Patterns of Relational Paradigm


Twofold Operators

Twofold Operators

EMERGENT AXIOMS ARE NEEDED TO EFFECTIVELY DEAL WITH THE FOLLOWING TWOFOLD OPERATIONS

 


 

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Overview

Patterns of Relational Paradigm

Introduction

Twofold Operators

Form/Process

Hierarchy/Network

Sequence/Jump

Measure/Count

Known/Random

Balance/Relationship

Summary of Emergent Axioms

Threefold Operators

Fourfold Operators

Fifth Business

Relational Organization

Relational Structure & Root Language

        The twofold operator is a concept that I believe to be present in some form in all philosophies. The particle and the wave in Western physics, the Yin and the Yang in Zen, Mother Earth and Father Sky of the Native Americans, and good and evil in Christianity are all twofold operators.

        I have taken the name twofold operator from Arthur Young’s book The Geometry of Meaning. Young defines the twofold operator in terms of clockwise versus counterclockwise rotation, a left-handed versus a right-handed spiral. The one is a mirror image or an inversion of the other, a reversal of cause and effect.

        The concept of complementarity proposed by the physicist Niels Bohr is the same as the twofold operator. Using the work of the Danish philosopher Soren Kierkegaard as a springboard, Bohr contended that objective and subjective are two different ways of looking at a thing that is unknowable directly. Complementarity is a belief that everything has two sides and that if great ideas are true, their opposites are also true

         I have expanded the twofold concept to include all aspects of our reality. If you cannot identify the complement, the mirror or inversion, then you don’t have a complete map of the territory. I’m not saying that the one or God does not exist. I am saying that any manifestation in the reality of the existing universe is twofold. If there is man, there is woman. If there’s woman, there’s man. If there’s light, there’s dark; if there’s heaven, there’s earth; if there’s good, there’s evil, and vice versa.

        The twofold is not the same concept as duality. Cartesian dualism says that there is a separation (i.e., Rene Descartes’ separation of mind and body). Complimentarity says that there is both separation (the many) and connection (the one).

         Although the existing world views have acknowledged the twofold operator, none of them to my knowledge have dealt effectively with this basic pattern. Most world views emphasize one part of the twofold but do not effectively deal with its complement. Western science has emphasized the form but not the process, the hierarchy but not the network and the sequence but not the jump. In general, Eastern science has reversed this emphasis.

         This section will add missing axioms to the Western scientific world view—additions which will enable us to deal with the twofold nature of our reality. Most of these additional axioms are discussed in terms of mathematics, philosophy or physics. Don’t let the technical terms confuse the issue. These are basic concepts and everyone deals with them. You may use a different terminology, but all intelligence must in some way understand and use these concepts. I believe that most of them will be intuitively obvious once they are understood.

         One of the major problems of communication is the words which we have in our language to describe these simple concepts. Often the name of one of the twofold is used to describe the set of both entities. For example, the set man/woman is called man; the set measure/count is called measure. When we use the word man or measure, it is often unclear whether we are referring to both members of the set or only to the member named.

         In other cases we have no word for the set consisting of both members of the twofold operator. There is no common word which means form / process, hierarchy / network, or known / random.

         To avoid confusion, I will use both words, e.g., measure/count, when referring to the set, or words such as human when the meaning is clear. When I use the name of one member of the set, it always will refer to that member and not to the set. Man will never be used to indicate the set man/woman. My feeling is that this simple problem with language is one of the major barriers to effective communication.

         It has been my experience that most scientists are not comfortable with the concept of axioms. They would like to believe that science is based solely on logic and objective experimental results. Axioms simply don’t fall into this category. Axioms by definition are not subject to logical verification; they are the building blocks from which logic is derived.

         Gregory Bateson in Mind and Nature states:

Science never proves anything. Science sometimes improves hypotheses and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again.

         It has been a long personal search to even find the axioms of any given branch of science. Seldom are they clearly stated. The following discussion of twofold operators is an attempt to make clear and concise statements of the axioms of the relational paradigm.

Form/ProcessHierarchy/NetworkSequence/JumpMeasure/CountKnown/RandomBalance/RelationshipSummary of Emergent Axioms

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