Spatiomaterialism. Given these three assumptions of ontological philosophy, the final step in securing its foundation for necessary truths is to use them to decide what to believe about the basic nature of existence. As it turns out, the empirical method is decisive. There is one ontology that we must choose over the others, if we follow the empirical method, and it is different from the currently accepted ontologies. The two received views are both ontologies of science. They come from realism about contemporary physics. One is materialism, the view that matter is the only kind of substance constituting the world, whereas the other maintains that an opposite kind of basic substance helps matter constitute the world, namely, spacetime. But as we shall see, naturalists who take ontology to be explanatory and follow the empirical method in deciding what to believe ought to reject both in favor of the view that the world is constituted by space and matter, both existing as substances in time, or what I will call "spatiomaterialism."
We can see that spatiomaterialism is the best ontological explanation of the natural world by considering the various possible theories on each of the basic issues about what exists in the natural world: time, space, and matter. In each case we will decide what to believe by which theory offers the best ontological explanation of what is found in the natural world -- the one that explains the most with the least.
Our conclusion will be, however, that we ought to accept these ontological position if they are otherwise possible. There are ways they may be falsified by certain unobvious phenomena which we are not currently taking into account. I mean the observations used as evidence for Einsteinian relativity, as well as the fact of consciousness, the real difference between good and bad, and the validity of the belief that there is something worthy of worship. We will not be in a position to show how those phenomena can also be explained until we take up the necessary truths of ontological philosophy.
Possible explanations. We know from our experience of the world that objects are in time as well as in space, but as we saw in Ontology: Temporality , there are two possible theories about the nature of time. We are looking for an explanation of the world by substances, but we can believe either that substances endure or that they perdure over time.
Endurance theory of time. To hold that substances endure through time is to hold that they exist only at the present moment. Existence itself is in time. The past and the future do not exist. This view is sometimes called "presentism," but we are also assuming that what exists are substances. Thus, since substances never come into existence nor ever go out of existence as time passes, the substances that exist now did exist in the past and will exist in the future. In other words, substances are identical across time. Each substance that exists at one moment is identical to some substance that existed or will exist at every other moment in the history of the world.
Perdurance theory of time. To hold that substances perdure over time is to hold that all the moments of their histories exist in the same way. Time is just a relation that holds among those moments. The past and the future exist in the same sense as the present, for "past’ and "future" are just ways of referring to other moments relative to some moment taken as present. Though the perdurance theory of the temporal existential nature of substances can agree that substances never come into existence nor go out of existence over time, what they mean is that substances are wholes made up of parts, with each substance having a momentary part for each moment in the history of the world.
The best ontological explanation of time. Between these two theories, the empirical method requires us to prefer the one that explains more with less, that is, the one that uses fewer and simpler ontological causes to explain more phenomena as effects. According to each criterion, the endurance theory is clearly superior. Consider, first, simplicity.
Simplicity. The perdurance theory must postulate many more substances as ontological causes than the endurance theory, because it holds that every moment in the history of each permanent substance has a distinct and equal existence.
In fact, each moment is like a substance, according to the perdurance theory, for it is a distinct ontological cause that must be postulated separately in order to explain the world ontologically. But if such moments are substances, they are rather unusual substances, because they lack the temporal aspect of the existential aspect of the nature of substance as substance. (Though they are as eternal as the world, they do not exist at every moment in the history of the world, for they are only one moment in the history of a permanent substance.) Still, they have particularity. Each moment is a particular substance with an existence that is distinct from every other substance (including all the other moments in the history of the same permanent substance). Thus, each has both an existential and essential aspect to its nature (its essential nature being whatever properties hold of the permanent substance at the relevant moment in its history). So let us grant that they are substances of a kind. I will call them "momentary substances," since they do not endure through time but exist non-temporally (if not eternally) as one moment in the history of a permanent substance.
Since every momentary substance must be postulated separately, the perdurance theory requires many more ontological causes to explain each permanent substance postulated by the ontology. Indeed, the perdurance theory must postulate (indenumerably) infinitely many momentary substances for each permanent substance, since time is continuous (as evident in its infinite divisibility), and may well be eternal (that is, infinite in extent). Judging simplicity by the number of ontological causes required, therefore, the empirical method requires us to prefer the endurance theory. The endurance theory needs to postulate only one enduring substance to account for each permanent substance in the world.
It may seem, however, that there is a defense for the simplicity of the perdurance theory. Though its "momentary substances" are greater in number, each is simpler in its nature than enduring substances, and thus, its ontological causes are simpler.
What makes momentary substances seem simpler than enduring substances is that momentary substances do not have to endure through time, but can simply exist eternally as one moment in the history of a permanent substance. But why is that simpler?
Perhaps, the simplicity comes from having a temporally simpler nature. Momentary substances cannot have temporally complex properties, because they are what exists at only one moment in the history of a substance that never comes into existence nor goes out of existence. But that does necessarily make them simpler than enduring substances, for enduring substances can also have essential properties that exist completely at each moment of the existence of the substance. On both views, therefore, the essential properties of substances can exist completely at each moment of the existence of the substance. Thus, the only difference between them is that enduring substances exist at many more moments than momentary substances. But that is just the difference between them. To take that as showing the greater simplicity of the perdurance theory would be to beg the question.
On the other hand, perhaps the greater simplicity is supposed to come from its theory about the nature of existence. The endurance theory holds that existence itself is in time, and since that means time is an aspect of existence, a permanent substance must endure through time in order to exist as a substance. Thus, it might be argued that the perdurance theory is simpler, because it takes existence to be just the self-subsistence of the momentary substances making up the histories of permanent substances. Existence is non-temporal, rather than being in time. And this greater simplicity about the perdurance theory enables it to explain ontologically why permanent substances exist at every moment in the history of the world: each permanent substance is a whole made up of many momentary substances as its parts.
However, that supposed ontological explanation brings out the cost of not assuming that existence is in time. Not only must the perdurance theory postulate infinitely many momentary substances to account for each permanent substance, but it must also assume a basic relationship that gives those momentary substances infinitely many relations to one another. The events in the history of a permanent substance occur in a certain order, and so the momentary substances that must be related in a certain way in order to constitute it. Though those relations may be simply how the momentary substances exist together as a world, they must all be assumed in order to deny presentism.
Thus, not only are momentary substances not simpler than enduring substances in virtue of having temporally simple essential natures, but the perdurance theory must also postulate infinitely many momentary substances with infinitely many relations among them to account for each permanent substances.
As far as simplicity is concerned, therefore, endurance theory is clearly superior. It postulates one enduring substance to account for each permanent substance, whereas the perdurance theory must postulate infinitely many momentary substances with infinitely many relations among them in order to explain each permanent substance. But this ontological extravagance might be justified, if the perdurance theory can explain why permanent substances are in time, and so let us turn to the criterion of greater scope.
Scope. The criterion of greater scope requires us to prefer the theory about the nature of time that explains more to the one that explains less.
It may seem that the perdurance theory does have a greater scope, because it explains at least one phenomenon ontologically that the endurance theory simply assumes. It explains ontologically why permanent substances are in time by showing how they are constituted by momentary substances and relations among them. But this claim to have an ontological explanation of substances being in time does not stand up, for two reasons.
First, it is ad hoc. Nothing is explained by the assumption that permanent substances are constituted by momentary substances and relations among them except their being substances that exist at every moment in the history of the world. To postulate infinitely many ontological causes to explain a single aspect of the world is to explain the least with the most, the opposite of the empirical criterion. To be sure, the endurance theory does not explain this aspect any better. But there is nothing to prefer over the assumption that existence itself is in time.
Second, there is an aspect of this phenomenon whose possibility the perdurance cannot explain. That aspect is how the present moment is different from all the other moments in the history of the world, both past and future. It is something for which the endurance theory can account. And the failure even to account for it (that is, the failure to explain its possibility) means that the perdurance theory is falsified by it.
Endurance theory can account for the fact that one moment in the history of the world stands out as different from all the others, because it holds that only the present moment exists. The present is different from the past and the future in the most basic way, as far as ontology is concerned, because the present exists, while the past and future do not. That is what it means to hold that existence itself is in time. (This is not to explain the phenomenon of the present ontologically, because it is simply what the endurance theory assumes about the nature of existence. But the endurance theory does not have to deny that present is different from the past and future.)
The perdurance theory, on the other hand, cannot even account for the fact that the present stands out as different from all the other moments in the history of the world. It holds that all the moments in the history of a permanent substance exist in exactly the same sense, and so there is nothing ontological that can distinguish any one moment from all the rest that help make up its history. To be sure, the perdurance theory can say how any moment in the history of a permanent substance that is taken as the present differs from those that occur earlier and those that occur latter, for its momentary substances are all related to one another in a certain order. But it has no way to single out any moment in the history of a permanent substance as "now."
This blindness to the present is implicit in what the perdurance theory says about the nature of existence and time. Instead of taking time to be an aspect of the nature of existence, it takes time to be part of the structure of what exists, that is, a certain kind of relationship that exists among its momentary substances. It sees time as a dimension of what exists, much like spatial dimensions, and thus, time contains different moments in the same way that space contains different point, which means that all moment are contained in the same way.
Thus, far from explaining why permanent substances are in time, the perdurance theory cannot even explain the possibility of the most basic aspect of it. Indeed, the phenomenon of the present being different from the past and future would seem to show that the perdurance theory is false.
What the perdurance theorists can do, however, is explain away the phenomenon. That is, it can explain why we experience the present as being different from all the other moments by holding that it is just an appearance that holds for each and every moment in the history of beings like us. We are rational beings, capable of reflection, and it is by reflecting on our experience that we come to believe that the present moment is different from the past and the future. But if the perdurance theory is correct, each of us is just a set of momentary substances that makes up a personal history. Thus, it is possible to hold that the essential nature of every momentary substance constituting a being like us includes the appearance that that moment in one's history is the present and, thereby, different from all the moments in the past that may be remembered and all the moments that may be anticipated. That is, each moment in the life of a reflective subject includes the subjective appearance that it is present, even though it is just another momentary substance that exists non-temporally.
But this is not to explain the present. It is to claim that our sense of the present is an illusion. That is surely an alternative that we want to avoid, if possible, for it is ad hoc. Anything found in the world could be explained away the same way, that is, explained as a mere appearance to the subject by holding that it is actually part of his essential nature as a substance. If it is possible to explain our sense of the present being different from the past and the future in a way that makes it true, we must prefer the theory that does so. Hence, the empirical method requires us to prefer the endurance theory on the grounds that it explains more than the perdurance theory.
This point can be seen more clearly if we consider how the present being different from the past and the future is something found in the world by perception, not just by reflection on how it seems to us. We perceive change in the natural world, and if we articulate the beliefs implicit in such perceptions, we find that what we believe is that certain properties go out of existence and other properties come into existence as time passes.
Consider, for example, a bus passing by us on the street. The property of approaching us goes out of existence as the property of being in front of us comes into existence, and then the property of being in front of us goes out of existence as the property of moving away from us comes into existence. That is how we perceive change in the natural world, and it implies that the properties that the bus had in the past do not exist any longer, and that the properties that it will have in the future do not exist yet. That is what we mean by their coming into existence and going out of existence as time passes.
To be more precise, reflecting on our observation, we find that the experience involves past, present and future. At the moment we see the bus is in front of us, we remember seeing it approach and anticipate its moving away. Were the immediate past and future not part of our experience, we could not observe that the bus is moving. But while the present is seen as existing, the past and future are seen as not existing, albeit for opposite reasons. The past event is seen as not existing because it is over, while the future event is seen as not existing because it has yet to happen.
That only the present exists may be only implicit in the observation. But that does not mean that it is not part of what we observe, only that we have not formulated that aspect as a sentence. The belief that the bus’s past and future do not exist now is as much part of the observation of the bus’s motion as the belief that that the bus is a distinct object in space is a part of the observation of the bus itself. It is not surprising, therefore, that this is called the ordinary view of the nature of time. It is what the “man in the street” would say about the past and future if asked about their existence (see, for example, Putnam , p. 240).
The perception of change as "real" in this sense discloses something about the world that cannot be explained by the perdurance theory, because it must deny that any properties come into existence or go out of existence over time. The perdurance theory holds that every moment in the history of every substance exists in exactly the same sense, and so the properties that hold at earlier moments still exist in the same sense as the present, and the properties that hold at latter moments already exist in that sense.
Again, the only way that the perdurance theory can account for this perceived fact about the world is to deny that it is a fact and to hold that what we think is perception of an independently existing world is just an illusion. That is, its defenders can hold that each of the momentary substances making up the histories of beings like us involves, as part of its essential nature, the appearance that change really takes place as time passes. That would mean that, relative to any given moment, we perceive the past and future states of the world as not existing, even though, in fact, they do.
But this is, once again, to explain away the phenomenon, not to explain it ontologically. It could be used to explain anything found in the world, and thus, it should only be invoked, if it is not possible to explain phenomena as what really exists. The perdurance theory has no alternative, because if change is real in this sense, it is false. But we have an alternative, because the perception can be accounted for by the endurance theory.
The perdurance theory does not, therefore, have greater scope than the endurance theory. Its explanation is ad hoc, and what is worse, it is falsified by the phenomenon that it claims it alone can explain, unless we accept further ad hoc assumptions that make the phenomenon illusory.
Nor do any of the arguments for the perdurance theory offered by defenders of the so-called tenseless theory of time give us any reason to accept it.
The empirical method requires us, therefore, to prefer the endurance theory over the perdurance theory. It is simpler in both relevant ways (the fewest and simplest ontological causes), and it has a larger scope (in the sense that it can, at least, account for our sense of the present and our perception of change as really occurring in time). It clearly explains more with less.
Nor are the basic aspects of the world that only the endurance theory can explain trivial. The ability to explain change by the endurance of substances through time is the foundation for explaining regularities about change ontologically. If ontological philosophy had to accept the perdurance theory, it would not be able to show the ontological necessity of the connection between cause and effect in efficient cause explanations. Nor would it be able to demonstrate the ontological necessity of global regularities, on which most of the new ontologically necessary truths depend. Without the endurance theory, ontological philosophy would not be a new way of doing philosophy.
This does not necessarily mean that it is true. It is only to say that we must prefer it, if it is possible, for it may turn out that there are other things found in the world contradict the endurance theory. That is what contemporary Einsteinian believe, as we shall see when we take up spatiotemporalism, and thus, they will have to be answered before we can be confident about the truth of the endurance theory.
 It may seem that there is a way to for the perdurance theory to explain the present without dismissing the phenomenon of the present as an illusion, and it is relevant to mention it here, because it was first suggested by Hermann Weyl (, p. 217) in defense of the perdurance theory entailed by taking spacetime to be a substance. Einsteinian relativity had led, as we shall see in the next section, to the belief that what exists is a spacetime world in which the momentary substances making up permanent substances are spacetime events, and Weyl said, "The great advance in our knowledge . . . consists in recognizing that the scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither “time” nor “space”. Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet and passes behind it, as history that is, as the process that is going forward in time and takes place in space."
Weyl is assuming that empirical falsification of substantivalism about spacetime can be avoided by holding that the present is just how spacetime and the spacetime events it contains appear to “consciousness”. Though such a response may be acceptable in epistemological philosophy, it leads to an ontology that is decidedly inferior to the endurance theory, because it is more complex and problematic. To assume that consciousness “passes on” is to assume that it undergoes real change, and thus, to follow Weyl is to postulate, in addition to spacetime and the spacetime events that it contains, some substance that does endure through time, always existing at each moment as it is present, namely, consciousness. If consciousness is postulated as a subjective substance, spacetime substantivalism will not only be more complex (now postulating three basic kinds of substances), but it will also face a serious ontological problem, for it must then be explained how enduring substances can be related to non-temporal substances. Indeed, it would be an ontology with two different concepts of time, one that is part of the structure of spacetime and another that characterizes the existence of consciousness (as a substance enduring through time). That twofold use of time complicates the perdurance theory in a way that makes it not only more complex simpler, but also far more problematic.
Weyl's approach is still a common response, however. For example, see Penrose , pp. 442ff. And though McCall  is only trying to rescue the openness of the future, his ontology (or “model of the universe’) is also made more complex and problematic by requiring both these concepts of time.
 To hold that only the present exists is to take sides with the so-called “tensed theory of time” in a current dispute in the philosophy of language (Oaklander and Smith, ), but that does not mean that the perdurance theory can be defended by endorsing the “tenseless theory of time”. The endurance theory would hold that the tensed theory of time is correct in holding that statements about past, present and future say something about the world that is not implied by tenseless descriptions of before- and after-relations that hold among events (or by analyzing the truth conditions of such statements as indexical references to the moment of their utterance) The tenseless theory must deny that only the present exists, for otherwise it would have to admit that statements about past, present, and future are something more than descriptions of an event’s before or after relations to the moment of their utterance. Such statements uttered at present would also be (true) descriptions of how the event is related to what exists. And those uttered at other moments would have no truth value, for they wouldn’t exist at all.
There may be a standoff between these two views in the philosophy of language. But that is not relevant here, because our reason for preferring the endurance theory is not based on analyzing truth conditions of statements about the past, present and future. It is an argument in empirical ontology. I am arguing that the best ontological explanation of the world disclosed by perception, including the observation of real change, is to postulate only enduring substances.
The tensed theory has not been defended in this way in the recent debate. Appealing to what we observe is not the same as appealing to phenomenology, as in Part III of Oaklander and Smith . The former argument is not refuted by pointing out that the observation would have the same causal connections on the timeless view, for it is about the content of the observation, not its causal role. And though this view implies that there are properties of “presentness”, “pastness” and “futureness”, their meanings are explained in terms of existence: the present is what exists, while the past and future do not, albeit for opposite reasons. Thus, contrary to Williams , there is a basic disanalogy between “presentness” and “hereness”, for what is opposed to the former (past and future) does not exist, whereas what is opposed to the latter (what is over there) does exist.
Nor is a theory that explains how the present is different from the past and future by its existence plagued by the paradoxes that are supposed to undo the tensed theory of time. For example, it avoids McTaggart’s paradox about time, for it is not committed to there being events that have first the property of being future, then the property of being present, and finally the property of being past, for nothing exists but what exists at present. Nor are there sentences about past, present and future changing truth values, for the only sentences that exist (and are capable of being either true or false) are in the present.