Ontology is the branch of metaphysics which deals specifically with the nature of material existence.
Material existence is all that exists independently of anyone's knowledge or awareness. "Independent of" does not mean separate from, but, "whether or not anyone knows or is aware of that existence." Material existence includes what is usually referred to as, "physical existence," which is all that we can directly perceive and is the subject of the physical sciences. It also includes life, consciousness, and the human mind, which also exist independently of anyone's knowledge or awareness, but are not physical. (Of course no consciousness or mind exists independently of the one whose consciousness and mind they are.)
Ontology provides the basic concepts by which the essential nature of material existence can be understood. Since all we can know is what exists, it is our understanding of material existence which is the foundation of epistemology, especially the physical sciences.
Material Existents - Three Corollaries of the Axiom of Identity
Metaphysically, existence consists of everything that exists, without regard to its mode of existence. Ontologically, existence consists of all material existents or entities. All other things that are sometimes thought of as material existents, qualities, events, and relationships, only exist as aspects of entities with no existence independent of those entities. Qualities exist only as qualities of entities; events exist only as the behavior of entities, and relationships exist only between entities; there are no qualities, events, or relationships independent of the entities they are the qualities of, behavior of, or relationships between. In the physical realm, qualities, events, and relationships are physical existents (because they exist), but not entities, because they have no independent existence.
Those qualities of an existent that are the existent and by which it is identified epistemologically are called intrinsic qualities. An existent's behavior and relationships are called extrinsic qualities because an existent would have the same intrinsic qualities independently of its behavior or relationships with other existents. Ontologically, no existent can exist independently of its actual behavior and relationships.
[NOTE: Some philosophers use the terms "characteristics," "attributes," or "properties," instead of qualities. The word, "qualities," is used here because it is the traditional term in philosophy that subsumes "characteristics," "attributes," "properties," "aspects," and "states."]
The axiom of identity, originally stated by Aristotle, is, A is A, or "a thing (or existent) is what it is." But what exactly is a thing's identity?
It is one of the most important questions of philosophy. "A is A," is fine, but what exactly is A? A thing certainly is what it is, but what is a thing anyway? There are three corollaries to the axiomatic concept of identity which answer this question. Those corollaries are, the necessity of qualities, the necessity of difference, and the necessity of relationship. By necessity is meant that all three corollaries are true of all existents and there can be no existent of which all three are not true.
[NOTE: By, "axiomatic concept," is meant a concept that is valid because to deny it would be a self-contradiction. It is not an assumption.]
Corollary 1: The Necessity of Qualities Anything that exists must have some qualities and those qualities are its identity, that is, what it is.
It is true of all existents, epistemological, as well as material (ontological), that a thing is whatever all of its qualities are. Note, however, the qualities do not make a thing what it is, the qualities are what they are because a thing is what it is. Identifying a thing's qualities (an epistemological function) is not identifying why a thing is what it is, only what it is.
[NOTE: This article pertains only to the ontological material existents with material qualities. Existents with material qualities are called entities. The epistemological identification of existents, including entities, will be described under epistemology.]
An entity is whatever all its qualities are, and those qualities do not exist independently of the entity of which they are the qualities. Conversely, since an entity's qualities are what the entity is, the entity cannot exist independently of its qualities. An existent sans qualities is a contradiction.
For example, the redness, elasticity, and roundness of a red rubber ball are qualities of the red rubber ball, but they are not things impressed on or added to something else that somehow transforms it into a red rubber ball. The qualities are simply the qualities of a red rubber ball, and have no independent meaning or existence apart from it. If there were never anything elastic, or red, or round, none of those qualities would exist or have any meaning.
An entity's identity, ontologically, is all of it's qualities. This must not be confused with an existent's epistemological identity, which is dependent on what is known about it. The entity identified, both ontologically and epistemologically is the same entity. An entity is what it is regardless of how much is known or not known about it.
Corollary 2: The Necessity of Difference Anything that exists must be different in some way from everything else that exists. No two things can be identical.
It is obvious if there are two things, something must make them different, else they would not be two things. Since it is an entity's qualities that determine what an entity is, if entities are different (which they must be) they must have at least one quality which is different.
Therefore, since, "anything that exists must have some qualities (corollary 1.) and "anything that exists must be different in some way from everything else that exists" (corollary 2.) and it is a thing's qualities that determine what it is; this corollary may be restated as:
Every existent has some quality or combination of qualities which is different from some quality or combination of qualities of all other existents.
While there is probably nothing we can directly perceive that is identical in every way to any other entity, there is no logical reason why there could not be two things that are identical in terms of there qualities, nevertheless they can be different if their extrinsic qualities (behavior or relationships) are different.
For example, though we cannot directly perceive individual molecules of water, we know if they have the same energy levels they are assumed to be identical. If they are identical, the second corollary says they cannot exist, so they must be different in some way, and that difference cannot be any of the intrinsic qualities. The quality that differentiates things that are otherwise identical must be an extrinsic quality. In the case of water molecules, the quality that differentiates them is the relative quality, position. Two water molecules may be identical in every way, but if they are really two, they cannot be in the same place (position) at the same time.
Corollary 3: The Necessity of Relationship Anything that exists must have some relationship to everything else that exists. Nothing can exist that does not have some relationship to everything else that exists.
This corollary is actually the converse of the previous. It really says that everything that exists must share some quality or qualities with other things that exist. Nothing can be totally unique or isolated.
This is the least obvious of the three corollaries and is easiest to grasp from the relationship aspect. If there could be something that shared no qualities whatever with anything else that exists, it could not possibly have any relationship to anything else that exists. It could not have any spatial relationships, because it would then have spatial qualities; it could have no physical relationship, because it would then have physical qualities; and it could not have perceptual relationships (ones that can be perceived), because it would then have perceptual qualities. If a thing has any relationship with any other existent, whatever the relationship is, there is some common quality or characteristic which that relationship shares or is a variation of.
This corollary contradicts all of those mystical and pseudo-scientific notions of other worlds and other existences, for example. There is only existence and whatever exists is part of that existence and has some relationship to everything else that exists.
[NOTE: The statement that, "a thing is whatever all of its qualities are," must not be confused with various spurious hypotheses such as "bundle theory," or, "tropes," or any other view that treats qualities (characteristics, attributes, properties, aspects, or states) as independent existents that can be added to or applied to something to make it what it is. An entity and its qualities cannot be separated because an entity's qualities are what it is.]