The Integration of Conceptual Form
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A Universal Foundation
for Ontology

The closed loop contains
all primary definitions

Closed Loop Ensemble
Primary elements of the core logic

Properties of the Closed Loop
Embodied features of this form

Project developed by
Bruce Schuman


This project has roots in many sources and influences. One that is especially fascinating is the concept of "Monad", particularly as understood by the great 17th C philosopher Gottfried Wilhelm von Leibniz.

Our discussion of "Closed Loop Interval Ontology" follows several ideas shown in this model of Monad.

  • The closed loop when seen in two dimensions does appear as a "circle with a center-point"
  • Leibniz wanted to build a model of all of reality constructed from Monads, somewhat like atoms.
  • Closed Loop Ontology proposes that the foundation of all human understanding of reality is defined in "concepts" -- ideas, which we say are constructed from primary and "atomic" elements, which can be described in various ways, including "units" or the boundary values (distinctions, cuts) that shape the particulars of any unit.
The "decomposition" of some "object" in the world down into finer and finer (smaller and smaller) elements raises the challenge of what is meant by "object". What is the difference between a "map" (an abstract symbolic representation) and the "territory" (some physical thing) that it describes? If the map becomes "absolutely accurate in every detail", what is the difference between the map and the territory?

The Monad

According to Hippolytus, the worldview was inspired by the Pythagoreans, who called the first thing that came into existence the "monad", which begat (bore) the dyad (from the Greek word for two), which begat the numbers, which begat the point, begetting lines or finiteness, etc. It meant divinity, the first being, or the totality of all beings, referring in cosmogony (creation theories) variously to source acting alone and/or an indivisible origin and equivalent comparators.

Pythagorean and Platonic philosophers like Plotinus and Porphyry condemned Gnosticism (see Neoplatonism and Gnosticism) for its treatment of the monad.

For the Pythagoreans, the generation of number series was related to objects of geometry as well as cosmogony. According to Diogenes Laërtius, from the monad evolved the dyad; from it numbers; from numbers, points; then lines, two-dimensional entities, three-dimensional entities, bodies, culminating in the four elements earth, water, fire and air, from which the rest of our world is built up.


Gottfried Wilhelm (von) Leibniz (1 July 1646 – 14 November 1716) was a prominent German polymath and one of the most important logicians, mathematicians and natural philosophers of the Enlightenment. As a representative of the seventeenth-century tradition of rationalism, Leibniz developed, as his most prominent accomplishment, the ideas of differential and integral calculus, independently of Isaac Newton's contemporaneous developments. Mathematical works have consistently favored Leibniz's notation as the conventional expression of calculus. It was only in the 20th century that Leibniz's law of continuity and transcendental law of homogeneity found mathematical implementation (by means of non-standard analysis). He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is the foundation of nearly all digital (electronic, solid-state, discrete logic) computers, including the Von Neumann machine, which is the standard design paradigm, or "computer architecture", followed from the second half of the 20th century, and into the 21st.

In philosophy, Leibniz is most noted for his optimism, i.e. his conclusion that our universe is, in a restricted sense, the best possible one that God could have created, an idea that was often lampooned by others such as Voltaire. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th-century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also assimilates elements of the scholastic tradition, notably that conclusions are produced by applying reason to first principles or prior definitions rather than to empirical evidence.

Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibniz also contributed to the field of library science. While serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would serve as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German but also in English, Italian and Dutch.There is no complete gathering of the writings of Leibniz translated into English.

We mere humans somehow know there is a perfection in reality and in nature. There is something we can see in organic form that tells us there is innate order in existence. We can see it in the stars, in the rocks, in the oceans, in the trees. There is something beautiful, something whole, something deeply true from which reality emerges, and by which somehow all natural and healthy order is maintained.