Spatiomaterialism is the belief that the world is constituted by space and matter existing as substances enduring through time and that all the bits of matter are contained by space, that is, that each bit of matter coincides with some part of space or other. Rational beings who accept the three assumptions of ontological philosophy (naturalism, ontological explanation, and the empirical method) must accept spatiomaterialism, for it is the best ontological explanation of the basic facts about natural world. It could fail to be true only if there is some special kind of phenomenon that is incompatible with it.
Time is the first of three disputed issues about the nature of existence in the natural world. The phenomena to be explained have to do with how everything in the world is in time (that is, the temporal aspect of the existential aspect of substance as substance).Naturalists who accept the empirical method must believe the best ontological explanations of it, which is the endurance theory.
There are two views about the basic nature of time and how it is related to existence. We have already assumed that what exists comes down to substances of some kind, which are in time, but are permanent in the sense of existing at every moment in the history of the world. One theory holds that existence itself is in time, implying that only the present exists. The other holds that time is in existence, implying that each moment is a different part of each substance.
The endurance theory assumes that existence itself is in time in the sense that only the present exists. Thus, it holds that substances exist only at the present moment. The past and the future do not exist. Substances nevertheless exist at every moment in the history of the world as it is present, because they never come into nor go out of existence as time passes. That is, substances are permanent) in the sense of enduring through time. They are identical as time passes.
The perdurance theory assumes that time is within what exists in the sense of being just a relationship that holds among moments in the history of the world. That is, it holds that all the moments in the history of every substance exist in exactly the same way. Thus, substances are wholes made up of moments as parts. But since each substance exists at every moment in the history of the world, it holds that substances never come into existence nor ever go out of existence (that is, are permanent in the sense that every substance has a part for each moment in time).
Endurance is a better ontological explanation of the world than perdurance because it explains more with less. It explains more because it explains why the present is different from the past and the future, which is something that we know not only by reflection on our experience, but also by the perception of change in nature. Perdurance theory does not. And endurance theory requires fewer ontological causes, for one substance can explain what purdurance theory needs an infinite set of momentary entities and relations among them to explain.
The natural world includes everything in space and time, and the simplest theory is that there is nothing in space and time but matter, that is, substances of kinds that are described by the basic laws of physics (other than space). In other words, materialism assumes that physics is causally complete and can, in principle, explain every kind of event in the world.
Matter is the third disputed issue about the nature of existence in the natural world. The phenomenon to be explained in this case is the apparent existence of substances other than space itself in space and time. Since the simplest explanation of it is obviously materialism, the the question is whether materialism can account for everything about the natural world, including various problematic phenomena.
Materialism is not the best ontological explanation of the world, if there are phenomena that it cannot explain. Each of the problems for naturalism mentioned at the beginning (consciousness, goodness, and holiness) can be used to argue that, in addition to material substances, there are immaterial substances in space and time. Thus, to defend materialism (or spatiomaterialism), it is necessary to show that they can be explained without postulating anything but matter (and space).
Though naturalists cannot believe in a transcendent, or supernatural, God, they can believe that there is something in space and time that is worthy of worship, such as spiritual substances. In order to fully refute the belief in immaterial spirit, materialists must show how matter in space and time can constitute something worthy of worship.
Though naturalists cannot believe that the difference between good and bad comes from a creator God (or Plato's The Good Itself), they might hold that it comes from final causes or other teleological causes working on matter in space. To counter this evidence for teleological substances, materialists must show how nothing but matter in space can constitute a real difference between good and bad. (This requires more than contemporary Darwinism, since its accidentalism precludes any such explanation.)
Though naturalists deny that mind is a substance outside space, they can believe that mind is a substance in space that reveals itself to be different from matter only at a certain level of complex organization. This is immaterialism either because it denies the causal completeness of physics or because it holds that matter has properties that physics does not recognize (or both). To avoid having to admit that there are mental substances, materialists must show that matter organized as a brain can do everything mind is supposed to do and that the properties of matter can explain why experience has an appearance to the subject.
Space is the second disputed issue about the nature of what exists in the natural world. In this case, the phenomenon to be explained is the fact that everything in the world is in space. The empirical method requires naturalists to believe the best ontological explanation of it, and that is spatiomaterialism, if it is possible.
Spatiomaterialism holds that space is a substance, like matter, existing in time. But space has an opposite essential nature from matter, because instead of being independent like bits of matter, each part of space has, as part of its essential nature, geometrical relations in three independent dimensions to every other part of space. Thus, space can only exist as a whole. That is what enables space to give all the bits of matter spatial relations to one another when they coincide with parts of space.
Spatial relationism is basically the denial that space is a substance. It reduces space to spatial relations. Spatial relationism is implicitly the materialist theory of space. Materialism is able to account for everything being in space by assuming that having spatial relations is the basic relationship by which bits of matter exist together as a world.
Spatiotemporalism agrees with spatiomaterialism that matter acquires spatial relations from another substance with an opposite nature, but it takes this substance to be spacetime, not space. Spatiotemporalism seems to be required by the Einsteinian denial of absolute space and time. However, by taking space and time to be aspects of the same substance, it is committed to the perdurance theory of time.
The empirical method requires naturalists to accept the best ontological explanation of nature, and that is clearly spatiomaterialism, if it is possible, because spatiomaterialism is better than spatial relationism and better than spatiotemporalism. In both cases is explains more with less.
Though spatiomaterialism postulates two substances, rather than one, it is as least as simple as spatial relationism, because the relationship by which it assumes that substances exist together as a world has a temporally simple nature, instead of a temporally complex nature. And it explains more, for not only does it explain spatial relations ontologically, rather than just assuming them, but it also explains the possibility of change ontologically, rather than just assuming it.
Spatiomaterialism is a better ontological explanation than spatiotemporalism, because it can accept the endurance theory of time, which we must prefer, whereas spatiotemporalism entails the perdurance theory. Though spatiomaterialism takes space and time to be absolute, it is not precluded by Einsteinian physics, for relativistic phenomena can all be explained on the assumption that space is a substance and spatial relations are absolute (though showing that is just a promise at this point).