Closed Loop Interval Ontology
       The Digital Integration of Conceptual Form


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Aligning the vision

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What is truth?
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The closed loop ensemble contains
all primary definitions

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What is a number?

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Digital geometry
Euclid in digital space

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The digital integration
of conceptual form
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Closed loop interval ontology
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The digital integration of conceptual form
Compositional semantics

This project is defined in "finite math". Though we talk about "infinity" and "the infinite" and "the continuum", all our structures -- or most of them -- are defined in discrete increments defined by boundary values in an interval.

We can build this structure up from the continuum, because we approach the continuum as a limit, and form an approximation to "the real number line" as "close as we wish" -- under the control of "acceptable error tolerance".

But these increments are always digital.

And these digital objects can be combined to build very complex structure that remain stable, because they are all defined in the same terms, and constructed in the same way.

So we make the claim that all human conceptual structure is defined within the single interval defined in the loop as bounded by "the infinite" at the top of the cascade and "the infinitesimal" at the bottom.


In this framework, the continuum is defined as a range of "pure uncertainty" within a bounded digital increment. It is approached as an ideal. We are exploring the idea that the continuum is somehow "orthogonal to" the incremental digital level above it in the decomposition cascade.


Inside this framework, we expect to build "all symbolic structure" -- by which we mean

  • All symbols -- letters, numbers, alphabets -- all "terminal characters", which are each unique and have some constructive role in assembling complex composite structures.
  • All words
  • All meaning, defined under context-specific top-down dimensional stipulation
  • Definitions of all mathematical and logical operations constructed from these elements

Everything built up from atomic distinctions

Everything built up from atomic distinctions
Sketch | Back

We affirm or postulate that all conceptual form emerges from the continuum by a process of motivated distinction, and we say this is true for the emergence of alphabets and written language.

We are building a "grand cascade" across levels.

And these levels are in a complex multi-type relationship.

Pure symbolic structure interacts with intuitive meaning and visualization and other sensory dimensionality.

This is a complex subject, and it is true in different ways at many levels. But it is an abstraction, an idealization.

In cognitive psychology, some of these "atomic" distinctions might be quite holistic, or gestalt-based. We see a "tree" as a whole, but we can also look at the parts of a tree and see them as units, and we can look at how these units are distinguished -- how their boundaries are defined, how their properties are assigned.

"Assigned" in an abstract model, "perceived" in direct experience.


Of course language has other levels -- such as sound, or visual imagery. See Susan Carey on the Origin of Concepts for powerful statements on this and the complex interaction between levels of analysis.

Sat, Apr 17, 2021