Why should anyone be concerned with Metaphysics?

Metaphysics is at once the most abstract and theoretical form of study imaginable, and yet also the most concrete and practical form of knowledge possible.

In considering only essence, metaphysics has very general applicability.

In being about essence, it is at the center of everything, at the core of the very nature of being itself.

The knowledge and truths developed from metaphysics are more certain, firm, unchangeable, and substantial than literal physical 'concrete'.

The descriptions and correspondences of metaphysics are absolute, even while they are also relative.

What are the limits of metaphysical thinking?

Metaphysics is abstract in that it considers expression and choice independently of who is choosing or what is chosen.

A knowledge of metaphysics cannot be used to describe any particular perception, expression, or experience, for the study is not about specific people, places, or things.

The descriptions of metaphysics do not cover anyone's personal viewpoint, or the individual basis of anyone's choices. However, the concepts, descriptions, and principles of metaphysics are applicable to any and all instances of choice; they apply to all choices, made by everyone, everywhere.

Metaphysics is specific in that anything that is inherent in the essential nature of choice itself is applicable to every choice that one makes. In that choices are involved in all aspects of life, a true knowledge of metaphysics is inherently and eminently practical, potentially influencing and enhancing the process of life itself.

What is Metaphysics the study of?

Metaphysics is a search for fundamental symmetries (invariants) and continuities (intrinsics) in the relation between self and reality.

The 'invariants and intrinsics of experience' would be those notions and descriptions which remain applicable even when changing either the content or the context (or both) of experience (1).

For example, as soon as someone makes an assertion "I experienced X", some aspects of metaphysical principle and insight are immediately applicable regardless of how rarefied, special, spiritual, or mystical that experience may be.

Anything which inherently intrinsic to the nature of any experience is validly applicable to all experiences.

For descriptions of essence to be applied, it only matters that a notion of "experience" has been used at all. It does not matter who (as a subject), or what (as an object), the assertion regarding experience happens to refer to.

For example, part of the aim of metaphysics is to consider experience, regardless of:
1) who is having that experience (i.e., as the subjective context of experience),
2) what they are experiencing (i.e., as the subjective content of experience),
3) why they are having that experience, and not some other,
4) when they have it,
5) where they have it, or even
6) how (i.e., the process, method, or sensory channel, by which) they have that experience.

Where considering perception, it does not matter how rare or dis-similar the content of a person's perception is relative to the norm, the nature of the inherent aspects of the process (and concept) of all of perception will be the same.

So it is all/only about experience?

No. It is about the relationship between self and reality, which includes expression as well. Moreover, there is the distinction between practice (being) and theory (modeling).

An interest in metaphysics is an interest in the nature of experience as an example -- an implementation -- of a more basic idea of a relation between self and reality. Questions like "What is experience?", and "How is the process/concept of experience related to other processes/concepts?", are central to the study, but they do not limit the study to just that.

To develop the concepts of metaphysics, a meta-physicist must do more than simply "have experience", she/he must also intellectually think about and reflect on the nature of experience in itself. Rather than being a reflection on what is (or has been) experienced, a meta-physicist would reflect on the 'fact' that there are these events called 'experiences' at all.

So you are suggesting that meditating is all that is needed to develop metaphysical knowledge?

To study metaphysics is to seek the intrinsic, essential, and invariant aspects of experience (perception, measurement, observation, causality, etc). More than just developing insight, the real test is to see if there is also developed clarity. Significant increases in the degree of clarity -- the 'reifying power' of a given concept -- is the 'measure' by which 'success' in metaphysical thinking is tested. In that way, the practice of metaphysics is somewhat more like what is known as the scientific method than it is 'just a meditation'.

However, the reflection of a meta-physicist is more than just the practice of the scientific method. It is a discipline of examining assumptions, of looking at the concepts and their relationships, in being, in themselves, as directly as possible.

Why not consider metaphysics to be the beginning of science?

As aspects of knowing and experience, the meta-physicist must also consider the nature of measurement, observation, and objectivity, in themselves, as concepts, in their own space, prior to assuming the usage of these notions in a given practice of thinking and reflection. Metaphysics involves a consideration of the very basis on which knowing itself rests, including that particular method of knowing which is called 'the scientific method'.

For example, one cannot use the scientific method to 'prove' and 'validate' the correctness of the use of the scientific method itself. Metaphysics extends beyond, and yet provides a semantic foundation for, a more conventional physics.

To study metaphysics is to consider and describe the essential nature of perception, expression, knowing and knowledge, etc., as they are in themselves. It is an attempt to develop comprehensive and essential descriptions of these notions.

Therefore, metaphysics cannot be considered a science in itself. At best, it provides the essence and substantive basis for science, without also becoming only just that.

So metaphysical knowledge is not scientific? What about phenomenology?

Metaphysics and science have different starting points and different aims. Science/physics is about identifying regular patterns of causality in the world.

Metaphysics begins as an inquiry into the nature of the relationship between self and reality (world). It is this relationship which is the essence of the study; it not just about what is in the world. However, insofar as this relationship is not a 'thing' this conception of metaphysics is in keeping with historical tradition of associating 'metaphysics' as "the study of that which is 'beyond' the physical". However, in this context, the word "below", as in 'below the physical' would be more meaningful.

A successful metaphysics (as contrasted with a successful physics) will be one which provides a clear description of the essential nature of this relationship.

Metaphysics emphasizes description (what relationship is), rather than explanation (why relationship is), as would be the the more central theme of science.

How is that relevant?

This form of knowledge -- "what is?" -- is actually quite relevant to modern physics. When considering 'things' at the scale of the deep subatomic, the notion of 'particles' can be more easily understood as being akin to the concept of 'an interaction'. As such, the nature of the concepts themselves -- as classes of characterizations, etc -- becomes quite important.

Furthermore, in considering the furthest developments of our known physics (QM and GR), we often find we need increasingly clear ideas of basic concepts and notions like those of 'time', 'space', 'force', 'probability', etc. Even the theories of physics themselves are more ultimately conceived as 'processes of signal flow' (aka 'measurements') involving abstractions like 'information' and 'entropy'. Therefore, having an absolutely clear description of what is meant by 'measurement' is therefore not only important, it is ultimately central to the very being and essence of modern science -- absolutely the most relevant set of concepts possible.

As a generalization, the concepts of self and world (reality) can be considered as 'the subjective' and 'the objective'. Metaphysics is, therefore, a study of the relationship between subjectivity and objectivity.

It is a consideration of the being of the relationship between the subjective and objective in terms of intrinsic aspects: those characteristic descriptions (and patterns of description) which are both necessary and sufficient (complete) for that relationship to be semantically meaningful in all contexts. Metaphysics does not attempt to account for how or why these intrinsic patterns of description have the form and qualities that they do.

How can we know anything about something so basic?

To consider the nature of what the essence of a relationship is, it is necessary to consider it in terms of what it does. This is, in effect, a methodology by which 'being' is considered in the terms of 'doing' (and 'becoming'). The study of metaphysics is, therefore, directly involved with both ontology and epistemology.

Whats that again?

Ontology is the study of beingness. It considers the nature of what something is in itself. Questions like "what is real?" are at the center of this topic.

Epistemology is the study of knowing and the nature of knowledge. The essential questions of epistemology are "how does one know?" and "what is knowing, known, and knowledge?", etc.

Insofar as epistemology is about methodology and process (a doing; the process of knowledge), then metaphysics is effectively the application of epistemology (a technique of knowing) to ontology (being in itself).

Thus, metaphysics studies (a doing) the being of relationship (ie, the relationship between self and world).

More generally, metaphysics extends to consider the relationship between being and doing itself. As such, metaphysics (as a being) considers (as a doing) the being and doing of relationship (a relationship which is itself between 'things' which are also in themselves a being and a doing).

Therefore, for a metaphysics to truly be effective, the scope of its description must include a description of the nature of the process of its own description (metaphysics is a relationship as well as being about relationship). Metaphysics must be able do coherently describe itself; it must be as semantically complete when it is its own subject as well as when it is its own object.

Why is that important?

Unlike physics, which can assume a minimal set of 'given' concepts, principles, laws, etc, without explanation, so as to provide a basis for all other explanations, metaphysics, which is providing that conceptual grounding, will nave no deeper basis upon which to depend, outside of itself. Insofar as metaphysics is about identifying, clarifying, and characterizing the foundations of all domains, there is no single domain that can be assumed as 'exempt' from that inquiry. Therefore, for a metaphysics to be coherently defined at all, it must have the capability to 'bootstrap' itself into existence. For it to be 'complete', it must be able to be fully self describing. This 'completed recursive aspect', therefore, constitutes a final measure of success for any metaphysics.

As such, in addition to the 'relative' comparative test of quality, ie, insofar as a metaphysics provides/brings clarity to a topic, there is also an 'absolute' criterion: the degree to which a metaphysics is fully self describing is also used as a 'characterization' and a 'measure' of the quality of the result.

In this way, there are true objective criteria -- real tests -- for assessing the quality of metaphysical thinking as much as there are similar measures of quality (testing) associated with high impact scientific thinking.

How does this 'recursion' connect to the notion of the 'real'?

By binding the notion of the concept of the objective to a/the/any/all actual being of objective reality(ies). This occurs in terms of their process of relation, as a side effect of an identity of interaction established in even deeper way.

At a certain level of consideration, the distinction between the identity of a concept, and the thing that it refers to, vanishes: the ultimately abstract wraps around back into the ultimately concrete.

In effect, the 'recursion' is only good if it also truly connects the being of 'the subjective', and 'the objective' in some sort of 'relational process' -- the notion of interaction -- as much as it does as a 'theory of relation'.

That is, after all, the central topic of metaphysics: the inter-relation between self and reality.

Insofar as 'theory' is itself 'a domain', then the 'metaphysical recursion' must also wrap the notion of theory and of reality, as well, ie, as an inherent aspect of its own self descriptive character.

In effect, just on the basis of the forgoing, we are enabled, via this logic, to identify/know immediately that, whatever else may be/become identified and known about the process of that interaction, there is necessarily an inherent 'abstract ring like structure' -- a kind of recursion, that must ultimately be built into its being.

Therefore, anything that is 'real', has somehow, as part of its process, an inherent recursive structure, if either of those concepts can be well defined, well conceptualized, at all.

Is there some way to make this simpler?

Yes. Rather than trying to understand the deep connections of process (2), the real (3), and recursion ('rings'), it is easier to consider 'things' in terms of 'being', 'doing', and 'becoming' (4).

As a case example of the above, consider the nature of consciousness (as in relation to 'the subjective' above). Consciousness is never 'just consciousness', rather it is always 'consciousness of'. It is always a consciousness of something, even when that something is itself.

The subject (the observer, consciousness) is never without an object (the observed; that which is regarded as being other than self). Being, as the being of consciousness, is never without doing, ('consciousness of' is an activity).

Thus, as an observation (a description) of the nature of consciousness, metaphysics can include a concept of inseparability between being and doing. The being of something, in this example, of consciousness, can be described in terms of its doing. Ie, the action of consciousness, as being, is always 'consciousness of'.

How about another example?

As a second example, consider the nature of existence (as in relation to 'the objective' as used above).

Historically (until very recently) the connotations associated with the term 'existence' implicitly included an idea of independence: that something will 'be existing' regardless of anyone's observation of it (a doing). In actual practice however, the independent significance of the term 'existence', or the absolute independent existence of any 'thing' has never been directly substantiated.

Insofar as practice in itself (pragmatism) must ultimately be considered as more significant (more real) than the philosophy of realism, metaphysics must consider the nature of the significance of this term 'existence' (the being of that which exists) in terms of the manner by which it is pragmatically established (in other words, a doing).

Therefore, metaphysics cannot consider ontology (being and existence) independently of (without relationship with) epistemology (a doing). The doing, in this case, is the manner by which the meta-physicist (as a subject) comes to know about the existence of the object (as objective). The notion of the 'scientific method' is a special case of this relationship, and therefore, becomes as an object of study, as a practice, within the larger field of metaphysics.

Therefore, insofar as the nature of relationship itself is primal to the study of metaphysics (by these examples and many others; hence the definition), the significance of a concept or a description (a being) cannot be considered independently of the manner by which it is arrived at (a doing).

How do we identify significance in this context?

In order to consider significance, or something as being significant, it must be positively distinguished from non-significance (that which is non-significant). This requirement is known as the 'Principle of Identity': "that which cannot be distinguished must be the same".

The significance of a term, concept, or state of being can only be established by some method or activity (a doing) which can, at least in principle, distinguish between it and that which is not it.

Why is the Principle of Identity important?

A definition which does not distinguish between that which is defined, and that which is not (everything else) is not a definition (it has zero semantic content; it is not meaningful). Minimally, the actuality of an identity (5) must be defined in terms of the possibility of its distinguishably (being is comparison; comparison is a doing).

As such, Metaphysics must consider (it cannot not consider) 'that which exists' (being) in terms the manner by which that existence is established (a doing).

In more pragmatic terms, the actuality of the semantic meaningfulness of the concept 'X exists' cannot not be defined by (at a minimum) the real possibility of interacting with X. To claim that X exists is to claim, at a minimum, that it is at least possible in principle to interact with X.

In other words, X must have measurable properties (a potentiality of interaction) in order for the assertion 'X exists' to have any semantic meaningfulness.

So the notion of existence depends on the possibility of interaction?

Yes. These three concepts are inseparable (6). There is no existence without interaction.

Suppose, for example, that someone were to propose that there is this substance 'Q'. Suppose that they were to further claim that even though they had some of this Q on hand, that it was in the nature of Q to have no measurable properties: "Q has no shape, color, or density" and "Q is invisible and undetectable to all instruments, scientific or otherwise, directly and indirectly".

If no one has any means by which they could interact with Q, by what basis can it be claimed to exist? What is the personal functional significance of something which, by never interacting with anything, will never interact with oneself.

When there is no possibility of distinguishing between the states of "Q exists" and "Q does not exist", there is no significance in the difference; pragmatically, they are the same (7).

So how does that become 'metaphysical knowledge'?

By the means of generalization: The actuality of existence cannot be considered independently of the possibility of interaction. Furthermore, it is the action of measurement (a doing) which is the very basis of the meaning of 'X exists' (a being).

The significance of the concept of existence, therefore, is not independent of interaction, but is rather dependent on the concept of interaction. The concept of existence cannot be considered without having already (at least implicitly) involved the significance of the concept of interaction. The concept of interaction is fundamental to the concept of existence. The notion of interaction (doing) is more fundamental than the notion of existence (being). These two notions (being and doing) cannot be considered separately (in either being or doing).

This idea of relationship and inseparability is so basic to the nature of these examples (and many others) that it is regarded as an Axiom of this metaphysics:

First Axiom: That relationship (doing) is more fundamental (8) than identity (being).

How does this figure in connection with 'self' and 'world'?

In returning to the relationship between the subjective and the objective, Axiom I asserts that the nature of both the subjective and the objective must be considered, understood, and defined (9) in the terms of the relationship between them.

Axiom I asserts that to consider the being of the subjective, the objective, and their relationship (10), there must be a 'doing', a methodology; that beingness cannot be, or even be considered as being, independent of doing.

There is no true independence; there is at best interdependence or dependence (11).

Is this somehow related to Descartes 'I think, therefore I am'?


As the primary example of a methodology of this type, consider that his program (a process) was to consider only those things which cannot be doubted. By defining Truth as "that which cannot be doubted", Descartes established a basis of methodology (a doing) specifically designed to cut away all that was false leaving only (the being of) Truth as the remainder.

This methodology is an epistemology -- a theory of truth -- which when enacted and implemented, would identify to the philosopher all of those truths which could be known with certainty; those things which would provide a basis for all other forms of knowing.

'Truth' in this sense is intended to be the 'bedrock foundation' (an ontology, a being of Truth) upon which all other forms of knowing (itself as a process) could be built.

Note that this theory of truth (an epistemology) posits as a principle that there are only two ontological states of being: a dualism of truth and falsity.

Furthermore, the concept of 'having doubt' in Descartes' methodology included the notion of 'can be doubted in principle'. As such, anything which could be doubted on the basis of any principle (reasonable or not) would be regarded as 'doubtful' and therefore as 'not-truth' (possibly false, and therefore as not-certain). By this methodology, Descartes was searching for that which could be known with absolute certainty, without any possible doubt -- anything which could not, even in principle, be doubted (12).

After much examination (books on the history of philosophy can describe the details), Descartes arrived at his famous dictum: "I think, therefore I am" as being the only thing which could be known with absolute certainty.

In effect, the dictum is a description of a relationship between doing (thinking) and being ('I am') which is so infinitesimally small that it cannot be disturbed (a doing) without inherently damaging its very nature (its being).

It is a ring between the subjective and the objective (between epistemology and ontology) which is so infinitely microscopic as to be atomic (13). 'Atomic', means 'un-splitable', in the oldest etymology of the term.

At this scale of relationship which is infinitely microscopic, the relationship between being ('I am') and doing ('I think') is described as a being in itself (that self as an object, the perceived, and self as a perceiver are the same as the process of perception; a relationship).

Descartes concluded that this monism of identity (the dictum itself, or rather, what it represented) was the only thing which could be known with certainty, and therefore as absolute Truth (that which cannot be doubted, even in principle).

Ok, so what is it about any of this is new?

There at least three other 'absolute certainties of truth' inherent in his methodology, just as basic, which have been overlooked.

In particular, anything which is inherent in the very process of doubt itself, which is intrinsic to that process -- or more generally, to any process at all -- must also be (cannot not be) considered as Truth.

Consider that the being of doubt -- as a process (a doing) -- inherently involves an assumption of both truth and falsity as notions in themselves (14). Doubt (as a process) also assumes that there are two subjective states: unknown and known (15). Doubt, as a method of enacting and instantiating a theory of epistemology (a theory of knowing in the terms of both knower, as subjective, and known, as objective) is understood to distinguish between truth and falsity, as aspects which are objective (things as they are in themselves), and known/unknown as aspects which are subjective (things as they are perceived to be). Finally, the dynamic of doubt must also implicitly assume that there is a distinction between doubt as a process and that which is doubted as a being.

These intrinsic aspects of doubt can be described in various terminology. For example, the concepts of truth and falsity can be considered as being about, in essence, the concepts of sameness and difference (16). Truth is where there is a sameness of being and principle (17). Falsity is where there is a difference between being and principle. The epistemology of doubt can also be regarded as a transition, a movement, from the unknown to the known in terms of time (18). Doubt (and Descartes' method in general) can be regarded as a means from moving from antecedent states (the unknown that is before) to consequent states (the known which is after) (19). Also, in distinguishing between the action of doubting and the being of that which is doubted, there is a distinction between content and context, the subjective and the objective.

All of these notions are inherently involved in the process of doubt. Insofar as these notions are intrinsic to the being of doubt as a process (a doing), any action of doubt cannot not instantiate (already pre-assume) these notions as objective, as things other than doubt, and which therefore are not -- in themselves -- doubtful. Thus, the intrinsics of doubt cannot be doubted, for the very action of doubting them requires that they have already been established as assumed (not doubted). The intrinsics of doubt are beyond doubt and therefore, by Descartes' own definition, they cannot be regarded as other than absolute Truth (as that which cannot be doubted). There is more to absolute truth than one's own thinking about one's own being.

The action of doubt and its intrinsics as a process, can be understood more exactly as an instance of the process of comparison (20). The concept of comparison involves as its intrinsics three pairs of other concepts: sameness and difference, content and context, subject and object. These intrinsics, which are inherent in the relationship between doing and being (between subject and object) are generally inherent in the nature of relationship itself (and therefore of both being and doing). They provide the basis of metaphysical description and are at the root of both epistemology and ontology.

What does it all mean? How do we generalize all of this? What do we actually know?

The persistent presence of these sets of concepts at all levels of consideration is formalized as its own Axiom:

Axiom of Three: Intrinsic in all relationship, being, and doing are three concepts (being, doing, and relationship themselves being examples) which are distinct, inseparable, and non-interchangeable.

As a last example of this relationship between being and doing, (a metaphysics of the relationship of subject and object; self and world), consider the process by which these concepts themselves are developed. It is an examination of the being of metaphysics in the terms of the doing of metaphysics.

Is this another example of that recursion you mentioned earler?


A detailed examination of metaphysical process (for example, as described here) begins with a consideration of the relationship between being and doing. Eventually, this relationship itself is defined as a being, a being which is then (by inseparability) related to a doing. Epistemology can be considered as a theory about the nature of theory, including itself among the theories to be so considered.

Hence, the relationship between the being of relationship and the doing of relationship may itself be considered as a being, which again is related to a doing, and so on, recursively.

This process of regress proceeds through multiple levels of consideration until it is realized that the dynamics of explanation at a given meta level are exactly isomorphic (the same as) the dynamics of explanation at a previous meta level. In actual practice of meta-theorization, there is a point at which the description 'wraps'; that the method of description includes a description of the method of description.

This type of regressive structure, where multiple levels of meta-consideration are involved, is inherent in the nature of process, and it occurs frequently.

For example, comparison can be a comparison of comparisons, which are themselves comparison of comparisons, etc, etc. In/with the concept/practice comparison, as with other concepts, there is a common mutual reciprocity between doing, being, and the relationship between them (21).

So how is this generalized?

Insofar as this relationship is known to be basic and inherent in the nature of process itself (the doing and being of truth; a being of sameness across multiple levels of consideration), it also is considered to be an Axiom of this metaphysics.

The Ring Axiom: The concepts of being, doing, and relationship undergo a definite sequence and progression of transitions when moving from one level of meta-consideration to the next; this sequence forms a closed ring of exactly three such steps (22).

Is that all? So what is next?

Not much. All that is needed is to complete the closure, to reach a point that the Axioms, taken as a set, can be made to apply to themselves sufficiently well as to be/become further self clarifying.

Basically, the 'Axioms' as described here can be further refined by additional progressive applications of these concepts to themselves (ie, 'exploratory recursion') and to other domains of consideration (extending the space of examples).

Insofar as the dynamics of the Axioms are themselves directly tied into the nature of both epistemology and ontology, the Axioms themselves have a direct epistemological and ontological status.

Finally, insofar as it is not possible to not involve the three Axioms in all process (doing) and being (relationship) they are necessarily considered to be 'Absolute Truth' as the basis inherent to the nature and consideration of truth itself. As such, these Axioms form the most basic level of the metaphysical consideration and description of the nature of the relationship between self and reality.

That's it. Were done.

[1] This usage specifically corresponds to the definition of symmetry.

[2] The general dynamic of process is described in terms of Axiom II. Axiom II dynamics is generally considered to be the most difficult topic to understand in metaphysics. As such, mention of it is usually left till last. However, insofar as understanding this topic is usually considered to be the end of the metaphysics, it also is recurring when considering the beginning of metaphysics. Insofar as the process of studying and learning about metaphysics is a process, then inherently that dynamic is also self-describing in terms of a closure under the ring of Axiom II.

[3] The concepts of 'process', 'real', and 'ring' (recursion) taken together, are called a triple, within the lexicon of the metaphysics. They have the modal associations of 'immanent', 'omniscient', and 'transcendent', respectively.

[4] The notions of 'being', 'doing', and 'becoming' are also a triple. This particular triple binds directly to the former one insofar as the notion of 'process' is as 'doing' (immanent), the notion of 'real' is as 'being' (omniscient), and the notion of a 'ring' (recursion) is a 'becoming' (transcendent). In other contexts, slightly different alignments may apply.

[5] The notion(s) of 'identity' with 'distinguishability' as 'possible' are functionally related as a triple of modes in the form of I, O, T, respectively.

[6] Also a triple; 'Existence' (as omniscient), depends on possibility (transcendent) of interaction (immanent).

[7] Ie, as a direct application of the Principle of Identity.

[8] This is only a preliminary statement of Axiom I, which will obtain further refinements of statement as increasing concept clarity is developed.

[9] Also a triple: 'considering' is as 'knowing' (plural; omniscient), 'understanding', as 'expression' (plural; transcendent), and definition, as a singular entity (singular; immanent).

[10] Naturally, this also is a triple: World (O), self (T), and their relation (I).

[11] Also a triple: dependence (T), interdependence (I), independence (O).

[12] In other words, an implementation of the Principle of Identity.

[13] the notion of 'ring' as used here is in direct reference to Axiom II, which is also, effectively, atomic to the nature to all process.

[14] ie, that the notions of 'truth' and 'false' are themselves part of a triple, of which the third aspect is the relationship of distinction between truth and falsity. In terms of static modes, the distinction relation is immanent, falsity is omniscient, and truth is transcendent. However, if mapping these concepts to the unit number line, false becomes 'zero', truth becomes 'one' (as equals to by proxy 'the infinite', representative of the measure boundary), and the relation of distinction between them is the unit interval. Under these circumstances, zero maps to omniscient, the interval is immanent, and the 'one' is transcendent.

[15] The notions of known, unknown, and unknowable are also elsewhere identified as a triple.

[16] The two terms/concepts identified as 'sameness and difference' are part of a triple with the notion of perception. All perception is a perception of sameness or of difference.

[17] The idea of 'truth' is here in reference to an established correspondence between 'a model' and 'a reality'. Insofar as this correspondence is in an inter-domain aspect, the notion of truth is considered to have the character of the transcendent.

However, insofar the terms in relation of 'model' to 'reality' as 'true' themselves form a triple, which insofar as it is occurring within an embedded domain, is subject to an Axiom II rotation, and thus therefore has the modal correspondences of 'plural Omniscient', 'plural Transcendent', and 'singular Immanent', respectively. Models and Realities are complex, composed of many elements, whereas the notion of 'truth' is a singular identity metric.

[18] In this context, 'unknown' can be considered to refer to 'future', whereas 'known' can be considered to refer to 'past', in relation to the abstraction 'time'. In this respect, the direct transform is with respect to a movement from the objective (external) to the subjective (internal), or in other terms, a reification of a multiple of probable states to a single possible state.

This is in contrast with the triple of 'past', 'present', 'future', with the modes of O, I, and T, respectively, as modeled within an implied transcendental/subjective context in relation.

By conjoining with the notion of 'time' rather than 'present' as a basis, there is a shift from a context which is inherently modeled from a 1st person perspective (present) to a context with is inherently modeled from a 3rd person perspective (the via abstraction time, itself being implicitly treated as a linear space dimensionality). As such, the there is modal alignment shift (a conjugate inversion) when conjoining {unknown / future / objective / external / probable} as a group and {known / past / subjective / internal / possible} also a group, collectively as a transition in time, itself all collectively as externally/objectively considered (ie, in a context of theory about a context of practice).

[19] This statement is important as it fully brings in the notion of a transition from 'plural/probable' and 'objective' to the 'singular/possible' and 'subjective'. This has the effect of completing the closure of the concept of doubt with the concept of comparison, insofar as under the principle of identity, only and exactly all of the intrinsics of comparison have been accounted for: sameness/difference, content/context, and subjective/objective. These six concepts are listed elsewhere under the label 'The Intrinsics of Comparison'.

[20] This is a connection identified elsewhere in the metaphysics as the 'Root Tautology'.

[21] in this context, as an example, the concept of comparison can be seen to hold all three roles in succession.

[22] The name "Ring Axiom" is used in contrast with the more general statement form elsewhere called 'Axiom II', insofar as the latter statement is significantly more general and precise, though only arrived at through much more careful analysis than presented in this dialog. The Axiom statement given herein is presented as an introduction as to how the central ideas of the metaphysics can be arrived at, rather than intending to be representative of a final and conclusive exact statement.