The first set of necessary truths has to do with the basic properties entailed by the natures of the basic substances. This provides a solution to the problem of consciousness by explaining the nature of phenomenal properties. It is the only new necessary truth established by ontological philosophy that does not depend on taking space to be a substance.
Properties are explained as aspects of substances by ontological philosophy, rather than as objects of knowledge, as epistemological philosophy does.
The two most basic properties of any substance are existence and essence. They define the nature of substance as substance (as an assumption of ontological philosophy about the nature of ontology).
Existence is the property a substance has by virtue of being self-subsistent. This aspect of substance as substance includes two aspects, particularity (having a distinct existence from every other substance), and temporality (enduring through time).
Essence is the property a substance has in virtue of existing in a determinate manner. In a world made up of more than one substance, this aspect includes two aspects, an intrinsic essential property and extrinsic essential properties.
The intrinsic essential aspect of a substance is what the substance is in itself, or the determinate way in which it exists apart from its relations to other substances. It must have such an intrinsic essential property in order to have a distinct existence.
The extrinsic essential aspect of a substance is what the substance is for other substances, or the determinate way that it exists in relation to other substances. It must have extrinsic essential properties in order to be related to other substances in a determinate way, if its relations to them are not part of its intrinsic nature (as in the case of space).
An inventory of the basic essential properties of the two kinds of basic substances can be generated by taking into account their opposite essential natures and the basic relationship by which they make up the world.
The total matter in the world is made up of many particular substances that can exist independently of one another. Each material substance must have both an intrinsic and an extrinsic aspect to its essential nature, because each bit of matter has an existence that is distinct from every other substance and is related to each of them in a determinate way .
Since each bit of matter has a determinate relationship to every other substance in the world, it must have an extrinsic nature relative to each of them. But there is a basic difference in its extrinsic nature relative to space and its extrinsic nature relative to other bits of matter.
Each material substance must have an intrinsic nature because it has an existence that is distinct from every other substance. Even if matter cannot exist without being contained by space, it must exist in itself in a determine way in order to have an existence that is distinct from space. And since particular material substances can exist independently of one another, each must have an intrinsic essential nature of its own. Kinds of intrinsic essential properties may vary with the varieties of material substances, if any.
Since all the bits of matter coincide with some part(s) of space or other, each must have an extrinsic essential property that characterizes what it is for space. That enables each bit of matter to be related to a certain part of space at any moment, but it may also include a way of moving across space as time passes.
Since each bit of matter coincides with some part of space or other, they are all related to one another by way of space. Hence, they may have other determinate ways of being related to other bits of matter. The extrinsic essential aspect of bits of matter includes all the ways bits of matter have of interacting with one another, or what are called their physical properties.
Since space is a substance that exist independently of matter, it must have an intrinsic as well as an extrinsic aspect to its essential nature relative to matter. But the intrinsic and extrinsic properties of space are different from matter, because the parts of space cannot exist without all being related to one another geometrically. That is how its essential nature is opposite to matter.
Space has an intrinsic essential nature because it is a distinct substance from matter. But since its intrinsic essential nature as a whole includes its parts being interdependent, the intrinsic nature of each part of space includes its relations to every other part of space (along with whatever it is in itself as something distinct from other parts). Thus, the parts of space do not have extrinsic essential natures relative to one another.
Space must have an extrinsic essential nature relative to matter in order to contain all the bits of matter. But its extrinsic essential property characterizes both the part of space and the whole. Though every bit of matter coincides with some part of space or other, a single bit of matter may coincide with many parts of space at once. And the way in which some bits of matter coincide with space may involve their moving across space as time passes.
The problem of mind arises from the naturalistic explanation of perception, because that leads to critical realism about perception. Critical realism reveals that there is a basic difference between two kind of properties, physical properties and their appearances to the subject in perception, or phenomenal properties.
There are basically two kinds of theories about the natures of the properties that are known by the subject, because there are two ways of doing philosophy, ontological and epistemological. Ontological philosophy can explain the difference between physical and phenomenal properties, because it takes substances to be ontological causes. Epistemological philosophy encounters insuperable problems, because it takes properties to be more basic than substances.
Epistemological philosophy attempts to prove necessary truths by taking some kind of knowledge as given and using it to justify another kind of knowledge, and realism affirms the existence of the objects that would be known, if it were successful. But whereas modern philosophy starts with phenomenal properties (as ideas) and tries to defend realism about the natural world, contemporary philosophy starts with the natural world and tries to defend realism about phenomenal properties of material objects (such as subjects).
The foundation of modern philosophy was a theory about how we know as individual subjects. Since the subject, for critical realists, is mind, the given includes all the ideas in the mind. The goal is to explain how we can know about the external, natural world. But realism about the external leads to mind-body dualism, and anti-realism avoids the problem by retreating to idealism.
Realism in modern philosophy leads to mind-body dualism, and the problem is how two such opposite kinds of substances can be related as parts of the same world. As Descartes argued, mind, because it thinks, has a unity that precludes division, whereas body and other objects in the external world can always be divided into parts. In other words, mind and body seem to be opposite kinds of substances, because mind has phenomenal properties, whereas body has physical properties.
The problem of mind in contemporary epistemological philosophy is basically the question of how a natural science of consciousness is possible. Contemporary philosophy is committed to naturalism, because it bases its theory of reason on reflection about our use of a public language. Science is such an intersubjective way of knowing, and realism about phenomenal properties leads to property dualism.
Realism about phenomenal properties leads to property dualism, the belief that objects in the world somehow have both physical and phenomenal properties. That is a problem for contemporary philosophy, because it is unclear how phenomenal properties can be known intersubjectively, in the way that physical properties are known by science. Each possible way of knowing about them poses problems for science or ontology.
Epistemological philosophy has no way to explain how phenomenal and physical properties are related because it takes properties to be objects of knowledge and that makes properties more basic than substances. Phenomenal and physical properties are simply different kinds of basic properties with no intelligible connection between them.