of anything is always inside space itself. Thus, as I have suggested, it may be better to think of substantivalism about space as what we must assume in order to have a God’s Eye View of the world. After all, space is something that God would have had to create, along with matter, in order to create the natural world. But neither can that description be taken literally, since, as naturalists we deny that there is any being that transcends the world. Thus, the best we can do is, perhaps, just to recognize that the existence of space as a substance enduring though time is just an independent, basic assumption of the most complete ontological explanation that we can give of the world. Everything else in the world is located within the three dimensions of space. That is the bottom of our understanding of the nature of the world, according to ontological philosophy.

Extrinsic essential nature of space. Just as bits of matter have an extrinsic essential nature that allows them to coincide with space space, so space must have an extrinsic essential nature that allows it to coincide with bits of matter. But since space is a whole with parts that differ from one another as different locations in its three dimensional structure, it is not clear whether this extrinsic essential property characterizes the essential aspect of space as a whole or its parts.

Particular bits of matter clearly coincide with particular parts of space. But if any bit of matter coincides with more than one part of space, coinciding with bits of matter is also clearly something that parts of space must do jointly. Furthermore, it is only because many different bits of matter are all contained by the same whole space that coinciding with space gives them spatial relations to one another. Thus, what coincides with them seems to be space as a whole as well as its parts. That is, bits of matter are contained by space

On the other hand, coinciding with bits of matter is something space does to each bit of matter separately, not how space relates to matter as a whole, because matter is not a whole, but just all the bits that exist. To be sure, space coincides with all the bits of matter in the world. But that is just the spatiomaterialist assumption about how these two basic substances exist together as a world, not something that characterizes the essential natures of space as a whole and matter as a whole.

What makes the nature of space problematic is its unique wholeness, or how space is made up of parts and yet is still one. For our purposes, therefore, it is enough to recognize that the capacity to contain bits of matter is the extrinsic essential nature of space, both whole and part, though each bit of matter coincides with some part (or contiguous parts) of space or other(s). And if different varieties of material substances are contained by space in different ways, it must have all the extrinsic essential properties required to do so.

Furthermore, space must also have extrinsic essential properties corresponding to all the extrinsic essential properties of bits of matter relative to space. That is, it must give bits of matter motion through space, if that is how they coincide with space, and it must enable them to interact in all the ways that are involved in the extrinsic essential natures of various kinds of bits of matter relative to other bits of matter. These are also extrinsic essential properties that space both has as a whole and in each part.

Nor is that necessarily all there is to the extrinsic essential nature of space (though relativistic physics holds, in effect, that it is). Since space is a substance, which exists independently of matter, it is possible for space to interact with bits of matter in other ways. Indeed, that is what we shall need to assume in order to explain ontologically how Einstein’s special and general theories of relativity are true. The basic assumption of our ontological explanation of relativity will be is that light always has a determinate velocity relative to space itself, and in explaining special relativity, we will hold that space imposes certain (Lorentz) distortions on material objects moving through space with high velocity. In the case of general relativity, we will assume, further, that the accumulation of large quantities of matter in space alters the velocity at which light moves in nearby regions of space.

This is to hold that the parts of space can contain bits of matter in different ways in the regions around centers of gravity But that is not to say that are any changes in the relations among the parts of space itself. It is only to say that there is a change in how bits of matter coincide with space in those regions. In short, the assumption we shall make in explaining Einsteinian relativity is that space has an absolute, uniform Euclidean three dimensional structure, and that that structure is not changed even though the extrinsic essential nature of space includes interactions with matter that change the state of certain parts of space and, thereby, change how bits of matter coincide with space in those regions. (See Change: Special theory of relativity and Change: General theory of relativity.)

In a more speculative way, I will suggest that space also plays a role in explaining the truth of quantum mechanics, the basic particles recognized by physics, and certain issues in cosmology. Those roles would characterize further the extrinsic essential nature of space, both part and whole. (See Change: Quantum mechanics and Change: Cosmology.)