Philosophy attempts to show that certain truths are necessary relative to beliefs established by ordinary arguments, such as science and ethics. But instead of using as its foundation a theory about the nature of reason based on reflection about how we know (as traditional epistemological philosophy does), ontological philosophy uses as its foundation a theory about the basic substances constituting the world based on an inference to the best ontological explanation of the natural world.
The first assumption of ontological philosophy is naturalism, or the belief that the world is just the natural world. The natural world is the world disclosed to us by perception. It includes everything that exists in space and time.
The second assumption of ontological philosophy is about the nature of ontology. It assumes that ontology is a kind of explanation that is different from the efficient cause explanations given by empirical science. An ontology would explain the existence of everything in the world (and thus everything about the world, including the truth of efficient cause explanations) by showing how the world is constituted by basic substances of certain kinds and their basic relationships to one another as parts of the same world.
The third assumption of ontological philosophy is that the way to decide what is true about the world is by the empirical method. The empirical method is to infer to the best explanation of what can be perceived, and in this case, that means inferring to the best ontological explanation of the natural world.
The best ontological explanation of the natural world is spatiomaterialism, which holds that the world is constituted by two opposite kinds of basic substances, space and matter, and that each bit of matter coincides with some part of space. This ontology is entailed by the three assumptions of ontological philosophy, and it will serve as the foundation for showing that truths hold necessarily. But since four mortgages have been taken out in order to use this ontological foundation, this proof of necessary truths depends on spatiomaterialism being able to explain four problematic phenomena: the existence of consciousness, the truth of Einsteinian relativity, the nature of goodness, and how there is something worthy of worship in a natural world.
Since spatiomaterialism is the best ontological explanation of what is found in the natural world, we conclude that it is true and use it to show that certain facts are necessary relative to what is known by ordinary means, such as empirical science and morals. If these implications were not true, the world could not have the basic nature described by spatiomaterialism. However, to have a clear title to the use of spatiomaterialism as the foundation for ontological philosophy, four mortgages must be paid off by explaining four problematic phenomena (consciousness, Einsteinian relativity, goodness, and holiness).
One kind of necessary truth proved by ontological philosophy has to do with what reason ought to believe about the world, or the true, which is discovered by theoretical reason. Beliefs are true when they correspond with what exists, and truths are necessary when the beliefs correspond to what exists in every possible spatiomaterial world. Such beliefs about what is can be divided into three classes depending on whether they are about the properties of particular substances, their relations to one another, or how such properties and relations change over time.
A property is an aspect of a substance that is entailed by its existence as a particular, self-subsistent entity. Properties include aspects of substances that have to do with how they are able to relate to other substances (or extrinsic properties), as well as aspects that have to do with what they are in themselves (or intrinsic properties). Intrinsic properties explain the existence of consciousness, or the problem posed by phenomenal character of experience, and that pays off one mortgage on spatiomaterialism.
Since substances exist together in a determinate way as a world, there are relations among them. These aspects of the world include both the relations among parts of space and the relations that bits of matter have because each bit of matter coincides with some part of space or other. These basic relations explain why mathematical propositions are true, and since they hold in every possible spatiomaterial world, this shows that mathematics is necessary relative to empirical science.
Because substances endure through time, bits of matter in a spatiomaterial world can move and interact with one another. This ontological explanation of the possibility of change entails necessary truths about how change takes place, including both local and global regularities. But it can also explain why the basic laws of physics are true, including Einsteinian relativity, and so it pays off a second mortgage on spatiomaterialism. And assuming that space and matter have natures that make the basic laws of physics true, the necessary global regularities entailed by spatiomaterialism include evolutionary change (through a series of inevitable stages) in the direction of natural perfection, which pays off the two remaining mortgages.
The other kind of necessary truth proved by ontological philosophy has to do with what reason ought to do in the world, or the good, which is discovered by practical reason. Such beliefs are true because they correspond to an aspect of what exists, and they are necessary, because that aspect holds in every possible spatiomaterial world. Beliefs about what ought to be can be divided into three classes depending on whether they are about self interest (the interest of the individual), ethics (the interest of certain groups of individuals, called "spiritual animals"), or religion (the interest of the world as a whole).
There is a real difference between good and bad, because evolution (as an ontologically caused global regularity) is change in the direction of natural perfection. That pays off a third mortgage on spatiomaterialism, because goodness is explained as contributing to natural perfection. The good is what ought to exist as far as reason is concerned, because reason pursues the good. What ought to exist for each rational being as an individual is one's self interest, or what contributes to one's own natural perfection as an individual. But self interest includes both necessary and optional goals.
What ought to exist for rational beings concerning the relationships among individuals is what contributes to the natural perfection of certain groups of individuals that evolve, or what are called "spiritual animals." Moral rules limit the pursuit of individual goals for the good of their spiritual animal, and rules of justice limit the pursuit of spiritual goals for the good of its individual members.
What is good for reason includes religious goals, because a perfect being can come to exist as the outcome of evolution, if rational beings pursue goals that contribute to the natural perfection of the world as a whole, as well as individual and spiritual goals. Since that being has all the perfections traditionally attributed to a transcendent God, there is something in a spatiomaterial world that is worthy of worship, namely, an immanent God. That pays off the final mortgage on spatiomaterialism as the foundation of ontological philosophy.
Rational beings like us inevitably evolve at a later stage of evolution, if evolution is a (reproductive) global regularity that is caused ontologically. Since rational beings eventually come to understand ontological philosophy, it is inevitable that there are beings in the world who know everything that reason can know about the basic nature of the world, including what follows about what is and what ought to be (or the knowledge represented by this diagram).