The whole diagram represents the structure of the argument of ontological philosophy. It has a place for everything that reason can know, including not only what is necessarily true, but also what is contingently true. Necessary truths provide the structure in which the actual is contained as one of the range of possibilities. While necessary truths are known to be true by deriving them from the best ontological explanation of the world, contingent truths require further experience of what actually happens in the world.
The distinction between truths about "what is" and "what ought to be" mirrors the two main functions of reason. Reason is both theoretical and practical, because rational beings need to know not only what to believe, but also what to do. In both cases, beliefs are true because they correspond to what exists. Truths are ontologically necessary when they correspond to what exists in all possible spatiomaterial worlds, though most of the necessary truths (of both theoretical and practical reason) derived in the following sections are only conditionally ontologically necessary. They hold only in every possible spatiomaterial world like ours, for they also depend on space and matter having the specific kind of nature they have in our world (that is, where the laws of physics are true).
Necessary truths about what is follow from the spatiomaterialist explanation of how space and matter constitute properties, relations and change:
Explaining the nature of properties ontologically solves the so-called “hard problem” about the nature of consciousness, for it explains why there are phenomenal properties as well as physical properties. (If properties are aspects of substances, then bits of matter must have intrinsic properties as well as extrinsic properties.)
The spatiomaterialist explanation of the nature of relations shows how mathematics is true, why math is ontologically necessary, and what makes it seem to be certain. (Recognizing space as a substance makes it possible to explain all the ways in which set theory can be interpreted, showing how they are all true.)
Its explanation of the nature of change solves Hume’s problem of induction by explaining change as an aspect of substances enduring through time. Since space is recognized as one of the basic substances enduring through time, that enables spatiomaterialism to show that certain “global regularities” hold necessarily. Those regularities include the conservation of matter, the second law of thermodynamics, the principles of mechanics, and evolutionary change.
Space causes evolutionary change in two ways, implying that that the overall course of evolution is an inevitable series of stages at each of which there is gradual change in the direction of maximum power.
At each stage, space causes some kind of (biological) machine to gradually become as powerful as possible in controlling conditions affecting its reproduction both individually and collectively. This is because those machines are not only able to control relevant conditions, but also reproduce. They inevitably impose natural selection on themselves by their own population growth. Since space is what makes cycles of reproduction add up to scarcity over time, space is an ontological cause of natural selection, helping to make it inevitable in a spatiomaterial world like ours.
Space is also what enables one stage to lead to another, because, once biological machines approach maximum power for their kind, they can be organized as so many different parts of a more complex biological machine. Their reproduction as a whole then causes them to become maximally powerful in the same way, that is, by natural selection. Space causes new stages of evolution, because space is what makes such higher levels of part-whole complexity possible.
Because evolution is an ontologically necessary global regularity in a spatiomaterial world like ours, the organisms that evolve at each stage are natural kinds with essential natures. Rational beings are the organisms that evolve at one of those stages, implying that we are necessary beings in a spatiomaterial world like ours. And given how the series of evolutionary stages leading up to rational beings like us is explained, spatiomaterialism even entails a theory about how the brain works, solving problems of neurophysiology. Thus, ontological philosophy explains the nature of mind (including consciousness), imagination, language, reason and even spirit.
Necessary truths about what ought to be also follow from the spatiomaterialist ontological explanation of the nature of evolutionary change. In a spatiomaterial world like ours, matter and space constitute rational beings with an individual self interest, a moral interest (deriving from their spiritual self interest), and a religious (self) interest. Besides showing what is good for rational beings, ontological philosophy explains why the good is good for rational beings, so that it compels rational beings choose what is good because it is good. In the end, that means that rational beings will recognize that they ought to do what is good for the world as a whole. That is the religious interest that they will come to recognize themselves as having.