Thr Principle of Duality

Establishing the Foundations

The Principle of Duality

Wholeness is the union of all opposites. This means that if we are to return home to Wholeness as a species, then we need to bring all opposites together in Consciousness. The result is a sense of Wholeness that is literally out of this world.

For this reason, it is quite impossible to describe this sense of Wholeness in words. To do so, I would need to make comparisons with something in your experience. This would inevitably be a violation of Wholeness, which is beyond compare. All I can do here is describe the process I have been through, which has enabled me to come ever closer to Wholeness. I trust that in so doing I can be of some assistance in your own search for Wholeness.

It is because Wholeness is ineffable that I coined the word paragonian in 1983. Paragonian is a word rather like maverick. Maverick cattle are those that are unlabelled, in contrast to other ranchers' cattle, which are branded with the owners' mark. Similarly, paragonians are those individuals who, at the root, cannot be categorized as belonging to a particular species, race, nation, religion, company, economic ideology, or whatever. In this sense, we are all paragonians, for we all share a common ground in the attributeless Absolute. But as a species, we have not yet learnt that we all live in a pathless land.

To remind you, paragonian literally means 'beyond conflict'. So when all opposites are merged in Consciousness, there is no longer any inner conflict, which brings us so much agony and suffering. We can live in peace, both within ourselves and with each other. Not that this is easy. For if it were, we would long ago have learnt to live in peace and harmony. For this is what we all yearn for deep down.

For myself, I cannot say that I have yet realized a full paragonian state of consciousness twenty-four hours a day. So I am still engaged in a process of freeing myself from the conflict of all opposites. But that does not mean that I cannot outline the process I have been going through for the past nineteen years. This I do on this page.

First of all, as relational logic is a nonaxiomatic, nonlinear form of reasoning, it is not constrained by Aristotle's laws of contradiction and excluded middle, as are mathematics and conventional deductive logic. Briefly, these state that an entity cannot have both attributes A and not-A, and that entities can have either the attribute A or not-A, but nothing in between.

But such laws cannot possibly apply to the Universe as a whole. There are many examples of entities with both attributes A and not-A. For instance, none of us is entirely feminine or masculine; we all have characteristics of both genders. Also, the world we live in is not black and white; there are many shades of grey.

So any model that purports to be a true representation of the totality of existence must take these essential features of the Universe into account. This means that as there are self-contradictions in the Universe, then the model must itself be self-contradictory. For if self-contradictions are eliminated from the model, just because they feel uncomfortable, then we would not be able to see the Universe just as it is.

Indeed, if I were to remove self-contradictions from my model, I would be violating my third principle of reasoning, namely consistency. I can only be consistent in my reasoning if I treat all patterns in exactly the same manner, including self-contradictions and paradoxes.

Alice in the looking glass We are thus about to enter a very strange world, a world that is not only unfamiliar to the Western mind, it also makes many feel most uncomfortable. But, at the same time, it can be quite attractive.

I can best illustrate this by Lewis Carroll's story of Through the Looking Glass and what Alice found there. Of course, Lewis Carroll was the pen-name of Charles Lutwidge Dodgson, a mathematics lecturer at Christ Church College, Oxford. And as such, Lewis Carroll/Charles Dodgson knew a thing or two about logic. Indeed, he wrote a book about it.

But as his profound stories reveal, he also subconsciously knew something about the world that doesn't fit neatly into our conventional reasoning patterns. That is why his stories strike such a deep chord in young and old alike. What Lewis Carroll is illustrating is a real world, but one that we rarely acknowledge in our culture today.

The story of Through the Looking Glass begins with Alice at home in a room that is familiar to her. Then she wonders what life would be like on the other side of the mirror. She pretends that there is a way of getting through it, and she suddenly finds herself in the looking-glass room, peering into the room she has just left.

Alice through the looking glass For me, this looking-glass room is not a room with walls at all. It is more like a vast open space where there are no borders, barriers, or divisions. The looking-glass is then more like a two-way mirror. While we are in the room, all we can see is the room and our own reflection in the mirror. But when we pass through the mirror, we can see not only into the room, but also the wide-open space outside.

It is a world of total liberation. In this world, there is no one around to shove you in a box, to nail the lid down, and to stick a label on the side saying SCIENTIST, BUSINESSMAN, POLITICIAN, SPIRITUAL TEACHER, or whatever. In this world, you are completely free to be and do whatever is in your innate nature to be or do.

However, this wonderful world is quite invisible from inside the room, from the prison cell that Alice left. For this reason, I really feel like an extraterrestrial on a visit to this planet. As I am invisible to those around me, I can watch the games that are going on on this planet, but I do not participate in them any more than I can help.

For I no longer belong to the cultural landscape that governs the world today. From the perspective of science, economics, and the traditional religious teachings of both East and West, I am quite invisible.

Be that as it may, you will recall that I began this experiment in learning by looking at the similarities and differences in the data patterns of my experience. Those that are similar, I put in one set, and those that are different, I put in different sets. In this way, I form concepts or mental images of both my inner and outer worlds.

Now there is one particular difference that is different from all the others. When I form a concept, I inevitably also form its opposite. For instance, darkness and light, night and day, morning and evening, and land and sea, some of the pairs of opposites mentioned in the opening verses of the book of Genesis.

There are, of course, many other example of opposites in existence. For instance, in physics light can be viewed as either a particle or wave, called complementarity by Niels Bohr. And the two fundamental theories of physics, relativity and quantum theories, have opposite properties, locality, causality, and continuity and nonlocality, noncausality, and noncontinuity, respectively. Then there are both physical and nonphysical energies at work in the Universe, the idea that triggered this synthesis of everything, of all opposites, back in the spring of 1980.

In society, there are Christians and non-Christians, Chinese and non-Chinese, capitalists and communists, men and women, black and white people, IBMers and non-IBMers, and so on and so forth. Then, of course, there are birth and death, growth and decay, creation and destruction, past and future, yin and yang, beauty and ugliness, solitude and companionship, excitement and depression, I and thou, science and religion, East and West. The list goes on and on.

Even the Absolute has the opposite properties of immanence and transcendence, of emptiness and fullness, of Oneness and Wholeness, of Godhead and God the Creator, of Consciousness-at-rest and Consciousness-in-action. And when we view the totality of existence as a whole, the formless, timeless Absolute is the opposite of the relativistic world of form. There is thus no escape from opposites. They exist wherever we look.

A wonderful sense of Wholeness arises when we embrace all these opposites, accepting them all, rejecting none. Wholeness arises when we look at both sides of every situation, of every story. It is a mark of natural intelligence. It is through Wholeness that all conflict ceases. It is by unifying all opposites that we can heal our sick society.

I encapsulate this basic property of existence in a statement that I call the Principle of Duality, an idea that came to me from the principle of duality in projective geometry during the third week in June 1980, just a month after I began this project. The principle of duality has been the fundamental guiding principle in my life ever since.

This is how I formulate the principle of duality in relational logic:

My conceptual model of the Universe consists entirely of dual sets.

A few points about this statement. By dual I do not just mean two, like twins or two apples. More specifically, I mean 'pairs of opposites'. In many instances, these pairs of opposites are opposing principles or ideas, like poles, but not always. So I prefer to use the word dual to polar here.

It is also vitally important to be clear about the distinction between duality and dualism. Dualism, as I use the term, refers to pairs of opposites that are seen as separate from each other. Cartesian dualism, which views mind and matter as two independent entities, is the classic example. But there are many others. Anyone who belongs to or identifies themselves with a political party, religion, business enterprise, nation, and so on opposed to other similar groups is acting in an essentially dualistic, exclusive manner.

From this, it is easy to see why we look at the world we live in in a dualistic manner. While we experience a self or ego that is separate from the Source of Life and hence from other selves, we are bound to create dualisms. It is only when the sense of a separate self disappears, even for a short time, that we can free ourselves of this schizoid behaviour.

In the first instance, this healing process leads to what I call duality, which embraces all opposites so that there is no division or separation between them, like two sides of the same coin. Duality, as I use the term, is thus opposite to dualism; duality is nondualistic. The principle of duality is thus unifying, not divisive.

The principle of duality is the second part of my data model of the Universe because it is true independent of any interpretation. Indeed, it would be better to say that it is the first part, for it is more fundamental than the statement about the unifying structure of the Universe. The way that I form concepts by looking at the similarities and differences in the data patterns of my experience is a reflection of the principle of duality. As is the fact that the underlying structure of the Universe consists of a network of hierarchies.

So, in a way, the principle of duality lies between the gnostic and ontological foundations of omniology; it is at a mezzanine level. This must be so, because as the Logos emerges to change formless into form, the first thing that happens is a bifurcation. This is well illustrated in the growth of the human body. Each and every one of us began our physical existence as a single fertilized ovum, which then divided into two cells, then into four, and so on.

But is the principle of duality completely true in the way that I have formulated it? Well, as it happens, it is not. There are many entities in the Universe that do not fall neatly into sets, they do not have a common property. I generally call such entities miscellaneous. So I cannot say that my conceptual model consists entirely of dual sets.

However, I can say that collections of entities with no common property have the common property that they have no common property. A collection of entities with no common property is then in the set of all collections of entities with no common property, which is the dual of the set of all sets by the definition of set.

Another way of showing that the principle of duality is an absolute truth is to deny it. Now this is just the opposite of accepting it, confirming the truth of this universal principle. The principle of duality is thus the governing principle of the Universe. When I say governing here, I do not mean this in a temporal sense, for the principle of duality embraces both time and the timeless.

Having shown that the principle of duality is false in some circumstances, this, of course, shows that it is after all true, as I have said. This must be so, for if the principle of duality is true, it must assert its own falsity. The principle of duality is thus something like the statement, "This sentence is false".

However, there is a difference. Statements like "This sentence is false" lead us into an endless loop. If this statement, and many others like it, is true, it is false. And if it is false, it is true.

On the other hand the principle of duality does not result in a loop. I can best illustrate this with Hegel's logic. If the thesis and antithesis are that the principle of duality is true and false, respectively, the synthesis is that it is true.

There is thus a primary-secondary relationship between these opposites, which is fundamental in learning to live beyond the conflict of all opposites.

Let us take the most fundamental of all dualities, nonduality and duality. We can regard nonduality and duality as the thesis and antithesis, which results in nonduality being the synthesis.

But then nonduality becomes the thesis to duality's antithesis, which once again can be resolved through nonduality, the synthesis. There is no limit to this process; it continues indefinitely, as the diagram illustrates.

This diagram showing the primary-secondary relationship between dualities represents the backbone of relational logic, the skeleton of the coherent body of knowledge that is produced when studying omniology. It is not very upright, but it is more convenient to draw it in this way.

But what exactly is nonduality? Is it just a concept that has no correspondence to human experience? We can best answer this question by looking first at duality. In a state of duality, opposites are distinct but connected to each other, not separate as they are in dualistic situations.

In a nondual state, on the other hand, all distinctions disappear; there is only a seamless unity. Now this is not a statement that the mind can understand, for it will immediately say that where there is one there is many. That is in the nature of the mind: to create divisions where there are none.

A nondual state of being is therefore mystical but not mysterious. It follows quite naturally from the process of reasoning that I am describing here. However, as we all live in the relativistic world of form, maintaining a state of nondual consciousness for twenty-four hours a day is not easy. Nevertheless, it can be done, as an increasing number of individuals in the world today are demonstrating.

Note here, that the principle of duality has taken us back to the gnostic level of the foundations of omniology. In this sense, it could equally be called the principle of nonduality; it just depends on which way we look at it. There is thus no more fundamental principle at work in the Universe. The nondual Absolute Whole embraces both itself and the relativistic world of form, as has been known in the East for the last few millennia.

The key point about nonduality is that it is timeless. In a nondual state of being, past and future are transcended in the eternal now. This means that there is no beginning and end of time. In Reality, there is thus no birth and no death. What we call birth and death are nothing more than energy transforming itself from one form to another.

In this nondual state of Consciousness, all fears die, for there is no longer any past to project into the future as worry and anxiety. It is a state of total liberation and utter stillness and peace. It is to this joyous, blissful realization that evolution is carrying us all.

The circle of duality

But back to the world of form. How can I accommodate Aristotle's Law of Excluded Middle or modern day fuzzy logic in relational logic? So far I have been considering dualities in terms of polarities or opposites. However, the universe is not solely black and white, as Aristotle apparently believed; it contains many shades of grey. So it is clear that Aristotle's Law of Excluded Middle does not hold in the Universe as a whole.

To see how we can represent these shades of grey in relational logic, let me consider a domain of discourse, 'all propositions'. Let us suppose that these propositions are either true or false. Then the Law of Excluded Middle holds, which we can represent by two points with nothing in between:

However, not all propositions are exclusively true or false. At any one time, we have many doubts and uncertainties about what is true or false. To represent these doubts, I can draw a line between the extreme points of the range to include the excluded middle, which represents statements whose truth or falsity I am uncertain about:

I now have a continuous domain of values for all propositions, which is bounded by those statements that are certainly true or false. So I can say that those propositions that are either true or false are in a set of certainties, which is the dual of the set containing those statements that are uncertain. In other words, the ends of the true-false spectrum of values can be considered to be the dual of the intermediate values.

Any domain of values that consists of a range from one extreme to the other can be put into the set of all entities with this property. This is a pattern that occurs very frequently in the Universe.

Now as the limits of such a domain of values have the common property that they are extreme values, I can bend the line that represents the spectrum of values to form a circle so that the ends join. I call this circle the Circle of Duality, which is depicted in this diagram.

Political systems provide a good example of the use of this tool of thought. Extreme left and right political systems, which are most commonly called communism and fascism, respectively, are both totalitarian forms of government, in contrast to more democratic systems that favour the individual, such as liberalism. Socialism and conservatism would then be represented by the left and right sides of the circle of duality, respectively.

I first saw this way of depicting the relationships between the main political attitudes in the world in a current affairs lesson as school when I was seventeen. The teacher who showed us this diagram was, of course, a liberal democrat.

Of course, political parties that represent these different approaches to politics are, of necessity, dualistic. This can be seen most clearly from the root of the word party, which is the Latin word partire, meaning 'to divide'. So to be attached to one or other of these parties for one's own selfish needs, or even to adhere to a political system consisting of parties, must inevitably lead to divisions in society. However, partire has some other meanings: 'to share out' and 'to distribute'. With this radically different view of party, we could, perhaps, begin to heal the divisions that exist in society today, and, who knows, all have a party to celebrate!

In this way, we could perhaps free ourselves of the tyranny of the majority, which so concerned Alexis de Tocqueville in the nineteenth century in Democracy in America, a concern taken up by John Stuart Mill in On Liberty. For in democracies as they function today, no one is responsible for what happens to individuals in society, as Barry Long points out in Only Fear Dies. In representative democracy, we give away our responsibility for the way we live our lives to the politicians. And they cannot possibly be responsible for all the suffering and unhappiness in the world. In consequence, we complain and blame others for our unhappiness and misfortunes, rather than taking the responsibility on ourselves.

Of course, no one is to blame for this tragic state of affairs, for evolution has brought us to where we are today. Paradoxically, it is only when we are free from the delusion that we have a free will that we can have the freedom to take full responsibility for our lives in community with others.

The triangle of duality

So, as we have just seen, Aristotle's Law of Contradiction does not apply universally, any more than the Law of Excluded Middle. It is not true that the attributes A and not-A cannot be applied to the same entity. Such paradoxes exist even at the foundations of mathematics. It is therefore necessary that a new, integrated approach to scientific inquiry is able to accommodate the reality of this situation.

Having considered statements that are either true or false and those that are neither true nor false, I must now consider statements of the type 'This sentence is false'. How can I represent this in my analysis of all propositions? I can do this by turning to the foundations of mathematics.

When Georg Cantor developed his set theory in the 1870s, it was soon realized that this theory could serve as the base for all mathematics. Until 1897, that is. For in that year, Burali-Forti discovered paradoxes in set theory; that is constructions that led to a contradiction. Subsequently other paradoxes were found in set theory, of which the best known is Russell 's paradox of 1905. This led to the famous 'crisis in the foundations' of mathematics, which has not been resolved to this day. For if set theory contained contradictions, it would be possible to prove any theorem and its opposite to be true, and the great edifice of mathematics would come crashing down. This situation is amusingly described in this little anecdote:

The analyst G. H. Hardy once made this remark at dinner, and was asked by a sceptic to justify it: 'Given that 2+2=5, prove that McTaggart is the Pope'. Hardy thought briefly, and replied, 'We know that 2+2=4, so that 5=4. Subtracting 3 we get 2=1. McTaggart and the Pope are two, hence McTaggart and the Pope are one.

I have seen a similar story where Bertrand Russell was the mathematician. I expect there are several versions of it. So how can I incorporate Russell's paradox into my conceptual model? Well Russell defined a set M as 'the set of all sets that do not contain themselves as an element'. Now is this set, M, a member of M or not? If it is a member, then M contains itself as a member, which is contradictory to the definition of M. But if M does not contain itself as a member, it should, by the definition of M, be included in M.

Let us see how we can represent such paradoxes in my conceptual model. I can define dual sets A and B that are the sets of all sets that do and do not contain themselves as an entity, respectively. If we assume that in the domain of discourse that we are considering that we are certain whether a set is a member of itself or not, then the Law of Excluded Middle holds. All sets must therefore be either in A or B. So which sets are A and B in? It is fairly obvious that set A is a member of A. But what about set B? As B is the set of all sets that do not contain themselves as a member, B cannot be a member of B for then B would then contain itself as a member. But neither can B be a member of A. For then A would include a set that was not a member of itself. So B, like M, is a set that is in neither A nor B.

Bertrand Russell and Alfred North Whitehead attempted to resolve this dilemma by their theory of types in the indigestible Principia Mathematica. But there is a far simpler way of resolving this issue. I have said that all concepts in my model are formed in exactly the same way, for if they were not, the model, as a whole, would not be consistent. So entities with similar properties are put into one set, while those with different properties are put into different sets. But now I have two concepts in my model, uncertainties and paradoxes that apparently have the common property that they are both neither true nor false. How I am to distinguish them?

Well, I have said that by the Law of Excluded Middle, all sets in the domain being considered must be either in A or B. So if set B is not in B it must be in A. Similarly, if B is not in A it must be in B. So I can say that paradoxes are those entities that are both true and false at the same time. By this definition we can see that the principle of duality, which is both true and false, is a paradox.

So, in conformity with the aim of the model to be complete and whole, I now have a means of classifying all propositions into three all-inclusive categories:

Certainties, which are either true or false.
Uncertainties, which are neither true nor false.
Paradoxes, which are both true and false.

These three classes form a complete set that can be represented by the vertices of a triangle, in which each vertex is the dual of the other two in some sense. I call this triangle the Triangle of Duality , which is illustrated opposite.

So paradoxes and uncertainties are those statements that cannot be handled by Aristotelian logic, the opposite of certainties. Certainties and paradoxes are combined because they both signify distinct values, in contrast to uncertainties. And certainties and uncertainties relate to each other because they both have a single value, contrary to paradoxes.

The cross of duality

This is as far as I took relational logic when I developed it between 1980 and 1983. However, I have long been aware of another geometric figure that well illustrates a common pattern with dualities, that is the cross. This figure arises when we consider two pairs of opposites, A and not-A and B and not-B. As this is such a common pattern, I think that it is worthwhile to consider it as part of the data model in relational logic. For this pattern exists across all disciplines, independent of interpretation.

The adjacent diagram illustrates the cross of duality. The characteristics of entities with all four possibilities of pairs of attributes can conveniently be placed inside each of the quadrants. There is no reason why this should be two-dimensional other than this is easily represented on a page or on a monitor. In principle, we could divide a domain of discourse into any number of pairs of opposites, resulting in a multidimensional cross of duality.

The example that I have used to illustrate the cross of duality for many years is Jung's psychological types. Jung considered four functions that we use to relate to the world, including our inner world. These are divided into two pairs of opposites, thinking and feeling, which Jung considered rational, and sensation and intuition, the irrational functions.

So in this case, we have additional pairs of opposites. In general, the pairs {A, not-A} and {B, not-B} are not related to each other. But in Jung's theory of psychological types, these pairs are themselves opposites. To illustrate the rational functions, thinking and feeling types make decisions based on an objective examination of the facts and by attaching a subjective value to something, respectively. In contrast, sensation and intuition types lead lives predominately based on what reaches them through the senses and the unconscious, respectively, without attempting to rationalize these perceptions.

On top of these two pairs of opposites, Jung also considered another dimension, his well-known extrovert and introvert types. So we really need to draw a three-dimensional cross to illustrate all these characteristics. There are thus extrovert and introvert thinking, feeling, sensation, and intuition types. Of course, no one individual is wholly within one of these eight categories. We all have characteristics in each of these octants. It is just that we have them in varying degrees as unique individuals.

This example illustrates a key point in relational logic. I do not need to understand Jung's analysis in detail to see the underlying patterns in his reasoning. This approach to learning helps greatly whenever I'm faced with any new domain. In conformity with the principle of simplicity, I begin by looking at the simple patterns, which I can then use to build more complex structures as necessary.

This is especially necessary when attempting to read as complex a writer as Ken Wilber. Which brings me to the primary reason why I have added the cross of duality to relational logic. In his recent writings, Ken makes much use of the simplicity of the cross of duality in explaining his four-quadrant model of the Kosmos.

In this model, A and not-A are individual and collective, and B and not-B are interior and exterior. The key point here is that we need to look at all four of these quadrants if we are to develop an integrative view of the Kosmos. Yet, because of our fragmented approach to learning in the past, few have yet been able to do this. Indeed, scholars in each of these quadrants have often been at war with those in the opposite quadrant, apparently unable to see all sides of the situation, such is the limitation of the dualistic mind.

The upper-left quadrant concerns the subjective realm of interior-individual, the world of I. The students of this realm are typically depth psychologists and spiritual teachers, such as Sigmund Freud and Gautama Buddha. The exterior-individual, objective world is studied by the behaviourists and mainstream scientists like B. F. Skinner, Stephen Hawkings, and Richard Dawkins. This is one half of the world of it.

The second half of the it-world is the lower-right quadrant, the exterior-collective, which concerns social systems viewed empirically. Systems theorists, such as Ilya Prigogine and Fritjof Capra, and economic philosophers, like Karl Marx, typify the scholars in this realm.

And fourthly, there is the interior-collective or cultural realm in the lower-left corner of the cross of duality. For me, this is by far the most important of the four quadrants because this provides the cultural context in which we interpret our experiences and relate to each other in community. It is especially important at this time with the approaching death of Western civilization and the global economy.

It is from this quadrant, then, that we shall make the scientific and cultural transformation that is so urgently needed in the world today. It is not surprising, therefore, to find that Ken puts Thomas Kuhn, the author of The Structure of Scientific Revolutions in this quadrant. Another I would put here is Erich Fromm, who sought to synthesize and deepen the two adjacent quadrants, most specifically the works of Freud, the Buddha, and Marx.

Now, the overall context for all cultures is the Absolute or Consciousness, the primary reality, as a growing number of people are acknowledging. We therefore need to look more carefully at Consciousness, which I do on the next page.

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