The philosophical development of Metaphysics has as its basis two ideas; that of foundational triplication and of type isomorphism.

The idea of foundational triplication is to model all that is real, and particularly the foundation of each and every domain, in terms of at least three essential concepts, which although inseparable, are always mutually distinct.

The idea of type isomorphism is to consider that the essential concepts of each domain are those which have similar patterns of correspondence (1).


Isomorphism: literally "one shape"; a term used to describe two concepts as having a deep sameness because they both belong to the same abstract class or type.

Metaphysics realizes greater generality in referring to the 'types' of basic domain concepts and predicates rather than to the concepts themselves. As such, metaphysical thinking often considers the class (or type) of each of the fundamental predicates as they appear in each domain, rather than to be referring only to the specific instances of those predicates in themselves. The fundamental concepts in each domain are seen as instances of a more general set of concept classes (types), which themselves are related to one another in specific patterns.

The term class refers to a general category to which many eventities (concepts, beings, relations) may belong. This usage of the term 'class' is borrowed from the language of computer science, and has much of the same meaning as found within the software development process for certain languages.

The term instance refers to a specific proper member of a category or class.

The term class has the connotation of context (a general whole).
The term instance has the connotation of content (a specific part).

The modalities define a terminology for the role that each of the archetypal terms play in each specific domain, rather than to the specific instances of those archetypal terms in some particular domain (2).

The fundamental consideration of any domain can be (must be) resolved into exactly three concepts, each of which are primal and necessary to the very essence of that domain. This is known to be possible for all domains.

These three concepts (the modalities), which form the most basic foundation and logic of that domain, have a definite and describable pattern of roles that each plays with respect to the other two, and in the domain as a whole.

The basic pattern of roles is common to the foundations of all domains. The same pattern of roles between these three fundamental, necessary, and intrinsic concepts will be found as the essence of all domains.

The term 'modality' is generally used to refer to a specific type of role, as selected from a finite set of available types. Three such types, (or roles), and the relations between them, are both necessary and sufficient to provide a complete description of this metaphysics.

In that the general pattern of relative roles is common to the foundations of all domains, each of the three roles is given a specific name, a modality, which is then used to refer to the class of all concepts that have that type of role.

The three modalities are the three terms used to refer to each of the three primal roles that form the essential basis necessary to the consideration of each domain. To consider the modality of a concept is to consider the essential role that concept plays with respect to other primal concepts.

The names given to the three roles (modalities) that domain primal concepts have with respect to one another are "the immanent", "the omniscient", and "the transcendent".

Within the lexicon of this metaphysics, the term "the immanent modality" refers to the entire class of all immanent modal concepts, (as instantiated within their respective domains). The omniscient and transcendent modalities are similarly defined, as references to classes of concepts.

The absolute description of the relative nature that each of the three modalities plays with respect to the other two, (i.e., the pattern common to all domains), is defined by the three Axioms. Insofar as the Axioms define the pattern of the three roles, then it is ultimately the Axioms which define the exact meanings of the three modalities (and also, eventually, of all of the metaphysics itself).

Since the Axioms are formulated in terms of the modalities (since no more primal concepts exist with which to formulate them), the exact definitions of the modalities themselves are necessarily abstract, and thus are not specific to any particular domain, including that of the IDM metaphysics itself. (The modalities are abstract; the Axioms are concrete).

Therefore, no exact and final (closed/complete) definitions can be given for the modalities, aside from those which are implicit and inherent within the Axioms (and all of their pure theorems), in whatever language they are expressed. For this reason, the pattern of the meaning of each of the three modalities must often be expressed in a metaphorical character, in the language of whatever domains one happens to be interested in considering. In this manner, eventually, with a large number of role correspondences to known systems, the essential nature of the pattern of meaning of each of the three modalities becomes clear.

Also, it is to be understood that the concept of a metaphor and the concept of an established system of correspondences is essentially equivalent in use (isomorphic) in this context. In effect, the modalities constitute the basis of a system of correspondences, the totality of which, for some large set of domains, will give particular meaningfulness to each.

Where the foundations of any domain can be subsumed by three necessary and sufficient concepts, known as the modalities, so too does the relationships between these three have a consistent pattern and form. This form/pattern, common to the foundations of all domains/worlds, is described by the three Axioms.

Axiom I: The immanent is more fundamental than the omniscient and/or the transcendent. The omniscient and the transcendent are conjugate.

Axiom II: A class of the transcendent will precede an instance of the immanent. A class of the immanent will precede an instance of the omniscient. A class of the omniscient will precede an instance of the transcendent.

Axiom III: The (classes/instances) of the immanent, omniscient, and transcendent are distinct, inseparable, and non-interchangeable.


In that the Axioms are statements of the relations between the modalities, the Axioms themselves are also associated (have a one-to-one correspondence) with the modalities. In this manner, the Axioms are fully self-describing.

Axiom I has the nature of the omniscient modality.
Axiom II has the nature of the immanent modality.
Axiom III has the nature of the transcendent modality.


The Axioms are (and represent) the concept of pure form, without quality. The Modalities are (and ultimately represent) pure quality without form.

These concepts, taken together as different representations of the same fundamental pattern, are the basis of all considerations of this metaphysics. All of the descriptive power of this metaphysics ultimately descends from the Axioms.




Notes:
[1] While the identification of isomorphisms is not arbitrary, it may depend on the exact context in which the concepts are considered. Considering the same (literal) concept in a different (semantic) context may result in varying associations of aspect and modality.

As such, it is especially important to remain aware of the assumptions and perspective in which one considers a given concept.

[2] For this initial description (as a rough simplification), the term "domain" refers to any instance of a world (or universe) which may be (is) experienced by a self.

In this consideration, it is assumed, in connection with definition, there is no world that is completely independent of all selves and there is no self which is completely independent of all worlds.


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