Chapter 3


“It is a primitive form of thought that things either exist or do not exist” (Sir Arthur Eddington, quoted by McFarlane 2002: 46).

“The closer one looks at a real-world problem, the fuzzier becomes its solution” (Lotfi Zadeh, founder of fuzzy set theory, quoted by Bart Kosko 1993: 148).

Contents: Introduction - Logic - Identity - Either/or Logic - Both/and Logic - Fuzzy Logic and Fuzziness - Semantic Interlude - Fuzziness in Science - Fuzziness in Religion - Fuzziness in Ethics - Fuzziness in Law - Fuzziness in Politics - Fuzziness in Everyday Life – "Mandala" as a Fuzzy Set - From Fuzzy Sets to Fuzzy Systems - Yin-Yang - Yin-Yang and Fuzziness - Nature is not Perfect - A Joke - Plato and Aristotle - Polar Opposites - Love and Hate - Life and Death - Other Polar Opposites - Beyond Polar Opposites - Standing Meditation - Standing with a Tree – Summary - References - Quotes

Introduction


Exactness seems to be appreciated by most people in our culture, whereas fuzziness is often perceived as negative and undesirable. In this chapter I want to show that, contrary to this common view and belief, fuzziness can be positive and desirable. In fact, it is not what most people think it is. But before I can go into this, I have to make some remarks about logic, which is considered the home of exactness. In this chapter,exactness is defined as sharpness. Hence, a more descriptive title of this chapter would be “Fuzziness and Sharpness.” However, if exactness is defined as precision, then it turns out that fuzziness is often more precise than sharpness as I will show below after a brief discussion of logic.

Logic

Science and philosophy are supposed to be logical, but life and living are often paradoxical, etc. Poetry speaks to the heart, to our intuition and emotions, often conveying its deepest message between the words and lines. Logic, however, involves exactness and appeals to the head and reason.

In the West logic originated in ancient Greece, especially with Aristotle. We can distinguish
four laws of logic that have become deeply entrenched in Western culture, science and philosophy. Arber (1964: 82) articulated them as follows:
1. The law of identity (“A is A”; for example, I am I).
2. The law of contradiction (“A is not both A and not-A”; for example, I am not both I and not I).
3.The law of the excluded middle ( “A is either B or not-B”). In other words, the law of either/or thinking; for example, I am wise or not wise.
4. The law of sufficient reason (“every consequent has a ground from which it necessarily follows”).

Although these laws appear to make much sense, they are only of limited
usefulness. With regard to the law of identity, it can be pointed out that I am not only I, but also my environment. Scientists such as Rose, Kamin, and Lewontin (1984: 272-277) and Lewontin (1991) pointed out the interpenetration of organism and environment. From this perspective, I am also my environment, at least to some extent. Mystics have gone further when they say: I am the Universe, or I am God (see also
Chapter 1 of this book).
The law of contradiction is limited for the same reason. I am not only I, I am also my environment, which may include the whole Universe.
The law of the excluded middle is often invalid because I may be both B and not-B, I may be wise and unwise, that is, wise in some respects and unwise in others (for more examples see below).
The law of sufficient reason may also be questioned because consequences do not always follow by necessity from their ground; there may be spontaneous events as well as capricious and chaotic changes; even in physics events are not always predictable (see Chapter 11).

Identity


Before turning to either/or thinking, which is one of the central topics of this chapter, a few remarks about identity. It has become fashionable all over the world to reassert and even fight for identity, identity such as personal identity, social, religious, ideological, ethnic, racial and national identity. People want to identify with something. Identification provides them with security, pride and other crutches.

All over the world we see much conflict and uprising because of the obsession with identity. People even go to war and kill in the fight for identity. Countries are torn apart or threatened to be cut up because of identity- seeking separatists. For example, French Canadian separatists have been trying for a long time to separate Quebec from the rest of Canada so that they can rejoice in their French Canadian identity. Atrocities in the name of identity occur when identity is taken as an absolute. But as I pointed out, neither logic in general nor the law of identity are absolutes. This means that I am not absolutely identical with anything or any group. I am always more than anything or any group. If there is any identity at all, it is identity with the whole universe. The experience of this identity requires, however, deep meditation or enlightenment.
Of course, we relate more deeply to some things or some groups than to others. However, this does not mean that there is an identity. As long as we retain at least some openness we can see that we also relate to many other things or groups. Our relations are manifold and varied. To single out one of them in the name of identity seems a gross oversimplification. For example, even if I feel very close to my family, there is no identity. I may also feel very close to friends and there is a varied closeness to many other people and things. Therefore, we can conclude that
identification with a thing or a group or whatever is a tragic misuse of the logical law of identity. Such misuse is, of course, unconscious most of the time. Awareness of our conditioning therefore seems of paramount importance.

Many people would insist that identification is an emotional issue, unrelated to logic. However,
emotions appear to be combinations of thought and logic with body sensations (feelings) (see, for example Shinzen Young 1997, Sessions 5, 6). Hence, logic is at least one of the roots of identification. And therefore it seems important to create more awareness of the logic we use and how it shapes our lives and living. I often encounter people who tell me that they are not interested in logic, yet they use a logic and often an inappropriate one such as either/or logic.

Either/or Logic


The law of the excluded middle, that is, either/or logic, is particularly relevant to fuzziness and exactness, whereby exactness should be understood as sharpness (having a sharp boundary).
Our culture appears deeply permeated by either/or logic. Therefore, we often take is for granted that, for example, someone must be either guilty or innocent, that someone is either good or evil, saint or sinner, enlightened or ignorant, that something must be either true or false, etc. This kind of thinking culminates in the attitude "I'm right and you are an idiot," as Hoggan (2016) put it, referring to it as a toxic state.

This kind of thinking in terms of either/or seems to be so much taken for granted that it even forms the basis of the questions we ask, which means that we ask either/or questions such as “Is this true or false?” or “Is it this or that?”
When confronted with such questions, we are expected to conform to either/or logic by answering in an either/or fashion. We could, of course, point out that the question seems inappropriate. But who does that? Not too many people. It requires deep insight. However, sometimes even less educated people - or especially less educated people? - point out that, although a statement appears to be false, there is a grain of truth in it, which cancels the either true or false logic.

Apart from our conditioning through an almost incessant stream of either/or questions and answers, we are increasingly dominated by computers, which are mainly digital computers that obey either/or logic, also called binary logic of either 1 or 0. Considering all these influences, it does not seem too surprising that many people tend to think that you are either with me or against me. And if you are against me, then the question is how do I deal with you. A violent person may attack you or even kill you. A violent nation may go to war if the “you” is another group or nation. Thus,
a strict adherence to either/or logic can have far-reaching and often disastrous consequences that may affect all aspects of our personal lives and society.

Both/and Logic


Contrary to a widespread misconception, either/or logic is not the only kind of logic available. There are alternative kinds of logic. Both/and logic is one of them. According to this logic, A is not either B or not-B,
A is both B and not-B. For example, an electron can manifest as both particle and wave; a man can be both good and bad; a nation can be both peaceful and aggressive. Many scientific theories that at first sight appear antagonistic to each other can be seen as complementary, and therefore the question does not arise which one has to be discarded; both can be accepted. Similarly, many philosophies and points of view that appear contradictory can be seen as complementary. For example, mechanism and holism can complement each other: thus it can be both mechanism and holism, both the outer and inner circles of the mandala of this book, both science and art, both science and spirituality (see Fischer 1987 for more examples).
Expressing this as a haiku, I can say:

The sun is setting in the West
And the moon is rising in the East
I can see both at the same time.

Ryokan, the Japanese Zen Master, wrote the following haiku:

Showing its back
and showing its front,
a falling maple leaf.


Whereas either/or logic appears antagonistic, both/and logic tends to be reconciliatory. If you propose a theory that is opposed to mine, according to both/and logic, I need not necessarily refute your theory and possibly fight with you as it so often happens between adherents of contradictory theories; as long as your theory offers something that mine doesn't, I can embrace your theory and you because your theory complements mine. Having two theories therefore seems better than just one; it can be seen as enrichment, whereas according to either/or logic it may be a thread. It is, of course, possible that one of the two opposing theories can explain more phenomena than the other. But this need not mean that therefore the other theory is totally useless. It might offer something that is lacking in the theory with greater explanatory power (see Complementarity and Chapter 9). Or in some cases one of the contradictory theories may indeed be completely wrong. But since neither proof nor disproof seems possible, we have to be careful before we discard any theory (see Science: its Power and Limitations)

Either/or logic seems exclusive, whereas both/and logic tends to be inclusive. The ally of either/or logic is fear, fear that I will be refuted by you, that I will be the loser. The ally of both/and logic is affirmation and love. I may affirm also your point of view and I can love you even when your point of view contradicts mine.

Both/and logic even accommodates either/or logic. Therefore, the question is not whether it should be only either/or logic or both/and logic. Such a question would entail either/or logic. Both/and logic in a consistent way implies that we can use both both/and logic and either/or logic. The latter can be useful to a certain extent and in certain situations. It becomes harmful when it is claimed that it is the only valid logic. When in addition both/and logic is recognized, we have a richer logic and are better equipped to deal with the world and ourselves.
Both/and logic has the potential to lead us beyond many stalemates and intractable situations; it can lead to deep transformation at a personal, social and global level; it can lead to profound integration and wholeness without inner and outer divisions (see, for example, Osho, 2000:216).

Both/and logic is part of Buddhist and Jain logic, which were founded long ago. Unfortunately, Western logic has been dominated up to the present time by Aristotelian either/or logic.

Fuzzy Logic and Fuzziness


Besides both/and logic and either/or logic still other types of logic have been developed, especially during the last century. One of them is three-valued logic in which statements may be true, false, or indeterminate. This logic seems useful when we deal with situations that may be indeterminate such as in quantum physics. In multivalued logic there are many values between true and false. Finally, instead of having discrete values, in fuzzy logic there is a continuum between the extremes; for example, a continuum of true and false ranging from 0% true (=false) to 100% true.

Now,
it is not only logical truth or falsehood that are fuzzy. Many phenomena are fuzzy so that Kosko (1993) in his book on “Fuzzy Thinking. The New Science of Fuzzy Logic” referred to a “fuzzy world view.” The importance and far-reaching consequences of this worldview cannot be emphasized enough. This worldview seems indeed revolutionary. It allows us to perceive the world differently. On this view, the world is not just black and white, but has a rich and varied gradation of grays; it is not just discrete colors, but has also a fascinating mingling of colors. In general, it is not only categorical, this or that, but a continuum spanning the categories.

In
Chapter 2 I illustrated the continuum between things or entities such as the earth and the sky. In this chapter the emphasis is on classes or sets of things or entities such as the set of all human beings. Although words may refer to individual entities such as your friend Diana, often they refer to sets of things or entities such as men or women.

How are sets defined? In traditional either/or logic, x is either a member of set y or not. For example, one is either a member of the set of men or one is not, that is, one is a man or not, or one is a woman or not. According to fuzzy logic, which is also called fuzzy set theory, this changes radically:
according to fuzzy set theory, membership in a set ranges from 0% to 100%. Thus one can be a partial member of a set; for example, someone could be a 50% member of the set of men and at the same time a 50% member of the set of women. And we know that such partial members do indeed exist. There are people who are physically intermediate and in the past (and still today?) they had to undergo painful operations to conform to our categories of either/or logic. They were violently forced into our man-made categories. This is only one example that shows the potential violent consequences of either/or logic. In contrast, fuzzy set theory does not harbor such violence because it accommodates the whole range of intermediates.

Fuzzy set theory does not only deal with relatively rare cases of intermediates such as the physical intermediates between men and women. More importantly, it reveals and emphasizes fuzziness where we do not expect it or do not notice it sufficiently. As a result, it changes our view of the world. After some semantic clarifications in a semantic interlude, the following sections will point to the significance of fuzziness in different aspects of life and living.

Semantic Interlude


As I pointed out already, in this chapter I use “exactness” in the sense of “sharpness”, sharpness that divides everything sharply into either this or that. This means I use “exactness” as a synonym to “either/or”. Obviously, “exactness” has also other connotations. For example, it can mean “precision”. If “exactness” is used in this sense, then fuzzy logic in the sense of fuzzy set theory is as exact as either/or logic and even more exact because it is quantitative. It is not vague.

“Fuzziness” in a broad sense may refer to fuzzy logic in the sense of fuzzy set theory as well as to a logic that recognizes the “more or less” without insisting on quantification as in fuzzy set theory. I use “fuzziness” in this broad sense and thus the following examples of fuzziness in life and living comprise both quantitative and non-quantitative fuzziness.

Finally, many people just do not like the words ‘fuzziness’ and ‘fuzzy,’ probably because they associate them with vagueness. But as I pointed out already, fuzzy logic is not vague; because it is quantitative it is even more precise than either/or logic and it represents the fuzziness inherent in reality more adequately than either/or logic. Nonetheless, without changing any of the meaning, the word ‘fuzziness’ could be replaced by ‘continuum’ and ‘fuzzy’ by ‘continuous,’ and thus we could refer to ‘continuous logic’ instead of ‘fuzzy logic’. Other alternatives are ‘grey logic’ or ‘cloudy logic’ (Kosko 1993: 292). But I prefer the words ‘fuzzy logic’ and ‘fuzziness’ because they are commonly accepted in the fuzzy literature and have been used by Lotfi Zadeh, the inventor of fuzzy set theory (see Kosko 1993).

Fuzziness in Science


To illustrate fuzziness in science let me use an example from my botanical research: the fuzzy sets of organs in plants (see, for example, Sattler 1994). According to the still prevalent view (called the classical view) that is based on either/or logic, the whole diversity of organs in plants (such as flowering plants) is reduced to three mutually exclusive categories: root, stem and leaf. This means that every plant organ we find must be either a root, a stem, or a leaf. Contrary to this classical doctrine of mainstream botany, my research and the research of some of my colleagues has shown that although the vast majority of plant organs are typical roots, stems or leaves, there is also a range of organs that are more or less intermediate between the typical organs. These intermediates share features of more than one organ category. For example, they may combine features of a typical stem and leaf. As a result, the organ categories overlap and thus are fuzzy sets. Sattler and Jeune (1992) and Cusset (1994) determined quantitatively the degree to which the intermediates are members of the fuzzy sets of root, stem and leaf. More recently, corresponding fuzziness has been reported with regard to the genetics of some of these intermediate plant organs (see Rutishauser and Isler 2001).

Now let us not throw out the baby with the bath water. Let us not conclude that categorical either/or thinking is totally inappropriate because the plant world is fuzzy. As long as we deal only with typical roots, stems or leaves it appears all right and convenient to use either/or logic because these organs can be clearly assigned to the root, stem or leaf categories. However, when we come across intermediates we need fuzzy logic. And when we look at the total picture that comprises typical as well as intermediate organs, fuzzy thinking is also required because only fuzzy thinking can deal with the whole continuum ranging from the typical organs to the more intermediate ones.

Many other examples of fuzziness from various scientific disciplines could be given. The more we know, the fuzzier the world appears.
Kosko (1993) concluded that everything is fuzzy when we have a very close and precise look at it.

Fuzziness in Religion


Religions have been divided into theistic religions such as Judaism, Christianity and Islam, and atheistic religions such as Buddhism and Daoism. Similarly, people have been assigned to two sets: theists and atheists. According to either/or logic, you must be either a theist or atheist, that is, you either believe in God or you don’t. Although this distinction may be useful as long as we restrict ourselves to typical representatives of theistic and atheistic religions, when we consider the whole spectrum of religious views and experience, the two sets of people become fuzzy. Why? Because God can be defined and experienced in so many ways that span the whole spectrum form the God of a typical theist to the denial of God by the typical atheist. Let’s begin with the God of the typical theist. I would say it is a transcendent God, a God beyond Nature. From this view, one step closer toward atheism, although not yet atheism, is the view that god is both transcendent and in Nature. One more step in the direction of atheism is the view that that God is in Nature. And finally there is the view that God and Nature are synonymous. This view is very close to atheism, if not atheism, because an atheist could argue that if there is no God apart from Nature, then Nature is all there is and God is just another name for Nature, but a name that an atheist will not use (see also Arber 1967: 34).

Fuzziness in Ethics


According to either/or logic, any action is either good or bad, good or evil. This again seems an oversimplification because there are actions that are more or less good and more or less bad. Some people would go even further claiming that no action could be 100% good or 100% bad (see below). Hermann Hesse (1957: 115) wrote in “Siddhartha”: “Never is a man or a deed wholly Samsara or wholly Nirvana; never is a man wholly a saint or a sinner”.

Fuzziness in Law


Fuzziness also affects law. In fact, as Kosko (1993: 263) put it, “Law is a fuzzy labyrinth. A legal system is a pile of fuzzy rules and fuzzy principles...Try to draw a line between self-defense and not self-defense or between contract breach and not breach... Every rule, principle, and contract has exceptions”. As a result the line between guilty and not guilty may also vanish in fuzziness. Yet where the line is eventually drawn more or less arbitrarily may enhance or ruin someone’s life or may even be a matter of life and death. “Lives and careers and psyches depend on how we split balls of legal fuzz into A AND not-A, how we work with guilt, intent, premeditation, malice, threat, duress, equity, fairness, reasonability, acquiescence, duty, obligation, partiality, conflict of interest, damage, and property right” (Kosko 1993: 263).

Fuzziness in Politics


Fuzziness occurs also in politics. We can see a continuum between the political right and left, between capitalism, socialism and communism, between grey and green. The labels that are often attached to people tend to obscure that they may be only partially characterized by those labels. We are often more or less than than what the labels say we are. Much injustice has been done to people because political fuzziness has not been sufficiently taken into consideration.

Fuzziness in Everyday Life


Our everyday life and living seems also permeated by fuzziness. Kosko (1993: 126) illustrated this by the response of an audience. When we ask an audience who is married, a clear-cut answer will be obtained because marriage is an institution regulated by law. However, when we ask who is happy, or honest, or moral, or jealous, or intelligent, or tall, or overweight, many people may often find it difficult to give a clear-cut answer because any of these issues and many others appear fuzzy: one can be more or less intelligent, more or less happy, etc. Where does one draw the line between happy and unhappy or tall and short? Any line seems arbitrary. For the extremes, an answer can be given. But between the extremes - and many people are between the extremes - only a more or less arbitrary answer seems possible. A very close look may reveal that even the extremes are not totally free of fuzziness because even a happy man may still harbor very small pockets of unhappiness. Thus, the recognition of fuzziness may create awareness that we are much more or less than we normally think we are according to the labels we carry. Kosko (1993: 127) wrote: “We are all left, right, center, straight, gay, bi, cool, square, plain, for, against, and indifferent.” We may be any of these only to an extremely small degree, or only potentially. But knowing that we are all that - and much more - can help us to connect to others who appear to be very different because they occupy a different place in the continuum.

"Mandala" as a Fuzzy Set

We can find all sorts of configurations that resemble typical mandalas more or less. Asking whether they are essentially mandalas or not is not helpful because mandalas cannot be sharply delineated from non-mandalas: mandalas are therefore best conceived as a fuzzy set. Thus, a configuration that does not represent a typical mandala but has nonetheless something in common with a mandala may be considered a mandala to some degree or some extent.

The following painting by Ulrich Panzer may be located somewhere at the fuzzy edge of mandalas. Like a typical mandala it has a circular form, but unlike a typical mandala the centre is not empty, unless one interprets the centre as emptiness.



Untitled painting by Ulrich Panzer

Another example of a configuration at the fuzzy edge of mandalas is Ken Wilber’s AQAL map of the Kosmos (see Chapter 2). Contrary to a typical mandala that portrays the unnameable (emptiness) in its centre, Wilber’s map has emptiness at the periphery. Reynolds (2016) presented an interpretation of Wilber’s AQAL map that resembles more a typical mandala. He also included a typical mandala (“Kosmic Mandala”) with spirit and mysticism in the centre and matter at its periphery.

One could define “mandala” in such a wide sense that it encompasses all the untypical cases. But even then one would encounter configurations that do not fit completely the broad definition and thus even the broad definition would become fuzzy.

From Fuzzy Sets to Fuzzy Systems


As I pointed out above, words can refer to fuzzy sets. Often it is a noun that refers to a fuzzy set such as “man” referring to the fuzzy set of all men. Adjectives also refer to fuzzy sets. For example, “old” is fuzzy because it has no sharp limit. The combination of a fuzzy adjective with a fuzzy noun such as “old man” obviously is fuzzy. Verbs also can refer to fuzzy sets. For example, since there is a continuum between walking and running, “walking” is a fuzzy set as well as “running”.


As words form sentences and sentences paragraphs, so fuzzy sets can be combined into fuzzy systems. A fuzzy system is “a set of fuzzy rules that converts inputs to outputs” (Kosko, 1993: 293). A fuzzy rule relates fuzzy sets. Every term in a rule is fuzzy (Kosko, 1993: 159).

Researchers using fuzzy systems have been able to built many smart machines: fuzzy air conditioners that prevent overshoot-undershoot temperature fluctuations, thus consuming less on-off power; fuzzy dishwashers, fuzzy humidifiers, fuzzy washing machines, fuzzy cameras, fuzzy camcorders, etc.

I find it interesting that fuzzy machines were first produced in Japan and the Far East. The West, including America, resisted the use of fuzzy logic because it contradicted its deeply embedded tradition of Aristotelian either/or logic. But Japan and the Far East, being predominantly Buddhist, has not been as deeply conditioned by Aristotelian either/or logic and for that reason has been more open to the use of fuzzy logic (Kosko 1993). The Buddha was not a logician and definitely not an either/or logician. According to Kosko (1993: 69), he said: “I have not explained that the world is eternal or not eternal. I have not explained that the world is finite or infinite”. Thus, for the Buddha, the question was not: Is it this or that? Because it is neither this, nor that, it is beyond this and that. And thus the Buddha transcended the limitations of either/or logic and logic altogether, which opened up the mystery (represented by the empty centre and ground of the mandala of this book and the mandala as a whole).

Yin-Yang


According to Daoism, the mystery arises out of the union and transcendence of Yin (contraction) and Yang (expansion), which are the two most fundamental energies of the universe. Yin and Yang are graphically illustrated in the well-known
Yin-Yang symbol.

Yin-Yang symbol


This symbol expresses both/and logic, fuzziness and the continuum in a double sense: 1. The Yin containing within itself the Yang, and vice versa, (indicated in the symbol by the small circles within the Yin and Yang), represents fuzziness and both/and logic. That is, since the Yin contains Yang, it is not purely Yin, but also to some extent Yang. Similarly, the Yang is also Yin to some extent. Hence, Yin is both Yin and Yang and Yang is both Yang and Yin, which renders both of them fuzzy. Either/or logic does not apply. 2. The Yin gradually merging with the Yang along the periphery of the circle, and vice versa, can be seen as a continuum. Again, either/or logic does not apply.

Since according to Daoism Yin and Yang are the two most fundamental forces in the universe and everything is an expression of them, there does not seem to be any room for either/or logic. However, a closer look at the notion of fuzziness in relation to Yin-Yang leads to a more balanced conclusion.

Yin-Yang and Fuzziness


As I pointed out, membership in a fuzzy set can range from 0% to 100%. 0% is total exclusion from the set, and 100% total inclusion. That is, 0% and 100% are the two values of either/or logic, no and yes. Thus, either/or logic can be seen as a special case of fuzzy logic that in addition to the two extremes of 0% and 100% also covers the whole range between these extremes.

Yin-Yang, although fuzzy, excludes the extremes of 0% and 100% because 100% Yin and 100% Yang do not exist. Yin and Yang always contain their opposites to some extent. 0% Yin and 0% Yang are equally impossible because some Yin or Yang are always present in their opposites. Since the Yin-Yang fuzziness excludes the extremes of 0% and 100%, it also excludes either/or logic as a special case. This kind of fuzziness I call radical fuzziness. It appears to be radically opposed to Aristotelian either/or logic. But a practical reconciliation seems possible nonetheless. Let me illustrate this by a circle. According to Kosko (1993:45) there is no perfect circle. There are only approximations to a perfect circle. In the case of a hand drawn circle this is obvious. But even in a circle made with a compass or other sophisticated technology minute deviations are detectable, if not macroscopically, at least through microscopic inspection. What does this mean with regard to fuzziness? It means that all fuzziness seems radical fuzziness and thus we can drop the term “radical fuzziness” because fuzziness implies that it is radical, which means that contrary to what I wrote above, the extreme values of 0% and 100% are not available.
It seems that only approximations of 0% and !00% exist; but at least some of these approximations may be so close that for all practical reasons we may consider them as 0% and 100%. And this I consider the practical reconciliation between Yin-Yang and fuzzy logic that includes Aristotelian either/or logic as a special case in a practical sense.

circle
Zen Circle

Nature is not Perfect


Nature is not perfect. Zen Masters know it. For this reason, it is not surprising that they have drawn obviously imperfect circles, imperfect from the point of view of traditional Western geometry. Contrast this with Plato’s philosophy. It is said that at the entrance of his academy was written: “Let no one enter here who is unacquainted with geometry.” Why? Because for Plato (probably at least in one phase of his life) pure, perfect forms were the essence of things. Perfection in this sense was crucial. And since Plato had such an enormous influence on the Western mind, the Western mind became obsessed with perfection. As a result, it became alienated (to some extent) from Nature, which is not perfect in this sense, but rather fuzzy. Nonetheless, as we enter the centre the mandala of this book and the mandala as a whole, even fuzziness is transcended. Absolute reality is neither binary, nor fuzzy. It just is. And what it is, cannot be expressed through language as Korzybski has demonstrated by his Structural Differential.

A Joke

Osho (!999: 200) told the following joke:

Randy Mustaver is telling his friend that he has toured the whole world looking for a perfect woman.
“Did you find her?” asks his friend.
“Yes, I did,” replies Randy. “But it is a sad story.”
“Why is that?” asks the friend.
“Well” says Randy, “she was looking for a perfect man.”


Plato and Aristotle


Plato and Aristotle tried to capture the essence of things and therefore it is often said that they espoused a philosophy or worldview of essentialism. What is essentialism? Different definitions can be given and there is a difference between Plato’s and Aristotle’s essentialism. But in general one may say that essentialism reduces the manifoldness of existence to essences and these essences are considered to be the ultimate reality behind the floating diversity of appearances. According to Plato’s essentialism, the essences are non-material and their manifestations are like shadows, whereas according to Aristotle’s essentialism the essences are inherent in their manifestations. Examples of essences are redness or goodness. Thus something may be essentially red or essentially good. It seems obvious that essentialism is based on or reflects either/or logic. If something is essentially good, it cannot be bad at the same time. Even if there appears to be something bad in it, it is just an appearance, not its essential nature. In a way such a view is misleading and distorting and therefore can be limiting, fragmenting and even destructive. If, for example, somebody is thought be essentially evil, how can he be related to people who are said to be good? He may be mistreated in the worst way as it so often happened during the history of humankind.

Both Plato and Aristotle continue to have an enormous influence on the Western mind. Whitehead wrote that the whole Western philosophic tradition can be seen as footnotes to Plato. Aristotle was considered
the philosopher by Thomas Aquinas who incorporated his philosophy into his own that became basic to Christianity. Both within and outside Christianity Aristotle’s logic has remained fundamental to our thinking up to the present time. Even in most of the sciences such as the life sciences his logic informs mainstream thinking to a great extent, and the logic of digital computers is binary, that is, Aristotelian. Fuzzy logic is still far from being generally recognized in science and society. Our everyday lives are still permeated by Aristotelian logic. Most people are not even aware of how much their lives are conditioned by this kind of logic. Therefore, it seems important to draw attention to our enslavement in either/or logic and essentialism.

Although the lasting domination of essentialism and either/or logic has been limiting and destructive in many ways, let us not put all the blame on Plato and Aristotle. Like all great philosophers, both Plato and Aristotle could also rise above essentialism. Unfortunately, this is often ignored or forgotten. If you read, for example, what Wilber (2000) wrote about Plato, you may see that his essentialism was only part of his total philosophy
and that his total philosophy was rather comprehensive. Aristotle’s philosophy was also broader than just an either/or philosophy, although the either/or was basic to his logic. In other writings he also referred to the “more and less” which is characteristic of fuzzy thinking.

Polar Opposites


After this historical diversion, let us return to Yin and Yang. Yin and Yang are considered polar opposites. Polar opposites are opposites that cannot be separated from each other because they cannot exist without each other. They are united in a larger whole, which is polarized. Electricity presents an example of polar opposites. An electrically charged rod has a plus and minus pole. These poles cannot be separated from each other. If you cut the rod in half, each half has again a plus and a minus pole. Therefore, trying to obtain the positive without the negative seems impossible.

In a broad sense Yin-Yang can be seen as a symbol for all polar opposites such as darkness and light, female and male, negative and positive, etc. (see below).

Love and Hate


It has been said that love and hate are polar opposites; not spiritual love, but erotic or romantic love. If this is so, then falling in love, sooner or later will generate hate. Observing lovers seems to confirm this. Schellenbaum (1998) distinguished three phases in romantic love relationships that may occur sequentially or more or less simultaneously. Thus, at first lovers become wonderfully absorbed with each other, feeling almost like one super organism. This phase has been called the fusion phase. It is usually followed by its opposite: the phase in which separateness and differences between the lovers are strongly asserted: “I am like this and I don’t want to be like you. Leave me alone.” In this phase waves of hate may confront or even overwhelm the two lovers. Often the relationship breaks up in this phase. However, a third phase of reconciliation, understanding and tolerance may allow lovers to reach a calmer sea. In this phase lovers try to accept each other as they are, and they learn from each other. This phase may culminate in spiritual love, divine love that has no polar opposite because it transcends ordinary love and hate. This love also opens the door to the universe. Through the beloved one loves all (see also Chapter 1).

Life and Death


Life and death can also be seen as polar opposites that belong together (see also Chapter 1). They follow each other in time and they coexist even at the same time. Look at a plant such as a flowering plant: in order to live, some of its cells have to die so that after the disintegration of their living content they can conduct water from the roots high up into the stems and leaves. A plant cannot live without the death of these water-conducting cells. The life of the plant requires the death of some of its cells. Thus life and death belong together.

In animals and humans cells also die regularly and are replaced by new cells so that the organism can function. Imagine for a moment you were one of these dying cells. You might bemoan your death and perceive it totally negatively as so many people in our society experience death. However, if you look at the death of this cell from the perspective of the whole organism, it is no longer negative. This death makes life of the whole organism possible. Similarly, the death of individual organisms supports the life of the whole ecosystem of which the organism is a part as the cell is a part of the organism.

Also remember that neither cells nor organisms exist as separate entities (see
Chapter 1 of this book). They are one with their environment, which ultimately is the whole Universe. From this perspective, no-thing dies because there are no things. Thus, there is only transformation. In this transformation the polar opposites of life and death are transcended.

Polar opposites exist only in the realm of the relative where we make distinctions such as those between cells and organisms. In ultimate reality polar opposites are transcended in oneness (nonduality).

When asked to speak about death, Kahlil Gibran’s Prophet said:

You would know the secret of death.
But how shall you find it unless you
seek it in the heart of life?
The owl whose night-bound eyes are
blind unto the day cannot unveil the mystery of light.
If you would indeed behold the spirit of
death, open your heart wide unto the body of life.
For life and death are one, even as
the river and the sea are one.


Other Polar Opposites


Are all opposites polar opposites? Many opposites have been considered polar by various authors. Here is an incomplete list:
matter and mind, body and mind, reason and emotion, pleasure and pain, tension and relaxation, self and not-self, self and other, inwardness and outwardness, good and evil, day and night, summer and winter, beauty and ugliness, success and failure, freedom and bondage, appearance and reality, becoming and being, being and non-being, separation and synthesis, unfoldment and infoldment, the many and the one, East and West, meditation (the art of being alone) and love (the art of being together), in and out breath, heaven and earth, local and universal, limitation and unboundedness, heat and coldness, wetness and dryness, softness and hardness, emptiness and fullness , rest and action, water and fire, sadness and happiness, substance and energy, gravity and levity, concentration and expansiveness, etc.

Even if some of the above opposites were not polar, there are still so many polar opposites that is seems no exaggeration to say that
existence appears largely polar. This means that if we want to have one of the poles, we also have to accept the other. Trying to have only one without the other seems a hopeless endeavour that is bound to lead to grief and sorrow. So what are we going to do in this situation? We accept both polar opposites and we transcend both.

Beyond Polar Opposites


As love and hate, life and death, so other polar opposites may also be transcended. They are transcended through their union in which they cease being opposites. In meditation we may taste this oneness beyond polar opposites (see the meditation at the end of Chapter 2). One way to become the oneness of heaven (sky) and earth is through standing meditation. Standing on the earth, as an extension of the earth, and reaching up into heaven can lead to the union and transcendence of both.

Standing Meditation


Stand still, preferably in nature. Breathe naturally. Your knees are relaxed (very slightly bent); your body is straight and relaxed. Your shoulders are relaxed with your arms dangling comfortably at your sides. Your feet are firmly planted on the ground so that you feel connected with the energy of the earth. This earth energy flows into you and through you. You feel your head, with your chin slightly tucked in, as if floating up to the sky. Thus you are connected with the energy of heaven and it flows through you. Standing and breathing like this, you become the meeting of heaven and earth; they become one and you are one with them.

Note: Standing meditation, like all meditation, requires regular practice. For details you may watch demonstrations by
Ken Cohen, tapes by Chunyi Lin and consult books such as The Healing Promise of Qi by Roger Jahnke (2002). If possible, it is, of course, highly advisable to learn standing meditation from a Qigong Master or another meditation master.

Standing with a Tree - Instead of standing alone, it might be easier at the beginning to stand with a tree. Trees have already the connection we try to acquire. Thus they can be very helpful to us. You stand close to a tree, touching the trunk with your hands. As you breathe in and out, feel the oneness with the tree that is connected to heaven and earth (see Chapter 2 and for details listen to tapes by John Milton (1999): “Sky above, earth below”).

Summary

This third chapter of my book on Wholeness, Fragmentation and the Unnamable deals with exactness and fuzziness. Exactness is understood as sharpness in contrast to fuzziness where we cannot find sharp borders. Fuzziness appears to be all-pervasive in nature and culture, in science, religion, ethics, law, politics, everyday life, etc. Fuzziness is often overlooked because we have been conditioned by Aristotelian either/or logic that makes sharp divisions between true and false, right and wrong, good and evil, beautiful and ugly, guilty and innocent, etc. However, upon closer inspection these and other distinctions become fuzzy. Kosko (1993), the author of Fuzzy Thinking. The New Science of Fuzzy Logic concluded that everything becomes fuzzy when we have a closer look at it. To better perceive and communicate this fuzziness we need fuzzy logic that was developed by Lofti Zadeh in the second half of the last century. Whereas according to the commonly accepted Aristotelian either/or logic x is either a member of a set or not, according to fuzzy logic membership is a matter of degree and may range from 0% to 100%. Thus, for example, a human being may be a member of the set of men to various degrees: a 100% membership would be a typical man, whereas a 0% membership would be no man at all, and an individual between these extremes would be a man to some degree. For the extremes either/or logic works well, but for the intermediate range it fails. Fuzzy logic works well for the whole range from 0% to 100% membership.

Yin-Yang thinking also recognizes that Yin and Yang are a matter of degree and not mutually exclusive because Yin contains some Yang and vice versa. But in contrast to fuzzy set theory, according to Yin-Yang thinking, 0% and 100% Yin or Yang do not exist, whereas according to fuzzy set theory 0% and 100% are not excluded. This contradiction can be resolved, if the 0% and 100% membership in fuzzy set theory are not considered as absolutes but as approximations. In any case, polar opposites represented by Yin and Yang such as love and hate, life and death, good and evil, etc. appear compatible with fuzzy logic.

Ultimate reality that cannot be grasped through reason and language transcends logic and polar opposites. In the mandala of this book it is represented by the unnamable empty centre and the mandala as a whole that comprises the unnamable and the namable, the centre and the periphery of the mandala. Exactness and fuzziness reside in the periphery of the mandala, the namable.

The transcendence of exactness and fuzziness may be experienced in meditation such as standing meditation, where the meditator feels connected to heaven and earth and thus transcends both.


References

Arber, A. 1964. The Mind and the Eye. Cambridge: Cambridge University Press.

Arber, A. 1967.
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Hesse, H. 1957.
Siddhartha. New York: New Directions Publishing Corporation.

Hoggan, J. 2016. I'm Right and You're an Idiot: The Toxic State of Public Discourse and How to Clean It Up. Gabriola Island, BC: New Society Publishers.

Jahnke R. 2002.
The Healing Promise of Qi. Chicago: Contemporary Books.

Kosko, B. 1993.
Fuzzy Thinking. The New Science of Fuzzy Logic. New York: Hyperion.

Lewontin, R.C. 1991.
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Milton, J. P. 1999.
Sky above, Earth below. Boulder, CO: Sounds True. Inc.

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Rutishauser, R. and Isler, B. 2001.
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Quotes

"The closer one looks at a real-world problem, the fuzzier becomes its solution" (Lotfi Zadeh).

"Precision increases fuzziness" (Bart Kosko).

"The hard and abrupt contours of our ordinary conceptual system do not apply to reality" (Bart Kosko).

"Everything is a matter of degree" ( Bart Kosko).

"We have to return to the fluidity and plasticity of nature" (Bart Kosko).

"Everyone should know how a fuzzy washing machine works" (Bart Kosko).


Preface (including the Table of Contents) and Introduction of this book.

Next Chapter:
Chapter 4: Openness and Closure

Preceding Chapter:
Chapter 2: Continuum and Discontinuum


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