Closed Loop Interval Ontology
       The Integration of Conceptual Form


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Project under development
Coalescing and evolving

Closed Loop Interval Ontology
How it works

Objectives and Strategy
Reconciliation and integration

Core Vocabulary
Primary terms

A Universal Foundation
The closed loop ensemble contains
all primary definitions

Core terms on the strip
Closed Loop framework

Reconciliation of perspectives
Holistic view on alternatives

Objectives and Strategy
Reconciliation and integration

Primary objectives of this project

  • Propose the interpretation and development of the Closed Loop as a universal container for all conceptual structure, including science, mathematics and philosophy
  • Define a common foundation for semantic ontology, cognitive science and the quantitative sciences
  • Reconcile major competing alternative perspectives within semantic ontology and the cognitive science of categories
  • Identify related technical disciplines where foundational definitions commonly overlap, particularly when that overlap becomes confusing or fragmenting
  • Help overcome what can be perceived as fragmentation in the sciences and the humanistic disciplines, as the world of intellectual inquiry appears scattered into thousands or millions of semi-independent fragments developed from a local point of view without respect to the larger whole.

Show how this works, in a precise way that is consistent with both engineering methods and the common standards for mathematics, logic and semantics.

Clarify the basic structure of the Closed Loop

Extreme simplicity as a foundation for extreme complexity

The Closed Loop is a structure of extreme simplicity which embodies a potent array of complex interpretations. Many foundational concepts in science, mathematics and philosophy can be understood as interpretations of this simple but subtle and beguiling algebraic structure. We understand it as a "general form" that functions as a container and ordering principle for the foundational definitions of science and philosophy.

These foundational definitions include number, measurement, the relationship between quantity and quality, systematic method for defining categories and concepts, the notion of abstraction and hierarchy, and the concept of dimension as common to both quantity and quality.

A spectrum of levels

The world can be understood through a natural spectrum of levels that is innate to human thinking, and which undergird and support all human understanding, in any discipline or social sector.

Abstraction and levels of generality are or can be directly linked to specific concrete instances, as is illustrated by a common taxonomy as originally conceived by Linnaeus. But this process becomes complex, and can be understood in endless numbers of alternative and logically-independent ways, which keeps the discipline of ontology and semantics fragmented and scattered and divided by what appears to be controversy.

We propose a single integral container, a single source from which all essential definitions can be derived, a single container which links all "concepts" together within a single framework.


In some sense, the Closed Loop "stands outside of time". It contains time. It is proposed as a single framework that contains "every concept at once". All concepts can be derived from it. All concepts are held within it.

Postulate a system

The idea of the Closed Loop is a proposed interpretation. It does not "exist" as a concrete empirical observable thing in the world. It is created, it is visualized, as a way to consistently interpret the phenomena of mind and intellect and science.

It is a "human design" -- a "synthetic creation" that we can visualize as a pathway towards integration and common ground. It is a method of reconciliation. It is a way to "fit the pieces together" into a single whole.

Definitions do not stand on their own, as independent objects or discoveries. Every concept or or idea within the Closed Loop model is defined within the context of "system", and has no precise or arguable meaning outside the context of system. It is in the relationships and interdependence of concepts that mathematical ideas become meaningful, and the fragmentation of the sciences cannot be overcome without recognizing this point.

Every definition becomes meaningful in an interdependent mutually-interconnected way. The fundamental postulate that holds all of this together, as the foundation and framework and invariant container for the system, is the postulate of the Closed Loop.

Assembling process
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We want to define precisely how it is that the moebius strip can be interpreted as a universal foundation for conceptual structure.

This is complicated with a lot of moving parts, and the idea is still unproven and intuitive. List these elements here to help guide the coalescence. We need a comprehensive list of these elements, and we have to explain or justify them all individually in a consistent way.

This list is a design for project architecture:

  • The pieces that are to be combined
  • The way in which the pieces are to be combined
  • The themes and principles and methods that are brought together in one place
  • The concept of "isomorphic recursion" defined across many simultaneous objects or concepts


  • Develop a list of terms and words that are synonyms for "category" -- any dimensionally-bounded unit
  • Develop a list of terms that are synonyms -- or can be defined as synonyms -- for boundary value or "cut" -- the "line that cuts a line" to form a distinction

Type of objects that are defined through isomorphic recursion and connected to build a model of reality:

  • Abstract
  • Symbolic - representational
  • Concrete (referent?) or "actual"

"What can be done with little boxes"?

Everything is defined by a box (a bounded interval) containing some symbolic structure, composed of alphabet or numbers..

Everything is matrix

matrix can define everything -- to within some error tolerance

Reconciliation of perspectives
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Philosophical perspectives on reality -- what is real

FRISO project standards

John Sowa on basic perspectives

Theory of categories

Classical view

Family resemblance

Metaphor and analogy

Integration of alternatives by recognizing unique value and authenticity of each perspective -- they are not really competing alternatives, but methods serving slightly different purposes