2 Basic Predicates


Relations, Domains, Identities

1.45-1 The three concepts of relation, domain, and identity are distinct, inseparable, and non-interchangeable.
In being, relations, domains, and identities are distinct, inseparable, and non-interchangeable.

A relation is that which divides, but which is itself indivisible.

An identity is that which has distinction, but which is otherwise indistinguishable.

A domain is that which contains (includes), but which is itself uncontained and uncontainable.

1.45-8 The concept of relation has the nature of the modality of the immanent. The concept of domain has the nature of the modality of the omniscient. The concept of identity has the nature of the modality of the transcendent.

1.45-5 1.45-6 Relation is more fundamental than identity and/or domain. The relationship between the parts (identities, instances) and the whole (the domain, a class) is more basic than the consideration of either the wholes or the parts.

The term Eventity refers to the combination of the meanings of an entity (thing) and an event. Each interaction, comparison, and being, is an eventity. In some contexts, the meaning of the term 'eventity' is also to be considered as a combination of the concepts of identity and relation.

1.45-7 Where domains appear to contain (seem to be contained/nested within) one another, an identity on one level (domain) of conception is a relation in the next level (domain) of conception. Similarly, relations become domains, and domains become identities.

1.46-1 The Principle of Identity: two eventities which cannot be distinguished by any property, logic, measurement, or interaction, (i.e. two eventities which cannot be distinguished even in principle), must be the same (in both identity and beingness). That which is indistinguishable by any means, mode, or method, must be the same. No semantic reference is to be assigned to that which is indistinguishable.

For example, if two "things" are in all characteristics alike (position in space and time, all properties, energies, characters, etc., or any other forms of dimensioned information) or have the same values for all defined/known (dimensional) measures, then, by the principle of identity, they are the same in both consideration and beingness. If they are not two (or different, if one cannot tell them apart) then they are (must be) the same eventity, and have common instance.


Zero Positive

1.82-1 The essence of an act of measurement constitutes a domain. Domains are zero positive.

1.82-2 All numerical (zero-positive) measurements involve as their concepts a zero, a unit, and an extent.
These concepts correspond with position, scale, and direction, respectively.

Position has the nature of the omniscient modality.
Scale has the nature of the transcendent modality.
Direction has the nature of the immanent modality.

1.82-3 The zero is representative of the limit of the microscopic boundary of a measurement domain. The unit defines the nature of the meaning of the mesoscopic scale. The extent is representative of the limit of the macroscopic boundary of a measurement domain.

1.82-4 Zero has the nature of the transcendent.
Unity (the unit) has the nature of the immanent.
Infinity (extent) has the nature of the omniscient (1).

1.82-5 In any scale of measurement, the absolute microscopic corresponds to the infinitesimal number (continuity), zero, the mesoscopic refers to the unit (one), and the macroscopic refers to infinity (symmetry).

1.82-7 Note: Negative numbers are specifically not mentioned, as the concept of negativity refers to the direction of a measure (as in a vector), rather than to measure itself (a scalar). For example, light is zero positive. There is an absolute limit (zero) to 'how much dark' is possible in any given space, yet there is no limit to how much light is possible in that same space. The two concepts 'light' and 'dark' cannot be considered/defined using equivalent contexts of meaning, and thus, cannot be considered as being in symmetric opposition to one another. Only various degrees of light-ful-ness (being) are defined; there is no "dark" (non-being, zero semantic value). Where no meaning can be given to the contrast class of that which is infinite, the concept of dark can have no independent meaning (definition, semantic basis) of its own.



Notes:
[1] Due to a shift in the context of consideration (Axiom II), the modalities of the position, scale, direction triple are phase shifted with respect to the triple of zero, unit, and extent.


The Basis of Theory

1.53-1 Theory consists of an object domain, a model domain, and a correspondence domain (the set of correspondences between the object domain and the model domain is itself a domain).
The object domain has the nature of the transcendent.
The correspondence domain has the nature of the immanent.
The model domain has the nature of the omniscient.

1.53-2 The object domain is described in terms of interactions.
The correspondence domain is described in terms of comparisons.
The model domain is described in terms of relations.

1.44-7 The notions of relation, of comparison, and of interaction are themselves also distinct, inseparable, and non-interchangeable. All three are zero positive metrics.

1.85-1 When considering the concepts of interaction, expression, and perception together (as a triple) interaction is immanent modal, expression is transcendent modal, and perception is omniscient modal.

1.53-3 A single comparison, as the simplest form of theory, objectifies a link between a sameness and difference and a content and a context, with respect to a given subject. There can be no comparison which does not implicitly imply the concepts of the subjective and the objective, a content and a context, and a sameness and a difference. Complex theory consists of many comparisons.

1.42-5 The Intrinsics of Comparison: The six concepts of sameness, difference, content, context, objectivity, and subjectivity, when taken together as a group.


Inclusion, Proximity, Similarity

1.44-2 &4 The three concepts of inclusion, proximity, and similarity provide the necessary and sufficient basis for considering the type of any instance of a comparison, perception, or relation.

The concepts of similarity, proximity, and inclusion are distinct, inseparable, and non-interchangeable concepts.
All three notions are zero positive metrics.

There is no perception, relation, or comparison which cannot be completely represented in and resolved into at least one or more of these pure types of "relations of similarity", "relations of proximity", and "relations of inclusion". For example, all comparison can be ultimately and fundamentally resolved into the three aspect types of "comparisons which establish inclusion" (i.e., containment; one thing inside of another), "comparisons which establish proximity", and "comparisons which establish similarity".

1.44-8 Relations of inclusion are more basic than relations of proximity and/or relations of similarity. Similarity and proximity are conjugate (1).

1.44-5 The relation type of inclusion (containment) has the nature of the immanent modality.
The relation type of proximity has the nature of the omniscient modality.
The relation type of similarity has the nature of the transcendent modality.

1.44-10 The essence of the meaning of similarity is always (at least implicitly) in reference to a collection of transformations (operators on forms/states). These transformations are typically across (transcendent to) domains. Similarity can have no meaning independent of these transformations.

1.44-11 The essence of the meaning of proximity is always (at least implicitly) in reference to a specific domain (a context of form). Proximity cannot be considered independently of this domain basis.

1.44-6 The Axioms are a defining basis for, and are defined by, the triple concepts of inclusion, proximity, and similarity.

Axiom I is a statement of proximity.
Axiom II is a statement of inclusion.
Axiom III is a statement of (dis) similarity.

The concept of relation can be understood in terms of the concept of proximity (in both classes and instances).
The concept of identity can be understood in terms of the concepts of instance and similarity.
The concept of a domain can be understood in terms of the concepts of class and of inclusion.



Notes:
[1] Expressed mathematically, the concept of conjugation may be expressed as I = O * T where I, O, and T are all strictly positive (I > 0, O > 0, T > 0). The implications of changing the relative values of these three variables with respect to one another express the dynamic of conjugation. For comparison, the concept of opposition would be formulated as I = O + T, with the only limitation being that I > 0 (with a possibility of O and T taking negative values or zero).


Interaction, Existence, Creation

1.72-1 The concept of universe, as a class (1), is to be understood only and exactly as the combined meanings of the instances of the concepts of existence, interaction, and creation (neither more nor less).

1.72-2 Creation, existence, and interaction are distinct yet inseparable from one another.
The being of one necessarily involves the other two.
Any consideration of one implies the (at least implicit) consideration of the other two (2).

1.72-3 The concepts of creativity, interaction, and existence have no opposites. For every domain, there cannot be zero or negative degrees of creativity, interaction, and/or existence (i.e., the degrees of each are always positive).

1.72-14 Interaction has the nature of the immanent modality. Interaction precedes existence.
Existence has the nature of the omniscient modality. Existence precedes creation.
Creation has the nature of the transcendent modality. Creation precedes interaction.

Reality is not prior to perception. Perception is not prior to self.

A multiplicity of self (aspects) yields an event of perception.
A multiplicity of perception (knowing) yields an identity of existence.
A multiplicity of existence (memory) yields an identity of self.

1.72-4 Creation involves the scale of the microscopic.
Interaction involves the scale of the mesoscopic.
Existence involves the scale of the macroscopic.



Notes:
[1] The concept of universe itself is not to be considered as the total summation of the instances of the beingness of (only) existing things and the (single) space-time that they live in. The meaning and being of 'universe' is abstract, not concrete.

The notion of universe is a special case of the more general concept of 'domain'. However, technically the notion of 'a domain' is not a 'container' or context in which a certain type of relations and identities are defined as content, so much as it is a placeholder or combined reference to three commonly associated fundamental defining notions. To understand (as distinct from "to know") the nature of the universe is to understand fully the nature and implications of only (the class concepts of) creation, interaction, and existence. This is at once necessary, and sufficient.

[2] For example, existence without perception (a special case of interaction) has no semantic value of its own. For example, to hypothesize the existence of a thing for which there is no conceivable interaction, direct, indirect, or otherwise (I cannot see it, touch it, sense it, smell it, measure it with any instrumentation, etc), would be meaningless. What does existence really mean if there is no way to personally establish its existence in one's own subjective context? Any form or establishment of an ontological status relies on and implements a relation, an immanent interaction of perception. A claim of existence prior to perception is un-provable and non-demonstrable.



Objective and Subjective

Any comparison will assume a sameness of content or a sameness of context as to be comparison. Also, the concept of comparison will assume a difference of content or a difference of context. The concept of comparison will also implicitly assume the distinction and instantiation of objectivity (what is) and subjectivity (who is). These are the intrinsics of comparison.

The concepts of content and context represent more about a way of thinking about interaction (subjective),
whereas the concepts of sameness and difference are more about interaction itself (objective).

1.43-9 The sameness/difference of eventities is itself always an eventity, one which is always more objective
(less subjective) than the eventities which are compared.
Comparison is an objectification of a sameness and a difference.
Comparison is a subjectification of a content and a context.

The very event of perception (observation) itself has (cannot not have) both subjective aspects and objective aspects. Each perception and observation, and each expression and communication event, must (cannot not) create and define both the objective and the subjective (an Axiom III relation) (1). Everything (and every process) has both a subjective and an objective aspect.

There is no objectivity that does not end in subjectivity. There is no subjectivity that does not end in objectivity.

1.75-2 &8 Nothing can be purely objective or subjective. All experiences have both objective and subjective aspects. No experience (or expression) is completely objective or completely subjective.

1.75-14 The concepts of objectivity and subjectivity are defined in terms of the relationship between self and reality
(interaction, perception, and expression). The objective is conjugate with the subjective.

1.75-1 The being of the objective and the subjective, and
the nature of the concepts of objective and subjective experience,
are distinct, inseparable, and non-interchangeable.

1.75-9 The essence of experience has the modality of the immanent.
The essence of objectivity has the modality of the omniscient.
The essence of subjectivity has the modality of the transcendent.

1.75-12 Objectivity is defined in terms of comparable forms.
Subjectivity is defined in terms of non-comparable feelings.
The meaning of objectivity has common basis with the meaning of
'that which is perceived or is perceivable' (physical content).
The meaning of subjectivity has common basis with the meaning of 'that which is invisible or is transparent' (non-physical context).

1.76-7 &10 &16 Objectivity and subjectivity are degrees/metrics, not states of being or condition. Objectivity is not an attribute of any single perception. Objectivity can only be associated with clusters of related perceptions. Perception, observation, experience refer to a single/simple condition of being, without aspect; whereas objectivity can only be considered as an aspect of complexes of many related perceptions.

1.75-15 Objectivity is the product of the degree of

1) the intensity of the self-to-world interaction,
2) the degree of macroscopic consistency of the self-to-world interaction, and
3) the degree of microscopic potentiality in the self-to-world interaction (2).

1.72-13 All interactions are described in terms of rings, either within a single domain, or across sets of domains.



Notes:
[1] For example, in communication there is an inherent aspect of subjectivity in the minds perceiving a message. There is an inherent aspect of objectivity in the coordination of subjectivity, as found in the common shared external references (the language used as a basis or "carrier" of communication meaning; the shared context of all participants). Similar considerations apply to comparison, which may also be modeled as a special type of communication event.

1.66-3 [2] Un-patterned form, unpredictability, and randomness are as necessary for the establishment of a degree of objectivity to any perceived actuality as are the consistent correspondences formed by a consensus among multiple observers in common communication.



Being, Existence, and Reality

1.76-1 The concepts and the meanings of (objective) 'being' (to be objective), 'to be real', and 'to exist', are considered identically distinct, and non-interchangeable concepts. On any finite or relative scale, these three notions are not synonymous. The concepts of being, reality and of existence are considered distinct concepts, with very dissimilar meanings and definitions. Each of these meanings has a different semantic basis, and as such, to say anything about any one is to have asserted little or nothing with respect to the other two. The scope of application of each is distinct from that of the other two.

To assert existence implies both necessary actuality and necessary potentiality. With any existing thing, there must always be at least a possibility of secondary or additional interactions within that same context with any and all other existing things.

The meaning of the term 'existence' is always relative to a particular world (even if it is considered independent of any specific self). The term existence cannot be considered to have meaning without implicit reference to a world (shared objective context). The term objectivity has no meaning without implicit reference to some (specific) self (shared subjective context) even if it is considered independently of any specific world.

1.76-2 The meaning of 'to exist' is to make an assertion that the omniscient modal aspects of a given set of interactions
are common and shared for all of those interactions.
The meaning of 'objectivity' is to make an assertion that the transcendent modal aspects of a given set of interactions
are common and shared for all of those interactions.

1.76-3 The meaning of the term 'objectivity' is in reference to certain characteristics of a (large) collection of perceptual interactions, relative to some implicit self. The meaning of the term 'exists' is in reference to that which is presumed to have (at least the potentiality of) an actuality without any perceptual interactions at all (zero observations).

The meaning of the term 'real' is in reference to the beingness of a single instance of an interaction (exactly one). To be real is interdependent with considerations/references to domains/worlds and selves/observers. This is in contrast with the notions of both objectivity (inherently involves many interactions) and existence (inherently involves no interactions).

1.76-4 The notion of 'Reality' refers to the beingness of an instance of a set of interactions (perceptions, observations, experiences). Multiple instances of that which is 'real' together form the class of that which is 'reality'. The notion of 'to be real' cannot be further analyzed.

The term 'real' can only be applied to the identity of the beingness of the interaction itself.
The term 'reality', then, can refer only to the quality of the instance-beingness of a (an arbitrary) collection of interactions.

Interaction is simple. Reality is complex.

1.76-6 The term 'existence' has the nature of the omniscient modality.
The term 'reality' has the nature of the immanent modality.
The term 'objectivity' has the nature of the transcendent modality.

As per their counterparts, 'that which is (objective) being' has the nature of the transcendent, 'that which is real' has the nature of the immanent, and 'that which exists' has the nature of the omniscient.

Existence is characterized in the terms of independence.
Reality is characterized in the terms of interdependence.
Objectivity is characterized in the terms of dependence.

The concepts of dependence, independence, and interdependence are triple. They are distinct, inseparable, and non-interchangeable. Typically, dependence has the nature of the transcendent, interdependence has the nature of the immanent, and independence has the nature of the omniscient (1).

1.76-8 All perceptions (comparisons in themselves) regardless of their 'type', are simply real. The stable patterns of comparisons of perception are reality. All Interactions are Real. Reality (an experience of a world) is constructed out of consistent sets of comparisons of those interactions (consensus, objectivity).

Only the content of that set of comparisons 'exists'. The context of those comparisons (the self), does not exist,
although it is an inseparable aspect of all that is real.

1.72-5 Interaction Is (2). Interaction cannot not Be. BEing is always Being-with (and therefore doing, and therefore becoming).
All interaction is zero-positive.

1.72-11 Interaction is neither something, nor is it nothing. Interaction is without any kind of existential status whatsoever (3).
Interaction is real, but it does not exist.

1.72-12 Interaction neither exists, nor is created.
Interaction is the basis of all existence and creation and
is more basic/fundamental than either existence or creation.
It is in-between, in all that is both being, and becoming.

1.76-9 The concept of 'real' refers to an intrinsic aspect of interaction. The concept of reality refers to an intrinsic of stable (with respect to the subjective/self) patterns of comparisons of interaction.

1.76-10 The concept of 'real' (perception) is inherently simple (an instance).
The concept of 'reality' (experience) is inherently complex (a class).

1.76-11 To make assertions such as the following: "there exists only one world" or even "there exist more than one world", "many domains exist", etc., would be applying the concept of existence outside of its range of meaning (4). There is no (single ultimate) ground domain/world in which all other domains are established as either existing or not.



Notes:
[1] The specific associations between a triple of concepts and the modalities depend on the specific context of consideration in which that triple is used. Where the context of the usage of a triple shifts, the modal relationships can change. If a given triple frequently occurs or is used in only one context of consideration, the modal associations will seem to be constant. Abstract concepts (such as dependence, independence, and interdependence) tend to have more fluid associations.

[2] As used here, 'Is' is in reference to being, as distinct from the notion of 'to exist'.

[3] The ontological status of interaction is defined in terms of beingness, but cannot be defined in terms of, or based only on the terms of, existence (i.e., that which is existential). A single interaction cannot be considered to have any degree of (or establish any degree of) objectivity.

[4] One can, however, assert "there are many worlds", or "many worlds are real", for the meaning of being is different from that of existing. Being is immanent (or in the case of worlds, transcendent), whereas existing is omniscient.



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