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Having now established spatiomaterialism as the foundation for ontological philosophy, it remains to discover the necessary truths that follow from it. The new necessary truths follow mainly from the recognition that space is an ontological cause of the natural world, for that entails the ontological necessity of several global regularities (at least in spatiomaterial worlds where the laws of physics are true), including evolutionary change. Those global regularities are one manifestation of the wholeness of the world. But we are at a major juncture in this philosophical argument, and it may help keep issues clear to step back and recall what philosophy is that ontological philosophy can claim to be a new way of doing philosophy. And see how an empirical foundation can yield truths of any kind, necessary or not, that have not already been discovered by modern science.


Nature of philosophy. Philosophy aspires to a more fundamental kind of knowledge about the world than is provided by ordinary ways of knowing (such as modern science and everyday practical reasoning). Any such superior knowledge would require a special foundation. Hence, philosophy is a two-step argument. First, it establishes its foundation, and, second, it uses its foundation to demonstrate necessary truths. Necessary truths are prior to what is known by ordinary means, because what is demonstrated from its foundation cannot be denied without giving up the philosophical foundation.

Epistemological philosophy. That is, at least, the structure of traditional philosophy. Though different foundations were used in different eras of philosophy, they were always epistemological. Traditional philosophy always used reflection on how beings like us know in order to establish some theory about the nature of reason (such as the intuition of forms, certainty about ideas in the mind, and the language-users’ understanding of language). The fruit of such theories was borne in the second step, when the foundations were used to show that certain propositions about the world hold necessarily. Those implications had an authority that was superior to ordinary ways of knowing, for they could be denied only by giving up the theory about the nature of reason. In other words, the necessity of the propositions defended by traditional philosophy was epistemological. Insofar as they were successful, what they showed was that certain propositions are certain.

It is now generally recognized in intellectual circles that traditional philosophy failed to make good on those claims. Indeed, its failure seems so obvious that philosophy itself now seems to be a bad idea. "Foundationalism," as it is called, is not merely eschewed by most contemporary philosophers. It is often cited as something so misguided that it is supposed to be a wonder anyone ever believed in it. The failure of foundationalism is the main support for relativism, and since the most common defense against the charge of relativism attempts to undercut it by denying that philosophy was plausible in the first place, both sides see traditional philosophy as childish. But it is not necessary to renounce philosophy entirely in order to avoid relativism, because there is another way of doing it.

Ontological philosophy. Another way of doing philosophy is possible, because epistemology is not the only foundation from which necessary truths can be demonstrated. It is also possible to use ontology as a philosophical foundation. Philosophical arguments of all kinds start from our ordinary knowledge about the world, in which we recognize that we all have bodies alongside one another and other objects in space. But instead of establishing a foundation for philosophy by using reflection on how we know to justify some theory about the nature of reason, it is possible to establish a philosophical foundation by using perception to justify some theory about the natures of the basic substances and relationships that constitute everything in the world. This is to move in the opposite direction from epistemological philosophy: deeper into the natural world, rather than stepping back and reflecting on how we know about it. But the role of perception means that ontological philosophy must rely on the empirical method to determine which specific ontological theory to accept; it must infer to fewest and simplest basic substances and basic relationship that can explain every aspect of the world. Then, in the second step, what follows from that ontology are the necessary truths of ontological philosophy. What is implied by the ontology has a claim on our credence that is superior to ordinary knowledge, because it can be denied only by giving up the best ontological explanation of the most basic aspects of the natural world. Those implications are, therefore, ontologically necessary. They are not, however, certain, because their ontological foundation can be falsified by experience.  

It may be surprising that there is a new foundation for philosophy to use, especially one established by the empirical method, for that is the method of science. But we have seen what makes it possible. It comes from recognizing that ontology itself can be explanatory, for that makes ontology different from scientific realism. Ontological-cause explanations are different from efficient-cause explanations. Indeed, they are prior to efficient-cause explanations, because ontological explanations can explain why efficient-cause explanations are true, but not vise versa. Thus, it is possible to use the empirical method and infer to the best ontological explanation of what exists in the world before we infer to the best efficient-cause explanation of what happens there. That makes it possible to have a foundation for ontological philosophy that is different from scientific realism, or what scientists must believe about substances in order to accept the truth of their theories about efficient causes.


How an empirical philosophical foundation is possible. Even those who recognize that it is possible, in principle, to found a new way of doing philosophy on empirical ontology may find it surprising that any empirically justified foundation could support new truths about the world. If they depend ultimately on perception of the natural world, they must surely have already been discovered by empirical science.

But we have already seen how empirical ontology can provide a philosophical foundation that is different from empirical science. It comes from the difference between the best ontological explanation of the natural world and the ontological beliefs to which empirical scientists (and philosophers of science) are actually committed by the efficient-cause explanations they accept, that is, as scientific realists. In particular, physics does not recognize that space is a substance. Physics infers only to the best efficient-cause explanation of what is observed in nature, and since the relevant observations involve precise measurements, it tries to find the mathematically simplest laws of nature that can predict the entire range of relevant measurements. Those laws do not mention space or time except to describe the spatial and temporal relations among particular events that are observed, and so when scientific realists use physics to determine what exists in the world, they fail to recognize that space is a substance.

There are, as we have seen, two popular ontologies defended through realism about contemporary physics: materialism and substantivalism about spacetime (or what I called spatial relationism and spatiotemporalism). Neither recognizes that space is a substance. Materialism reduces space to spatial relationism, and while spatiotemporalism recognizes that spatial relations are constituted by something that exists independently of matter, it denies the reality of absolute space in favor of spacetime. Thus, it is not so surprising, after all, that an empirical naturalistic ontology can demonstrate necessary truths that are not currently recognized.

By the same token, however, this difference between ontological philosophy and contemporary physics can be seen as a reason for doubting that spatiomaterialism is true. That is what forced us to take out a mortgage on spatiomaterialism in order to use it as the ontological foundation of our philosophical argument. We had to promise to show how it is possible for spatiomaterialism to explain the truth of Einsteinian physics, acknowledging that we will forfeit our foundation if we fail to do so. Such an explanation is given below (Contemporary Physics under Change).

The possibility of spatiomaterialism despite Einsteinian physics will be shown by making further assumptions about the essential natures of space and matter and showing how substances of those more specific kinds would constitute a world in which Einstein’s special and general theories of relativity make true predictions of what happens. This is not to give up the assumption that space, like matter, endures through time, even though that implies that space and time are absolute. On the contrary, it is by retaining our basic assumptions about space and matter that we show that it is possible for spatiomaterialism to be true of a world in which Einstein’s theories have been confirmed. But this demonstration of the possibility of spatiomaterialism will leave us with a more detailed conception of the nature of space and matter.

In a similar way, the truth of the other basic theories of physics, including quantum mechanics and what I currently holds about the basic particles, will be explained ontologically. That will require the assumption of still more detailed essential natures for both space and matter.

In order to be clear about the nature of the second step of ontological philosophy, however, we should recognize that this ontological explanation of the truth of contemporary physics is not a demonstration of ontologically necessary truths. It is, rather, part of the project of empirical ontology itself, that is, the attempt to infer to the best ontological explanation of the world. And since it goes beyond the general kind of spatiomaterialism that was established as the foundation of ontological philosophy, it is the job of empirical ontology as a more basic branch of science than physics.

The kind of spatiomaterialism that has been established as the foundation for ontological philosophy is quite abstract and general in its requirements. Space and matter are assumed to have opposite kinds of essential natures as substances in the sense that bits of matter can exist independently of one another whereas parts of space have spatial relations to one another as part of their essential nature. Their opposite natures explain how these two kinds of basic substances can exist together as a single world. Each bit of matter coincides with some part of space or other at each moment as both matter and space endure through time. These are the assumptions from which the ontologically necessary truths follow.

But that is not all there is to the essential natures of mater and space, for bits of matter also exhibit various more specific regularities about how they move and interact. Such regularities are described by the basic laws of physics, and if those more specific aspects of the behavior of bits of matter in space are to be explained ontologically, it will be necessary to make more specific assumptions about the nature of matter. That is how we will show the compatibility of spatiomaterialism with Einstein’s relativity theories: there are certain further assumptions about the natures of space and matter that would account for all the observation on which Einstein’s theories are based empirically. Likewise for all the other theories of contemporary physics.

Empirical ontology infers to the best ontological explanation of what is found in the natural world, and since what is found in nature include the regularities described by the basic laws of physics, it includes discovering the natures of the two basic substances that explains them best. But that is the project of empirical ontology as the most basic branch of science, prior to physics, and it is not quite what is offered in the following sections. The argument about physics in the following sections is only an initial contribution to that project. Since what is relevant for ontological philosophy is showing the possibility of spatiomaterialism, it is not necessary to identify the best spatiomaterialist explanation of why the basic laws of physics are true. It is only necessary to show that there is some more specific spatiomaterialist ontology that can explain their truth. Thus, what is offered below is not necessarily the simplest or most complete explanation of physical laws. The formulation of that ontological theory is left to be completed as part of ontological science. The ontological explanation offered here is meant only to show how such an explanation is possible within the constraint of spatiomaterialism.


Nature of Ontologically Necessary Truth. What follows from the ontology established as a philosophical foundation is necessarily true. In order to be clear about what that means, let me say something more about the nature of truth and necessity.

The Nature of Truth. We assume that propositions are true when they correspond to what exists. That is to accept the correspondence theory of truth, and that should not be problematic, because it is what is ordinarily assumed about truth. It is part of the natural attitude from which philosophical arguments of all kinds begin. Both the ontological theory itself and the necessary truths that follow from it are true in the sense of corresponding to the world, if they are true at all.

Even though we used the empirical method to choose which ontological theory to believe, to believe the theory is to believe that it is true, and thus, since we accept the correspondence theory of truth, we take that to mean that spatiomaterialism corresponds to what exists. The world is actually constituted by space and matter as substances enduring through time. As a theory in ontology, however, it corresponds to the most basic aspects of the world, which include not only the essential natures of the basic substances and their basic relationship, but also the nature of substance as substance (both existential and essential aspects) -- and even the fact that the world is constituted by basic substances that exist together as a world in a basic way.

What follows logically from the ontological theory that best explains the world ontologically is also true in the sense of corresponding to what exists. But our reason for believing they are true is different, because they must be true, if the ontological theory form which they follow is true, and we have other reasons for believing that the ontological theory is true. Given the truth of the ontological theory, what follows from it must be true, and that logical entailment is one sense in which they are necessary truth. But it is not all that is meant by saying that they are ontologically necessary.

The Nature of Ontological Necessity. In order for propositions to be ontologically necessary, they must follow logically from the ontological theory established in the foundation. But ontological necessity is more than mere logical necessity. What makes them ontologically necessary is that the premises from which they follow logically is the ontological theory that offers the best ontological explanation of what is found in the world. That is, what follows from the ontology inherits its authority, and that gives those implications a special claim to credence when it comes to settling issues that arise from our ordinary ways of knowing. It is a more fundamental truth about the world and deserves special respect relative to what is known by ordinary means.

Though ontologically necessary truths cannot directly contradict what is observed (since that would falsify the ontological theory from which they follow), they can settle issues that arise in ordinary ways of knowing. For example, when there is a dispute about what caused some particular event in the world and one of the alternative explanations is contrary to what is necessarily true, there is good reason to dismiss it in favor of the other alternatives. To insist that that alternative is possible would be to give up the best ontological explanation of the world.

The difference between ontological and mere logical necessity can, perhaps, be elucidated by suggesting that ontological philosophy is an explanation of why its implications are true. The premise from which ontologically necessary truths follow is an ontological theory, which describes the most basic aspects of the world, and thus, formal derivations from it involve the construction of further aspects of the world, showing either that they are possible or impossible. That is the content or meaning of the derivation, and since these aspects are fundamental, they can be seen as permitting some beliefs about the world because they could correspond to what exists in the world or as prohibiting them because they would not.

For example, since each bit of matter is assumed to coincide with some part of space or another, spatiomaterialism implies that bits of matter have spatial relations to one another that all fit together as a three-dimensional geometrical whole. Thus, observations of spatial relations that seem to contradict geometry should be doubted, because they cannot correspond to anything in a spatiomaterial world. And since space and time are both continuous, change is possible, for bits of matter can move from one part of space to another without changing their natures or basic relationship. Thus, we should expect reports of objects moving, because there can be aspects of a spatiomaterial world to which they correspond. But that explanation of the possibility of motion also implies that it is not possible for bits of matter to change their location in space without moving across space between their origin and destination. Thus, one should doubt reports of objects flitting about in space discontinuously because there is no aspect to which they can correspond in a spatiomaterial world.

We can understand formal derivations from spatiomaterialism as the construction of aspects of the world from ontological causes because we have, in addition to the use of language, a faculty of spatial imagination. Both these cognitive powers will be explained later as essential traits of rational beings (when we see why rational beings are necessary beings in a spatiomaterial world like ours). We do not, of course, need to understand how we are able to understand this argument in order to understand it. But it may help clarify how this argument for necessary truths is intended, if I make clear that I am assuming that we are able to think about the spatial aspects of the world in a non-linguistic way. This is what is involved in understanding ontological explanations as something more than the formal relationship that holds between the ontological theory itself and the propositions it implies.

The correspondence that makes the ontological theory and its implications true is, therefore, one that involves spatial imagination as well as the formal linguistic structure of the propositions: the images in spatial imagination must correspond to aspects of the world in order for the sentences whose meanings they are to correspond to them. That warning may help avoid confusion about the way in which the correspondence of sentences to the world will be explained, when we finally get around to explaining the nature of reason ontologically.

Ontologically necessary truths can be interpreted, therefore, as truths that hold in every possible world. In this case, the ontologically necessary truths are truths that hold in any possible spatiomaterial world. Spatial imagination enables us to survey the range of possible spatiomaterial worlds. That range is still rather broad, since spatiomaterialism is still a rather general and abstract about the nature of the world. Accordingly, the necessary truths that follow from it without further assumptions are not very exacting. They include the fact that bits of matter all have geometrically coherent spatial relations, that their spatial relations can change, that they can change only by motion, and a similar set of principles about interactions. But otherwise they are not very specific about how and why spatial relations change.

Conditional ontologically necessary truths. There is, however, an important distinction among ontologically necessary truth which arises from the ontological explanation of the truth of the laws of physics. Such an explanation of Einstein’s two theories of relativity is required in order to show that spatiomaterialism is possible and thereby repay one of the mortgages we took out in order to use spatiomaterialism as a foundation for doing philosophy. But the assumption that space and matter have essential natures of a kind that makes the basic laws of physics true will play an additional role in this philosophical argument. Together with the recognition that space is a substance, these more specific assumptions about the natures of matter and space give us such a complete representation of the essential nature of the world that we will be able to derive many additional profound and far reaching conclusions about the world. As we shall see, the assumption that space is a substance combines with the laws of physics to show that various regularities hold of whole, relatively isolated regions of space, and it is only because those “global regularities” include evolutionary change that spatiomaterialism is able to explain the phenomena that have raised doubts about materialism and seemed to lie beyond the limits of science. The nature of evolutionary change entails that certain kinds of organisms have essential natures, including rational beings like us, and if rational beings were not necessary beings, it would not be possible to explain consciousness, goodness, and how there can be something worthy of worship, or holiness, in a strictly natural world.

In other words, we shall need to assume that the laws of physics are true in order to pay off the other three mortgages that we have taken out in order to use spatiomaterialism as the foundation for our philosophical argument. Though the basic nature of consciousness depends only on the most basic ontological assumptions, both substantivalism about space and the truth of the laws of physics are required in order to show the ontological necessity of the rational beings who are conscious. And it is that evolutionary explanation of such rational beings that entails that there is a real difference between good and bad for them and that there is something in the world that is worthy of their worship.

These implications are also ontologically necessary, because they cannot be denied without giving up the best ontological explanation of the natural world. But since the ontology from which they follow is spatiomaterialism of a kind that can explain the truth of physics, they will be said to be “conditionally ontologically necessary truths.” The condition on which their ontologically necessary truth depends is that the basic laws of physics are true. If those laws should turn out to be mistaken, then the necessary truths demonstrated from our ontology may not be true either. In other words, most of the propositions derived in the second step of ontological philosophy are ontologically necessary only in spatiomaterial worlds like ours, where the laws of physics are true. Or in terms of possible worlds, most of the necessary truths demonstrated by ontological philosophy hold, not of every possible spatiomaterial world, but only of every possible spatiomaterial world like ours.


To whole diagram Survey of necessary truths. The necessary truths that hold in a spatiomaterial world like ours are represented in the Whole Diagram as following from the foundation. Some of the necessary truths are new in the sense that they were not previously recognized as true at all, and others are new merely in the sense that they have not previously been demonstrated to be necessary (though some have long been assumed to be certain or necessary in some sense).

There are two kinds of necessary truths, truths about What Is, and truths about What Ought To Be, or succinctly, about the true and the good. Moreover, these implications for science and ethics fall out in a certain order. What is good depends on what is true (as indicated by the horizontal arrow in the diagram of the whole argument between "What Is" and "What Ought To Be"). Likewise, within the true, what is necessary about science depends on what is necessary about relations, just as what is necessary about relations depends on what is necessary about properties. And within the good, what is morally good depends on what is naturally good, and what is absolutely good depends on what is morally good. (These dependencies are also represented by horizontal arrows.)

Since the ontologically necessary truths about what is entail both the nature and existence of rational beings like us in a spatiomaterial world like ours, and since it turns out that rational beings inevitably come to understand their world ontologically, there is a green oval toward the bottom of the Whole Diagram which represents reason's coming to know what can be known by reason in a spatiomaterial world like ours.

To What Is