An Experimental Development
"Closed Loop Interval Ontology" is an experimental research project exploring the development of an integral design as a common foundation for science, mathematics, semantic ontology and the humanities.
The design is based on the idea that all concepts share certain basic features, and that the structure of concepts in some important regards can be extended to all forms of description, including science and mathematics.
The project presumes that all concepts, regardless of discipline or sector or culture, can be "constructed" from certain very fundamental common principles, which can be described precisely in mathematical terms. These mathematical terms involve "symbolic representation" and are generally consistent with the needs and methods of computer science.
Closed Loop as universal container
We are studying the nature of boundaries, and considering alternatives, such as the circular framework of Venn diagrams, which define what is IN a set ("inside the circle") and what is NOT IN a set ("outside the circle") by the circular boundary.
A integral hypothesis
The Closed Loop is a postulate, an interpretation, that should be tested for its usefulness and consistency. It is an attempt at absolute broad inclusion and simple elegance. Is it valid? Is it helpful? Is it truly simplifying? Does it lead the way towards better understanding and better cooperation or interaction between projects and sectors and "silos"? Does it suggest ways that fragmentation can be addressed and overcome? Does it legitimately map the interconnection between traditionally unreconcilable facets of human thinking, such as "religion" and "science", or "science and the humanities", or between the worlds of quantitative measurement and qualities?
The map and the territory
Symbolic representation is a complex and sensitive subject, involving the relationship between an abstract symbol -- a sound, a letter, a word, a number, and each of these things somehow represented in some medium -- and some facet of "reality". It is related to the famous issue of the "map and territory" relationship. In essence, we are studying the properties of maps, while careful considering the relationship of the map (the abstract symbolic structure) to the "territory" (the physical reality or object) it represents.
Closed Loop ontology is a kind of compositional semantics, proposing a method to define all meaning in terms of a basic language of very simple primitive elements which can fully describe and characterize any concept or idea or "model of reality".
It works by proposing common structural features which are interpreted through (within) a closed algebraic space containing essential building blocks for developing all semantic and mathematical structures. We are calling the basic algebraic elements of this structure an "ensemble" because these concepts (taxonomy, abstraction, dimensionality, number, boundary, continuum, etc.) work together to complete characterize meaning.
That "closed algebraic space" is the "closed loop", a single bounded algebraic container which we believe might offer a strong way to overcome the fragmentation and inconsistent mutual definitions inherent in more traditional approaches to ontology and mathematics.