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.
With these definitions of definite and determinate, we can now derive the ADEPT depths as follows:
An obscure depth has no word [w] channel.
A shadow depth has a non-determinate obscure translation or an indeterminate shadow translation in its word [w] channel.
A manifest depth has a self-referencing word [w] channel or has another determinate manifest translation in its word [w] channel.
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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.
There are some important corollaries to be drawn from these definitions:
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...
An aside comment that will require future discussion can be made here.
In thinking of ADEPT as a deductive theory of the mind, the metaphysical derivation of depths should correlate as follows: manifest depth is behavior, shadow depth is conscious thought and obscure depth is subconscious or reflexive thought.
Manifest means that a node has a word channel that originates from a manifest translation. This requires the first translation in any manifest pattern to have a self-referencing word channel.
Obscure means that a node has no word channel.
Shadow means that a node has a word channel that originates from an obscure or shadow translation. This requires the first translation in any shadow pattern to not have a self-referencing word channel.