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

Project under development
Coalescing and evolving

"By trying and erring, by groping and stumbling -- so progressed our knowledge. Hampered and yet spurred by a hard struggle for existence, a plaything of his environment and a slave to the traditions of his time, man was guided in this progress not by logic but by intuition and the stored-up experience of his race. This applies to all things human, and I have made painstaking efforts to show that mathematics is no exception."

Tobias Dantzig, Number: The Language of Science, p.187

The Closed Loop project has been evolving for many years as studies in conceptual structure and categories, and is only recently beginning to take shape within the definitions and boundaries of the Closed Loop concept.

We are now approaching the project as a process of top-down integration, where after repeated testing and confirmation, we are tending to presume that this design makes sense, and it is indeed reasonable to pursue its highly inclusive objectives based on this approach to a universal container and body of definitions.

Some of the original work on category theory and synthetic dimensionality can be found at


What is a concept?
A few hundred elements
Numbers. alphabets, symbolic structures
What is a universal container?

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The FRISCO report is a 200 page technical and philosophical review of issues and methods that arise in the context of a project that involves broad integration across disciplines and common professional protocols.

We are likely to follow many of the principles and methods outlined in this report, and might cite a lot of it as precedent, at least in some regards.

What is a concept?
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We generally follow this definition from Wikipedia

Concepts are defined as abstract ideas or general notions that occur in the mind, in speech, or in thought. They are understood to be the fundamental building blocks of thoughts and beliefs. They play an important role in all aspects of cognition.

As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science.

In contemporary philosophy, there are at least three prevailing ways to understand what a concept is:

  • Concepts as mental representations, where concepts are entities that exist in the mind (mental objects)

  • Concepts as abilities, where concepts are abilities peculiar to cognitive agents (mental states)

  • Concepts as Fregean senses (see sense and reference), where concepts are abstract objects, as opposed to mental objects and mental states

Concepts can be organized into a hierarchy, higher levels of which are termed "superordinate" and lower levels termed "subordinate". Additionally, there is the "basic" or "middle" level at which people will most readily categorize a concept. For example, a basic-level concept would be "chair", with its superordinate, "furniture", and its subordinate, "easy chair".

When the mind makes a generalization such as the concept of tree, it extracts similarities from numerous examples; the simplification enables higher-level thinking.

A concept is instantiated (reified) by all of its actual or potential instances, whether these are things in the real world or other ideas.

Concepts are studied as components of human cognition in the cognitive science disciplines of linguistics, psychology and, philosophy, where an ongoing debate asks whether all cognition must occur through concepts.

Concepts are used as formal tools or models in mathematics, computer science, databases and artificial intelligence where they are sometimes called classes, schema or categories. In informal use the word concept often just means any idea.

A few hundred elements
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This project runs on an SQL database, and supposedly presents something like a hierarchical word processor, of a very basic sort. We are gathering elements to the database, generally organized in terms of "theme groups" -- major topic areas -- and "themes" -- subject areas that are aligned somewhere with that theme group. We are also developing a basic vocabulary -- like a glossary of basic concepts and terms, generally concerned with epistemology. What is a dimension, what is a unit, what is an interval, what is a metaphor, what is equivalence or identity or equality? What does it mean when we say "two things are equal" -- when clearly they are not the exact same thing -- but are "equal" in some sense that we have to clarify.

Today, at this early stage, put database system is starting to work fairly well, and we are starting to slowly load in data -- ideas, content, specific statements and interpretations -- all of which is intended to illustrate the broad thesis that "in significant ways, the Closed Loop contains philosophy and science and mathematics"

This is a big deal, and a very broad reach. What are the historical precedents?

You are putting together 100+ definitions, and this project is a house of cards -- it could collapse at any of 100 failure points, True.

As far as I can tell, from my limited research, "nobody has done anything quite like this" -- but maybe this project could be described as inspired by Leibnitz or Ramon Lull - and who knows how many medieval visionary philosophers who drew complex ontological diagrams as explanations of the universe.

Numbers. alphabets, symbolic structures
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Numbers and alphabets are finite-state digital objects defined in a finite set that can be fully ordered (numerical order, alphabetical order).

We are presenting the argument that "anything in the world" that can be described can be described by a limited set of finite-state variables.

Modesl are always defined for specific purposes.

What is a universal container?
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Set of all sets - Universal Set

In set theory, a universal set is a set which contains all objects, including itself.[1] In set theory as usually formulated, the conception of a universal set leads to Russell's paradox and is consequently not allowed. However, some non-standard variants of set theory include a universal set.


There is no standard notation for the universal set of a given set theory. Common symbols include V, U and ?.[citation needed]

Reasons for nonexistence Many set theories do not allow for the existence of a universal set. For example, it is directly contradicted by the axioms such as the axiom of regularity and its existence would imply inconsistencies. The standard Zermelo–Fraenkel set theory is instead based on the cumulative hierarchy.

Russell's paradox

Main article: Russell's paradox

Theories of universality

The difficulties associated with a universal set can be avoided either by using a variant of set theory in which the axiom of comprehension is restricted in some way, or by using a universal object that is not considered to be a set.

Restricted comprehension

There are set theories known to be consistent (if the usual set theory is consistent) in which the universal set V does exist (and {\displaystyle V\in V}V\in V is true). In these theories, Zermelo's axiom of comprehension does not hold in general, and the axiom of comprehension of naive set theory is restricted in a different way. A set theory containing a universal set is necessarily a non-well-founded set theory. The most widely studied set theory with a universal set is Willard Van Orman Quine's New Foundations. Alonzo Church and Arnold Oberschelp also published work on such set theories. Church speculated that his theory might be extended in a manner consistent with Quine's,but this is not possible for Oberschelp's, since in it the singleton function is provably a set,[4] which leads immediately to paradox in New Foundations.

Another example is positive set theory, where the axiom of comprehension is restricted to hold only for the positive formulas (formulas that do not contain negations). Such set theories are motivated by notions of closure in topology.

Universal objects that are not sets

Main article: Universe (mathematics)

The idea of a universal set seems intuitively desirable in the Zermelo–Fraenkel set theory, particularly because most versions of this theory do allow the use of quantifiers over all sets (see universal quantifier). One way of allowing an object that behaves similarly to a universal set, without creating paradoxes, is to describe V and similar large collections as proper classes rather than as sets. One difference between a universal set and a universal class is that the universal class does not contain itself, because proper classes cannot be elements of other classes.[citation needed] Russell's paradox does not apply in these theories because the axiom of comprehension operates on sets, not on classes.

The category of sets can also be considered to be a universal object that is, again, not itself a set. It has all sets as elements, and also includes arrows for all functions from one set to another. Again, it does not contain itself, because it is not itself a set.