Depth

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What is the meaning of certainty? 

What is the meaning of uncertainty or ambiguity?

How can these terms be defined in relational patterns? 

ADEPT answers these questions in the axiomatic ontological construct called depth.

Because it is difficult to find words that convey the desired distinctions in English, it is necessary to state a precise meaning for the use of the terms definite and determinate in ADEPT.

• Definite is taken to imply a certainty, or lack of ambiguity, as to what a node is, specifically as a positive statement of its logical cause as a result of its formative relationships. It represents actuality in the positive and potentiality in the negative.
• Determinate is taken to imply a certainty, or lack of ambiguity as to what a node can do, specifically as a positive statement of its logical effect as evidenced by its subsequent relationships. It represents gain of function in the positive and loss of function in the negative.

With these definitions of definite and determinate, we can now derive the ADEPT depths as follows:

1. Manifest depth is definite and determinate (it is and can) – representing actual gain of function
2. Shadow depth is definite and indeterminate (it is and cannot) – representing actual loss of function
3. Shadow depth is (also) indefinite and determinate (it is not and can) – representing potential gain of function
4. Obscure depth is indefinite and indeterminate (it is not and cannot) – representing potential loss of function

The surprising and puzzling result that stands out in the derivation of the three ADEPT depths is the mixed representation found in the shadow depth. Shadow depth is both indefinite/determinate and definite/indeterminate. It is both potential gain of function, and actual loss of function.

Furthermore, ADEPT trinary logic of secondary reference treats the shadow and obscure depths as logically equivalent. This means that a potential gain of function, an actual loss of function, and a potential loss of function all share the same negative logical effect.  This negative logical effect of the shadow and obscure depths is in contrast to the positive logical effect of the manifest depth.

The diagram below can help visualize these somewhat counter-intuitive facts.  The example shows the treatment of the concepts of "nothing", "anything" and "something" correspondingly representing the depths of obscure, shadow and manifest.  The light blue circles with labels starting with an "O" represent obscure depth rivulets; the medium blue circles with labels starting with an "S" represent shadow depth rivulets; and the darker blue circles with labels starting with an "M" represent manifest depth rivulets.  The variety and word channels are represented by directed arrows. For word channels, a determinate relationship is a solid line and an indeterminate relationship is a dashed line.

The word channel itself pertains to definiteness and its depth pertains to determinate-ness.

All nodes have a 1st consideration in which an optional word channel can assign an aspect of what that node is, but its depth (and what it can do) is determined by whether the node has an incoming word channel that is itself, from a manifest translation. 

• If it has an incoming word channel from a manifest translation, then it has manifest depth.
• If it has an incoming word channel from an obscure or shadow translation, then it has shadow depth.
• If it does not have any incoming word channel, then it has obscure depth.

There are some important corollaries to be drawn from these definitions:

1. Any manifest node that has a self-referencing word [w] channel must also be a translation in the 2nd consideration in order to self-reference, which means that it must also have an incoming variety [v] channel. Thus it is definite by means of its word channel and determinate by means of its manifest word channel. This pattern is shown at the bottom of the diagram.
2. Any obscure translation node in the 2nd consideration cannot have a word [w] channel by definition. Thus it is indefinite by the lack of a word channel and indeterminate by the lack of a manifest word channel.  This pattern is shown at the top of the diagram.
3. Any shadow translation in the 2nd consideration must have a word [w] channel, otherwise it would be obscure, but it may not have a self-referencing word[w] channel, otherwise it would be manifest. Thus it is definite by the presence of a word channel and indeterminate by the lack of a manifest word channel. This pattern is shown across the center of the diagram.
4. So what does it mean to be indefinite and determinate? This can also be stated as the representation of potential gain of function. We have already said that this is represented by the shadow depth but how? There would have to be a state in which there was no word channel, representing indefiniteness and also a manifest word channel representing determinate-ness. However, such an outcome violates the Law of non-contradiction because a word channel cannot be both non-existent and manifestly existent at the same time. ADEPT resolves this logical dilemma by acknowledging that indefiniteness precludes any evaluation of determinate-ness. If an existence is not definite, then its determinate “effect” is assumed to be negative. An explicitly negative statement of definiteness can conversely be understood as a general positive statement of definiteness that has indeterminate effect. Incidentally, this is analogous to Immanuel Kant’s treatment of the judgement of Infinite quality. Because it has already been shown in the previous corollary that an indeterminate effect can be expressed as a shadow depth, that is how this situation is handled in ADEPT. Thus the pattern of relationship for the representation of a potential gain of function, or indefinite determination, is a shadow translation of the 2nd consideration found in the word [w] channel. The shadow translation in this case would make a negative statement as to definiteness such as “non-green”. Such a negative statement would correspond to an infinitely positive statement of everything that is “non-green”. This positive statement would then be handled as a shadow translation representing the potential gain of function of the indefinite yet determinate concept of “non-green”.  The pattern is also shown across the center of the diagram.

If the outcome of corollary 4 seems ambiguous - that potential gain of function, potential loss of function and real loss of function are treated as logically indistinguishable outcomes - that's good!  This is exactly the point that needs to be made!  The shadow depth becomes the logical definition of ambiguity and its opposite, manifest depth, becomes the logical definition of deterministic certainty.

The resolution of certainty and ambiguity into recognizable patterns for the ADEPT notation is essential metaphysical work. Although it can be admittedly difficult to grasp these concepts, simply knowing the patterns of depth is generally sufficient to begin applying ADEPT. So to restate the patterns of Depth more simply and memorably...