"The hard and abrupt contours of our ordinary conceptual system do not apply to reality" (Bart Kosko)
"The closer one looks at a real-world problem, the fuzzier becomes its solution" (Lofti Zadeh)
The world is fuzzy to a great extent. If we use only our common Aristotelian either/or logic that does not take into account continuity or fuzziness, we cut it into pieces. The application of fuzzy logic can heal the cuts and wounds created by either/or thinking in situations where it is inappropriate.
Fuzziness is widespread. The colors of the rainbow are not clearly delimited but fade into each other. Clouds, winds, and storms have no sharp borders. The seasons gradually merge one into the other. The meaning of words is often not sharp, even when we use definitions because the defining words again may lack sharpness. Right and wrong can have many meanings. The same can be said for fairness, reasonability, guilt, malice, threat, etc. “Law is a fuzzy labyrinth. A legal system is a pile of fuzzy rules and fuzzy principles. And it is dynamic. Every day judges and legislators add new rules and laws and delete or overturn old ones” (Kosko 1993, p. 263).
We can, of course, point to many phenomena that appear clearly circumscribed. However, a closer inspection or a microscopic view reveals fuzziness. For example, physically, a human being seems sharply delimited from the environment. However, we know that there is an electromagnetic field radiating from the person. Or, one may try to pin down moral behavior, but a sharp border between moral and immoral behavior remains elusive.
Whether a phenomenon, thing, or event appears fuzzy or clearly circumscribed seems a matter of perspective. If we look at lakes from an airplane, their borders appear clear-cut. However, from close by lakes often gradually merge with the surrounding vegetation. Even for lakes surrounded by rocks, a microscopic inspection would show a lack of a sharp border between the water and the rocks.
Our commonly used logic that is based on the law of the excluded middle is either/or logic: it makes a sharp distinction between this and that, the human body and its environment, moral and immoral behavior, truth and falsehood, etc. When applied to fuzzy phenomena, this either/or logic can only draw arbitrary artificial boundaries, which leads to distortions, and distortions may have harmful consequences.
To avoid or minimize such distortions and harmful consequences, fuzzy logic is required that can deal more adequately with fuzzy phenomena. Although the principle of fuzzy logic has been understood for a long time and has been implied in ancient ways of thinking such as Yin-Yang thinking (as explained in Chapter 1), fuzzy logic in the strict sense and in a precise formal way was developed in the 20th century. “Fuzzy Logic” has at least two meanings. The first meaning is multi-valued logic, which, in contrast to our common two-valued either/or logic, has more than two values. The second meaning is reasoning with fuzzy sets, which was developed by Lofti Zadeh in 1965 (see Kosko 1993). A fuzzy set is “a set whose members belong to it to some degree. In contrast a nonfuzzy set contains its members all or none. The set of even numbers has no fuzzy members. Each number belongs to it 0% or 100%. The set of big molecules has graded membership. Some molecules are bigger than others and so belong to it to greater degree” (Kosko, ibid., p. 292).
Fuzzy logic transcends either/or logic but it also includes it as a special case when membership in the fuzzy set is either 0% or 100%. Either/or logic is often referred to as Aristotelian logic because Aristotle’s logic includes the law of the excluded middle. It has been pointed out, however, that Aristotle admitted that this law does not apply to future events and thus recognized its limitations (see Multi-valued Logic).
Nonetheless, the law of the excluded middle is often taken for granted.
Examples of Fuzzy Sets
As Kosko (1993) wrote, we live in a fuzzy world. Hence one could give endless examples of fuzzy sets: the set of tall men, mean men, aggressive men, violent men, compassionate men, loving women, nasty women, happy people, wise people, law-abiding people, honest people, dishonest people, reliable people, tolerant people, reasonable people, healthy people, sick people, mentally deranged people, intelligent children, friendly dogs, dangerous animals, healthy plants, poisonous plants, interesting discussions, boring movies, true statements, false statements, irritating statements, indecent remarks, racist remarks, racist actions, terrorists, etc. Kosko (1999) explored fuzziness in politics, science, and the digital age.
Harmful Thinking and Healing Thinking
Using simplistic black-or-white thinking (the law of the excluded middle) can be more or less harmful depending on the situation. If I say, “John is short”, this may be an inconsequential statement. But if John finds it insulting, he might start a fight and hurt me. Had I said “John is not very short” or something else indicating that he is somewhere in the range between short and tall, he may have reacted much less aggressively because I would not have put him into the category of short people that he detests. If I said, “John is mean”, this would have been even more harmful because John does not want to be paced into this category, although he knows that he can be a little mean at times.
If I say, “You are sick” or “You are mentally deranged”, this can be harmful and it is not encouraging. However, saying, “You are a bit sick” or “a bit deranged” is far less negative and more appropriate. As I shall point out in Chapter 4, avoiding the “is” (“are”) of identity encourages healing even more. Imagine how much harm medical doctors do, who diagnose their patients in terms of black-or-white thinking! Telling somebody that he is sick and that he has only six months to live is not encouraging and can be harmful. It can even be harmful to tell somebody “You are healthy” because this is also black-or-white thinking. Who is 100% healthy? If a medical test does not reveal a pathology that does not necessarily mean that the person is “ a healthy”, especially if that person feels a bit sick. But there are medical doctors who tell their patients that their symptoms are only in their mind. In any case, as there are many shades between black and white, there are many shades between health and sickness. It is not only a question of either/or. I should also add that I am not making generalizations about good and bad medical doctors, which would be just another example of harmful either/or thinking.
Another simplistic black-or-white distinction is the distinction between moral and immoral people. It can be rather harmful to classify someone as immoral because of one or a few immoral acts. It can also be harmful or at least misleading to classify someone else as moral because who can claim to be always moral? The distinction of moral and immoral people divides. Division creates wounds. Healing thinking avoids such division because it places people on a continuum ranging from moral to immoral.
Another simplistic distinction is between truth and falsehood. Most people can accept the fuzziness between black and white but not that between truth and falsehood, although it implies the same either/or logic. The harm that has been done and continues to be done by the refusal to accept truth and falsehood as fuzzy sets is beyond our imagination. How often have people claimed that they possess the truth and what atrocities have been committed in the name of that so-called truth? I have to add, of course, immediately that “atrocities” are also a fuzzy set ranging from 0% to 100%, from benign to monstrous (for more on this topic see Chapter 3).
There is much evidence that the world we live in is fuzzy to a great extent. Therefore, we need fuzzy logic to describe and deal with all this fuzziness. Either/or logic, based on the law of the excluded middle, portrays a world of black or white (metaphorically speaking). Shades of gray are ignored or arbitrarily forced into either black or white. Many people follow this simplistic binary logic. For example, they feel boundless optimism when things are going well and are plunged into total despair at the first setback. According to them, people are good or bad, moral or immoral, statements are true or false, etc. Such division into either/or is a fragmentation and distortion of reality. It is harmful because it cuts the world into pieces and thus creates wounds. In contrast, fuzzy logic, particularly fuzzy sets, connects what has been cut apart. It recognizes the continuum between the two ends of the spectrum and thus heals the wounds created by divisive either/or logic. Healthy thinking prevents wounding.
Kodish, S.P. and B. Kodish: Fuzzy Logic and General-Semantics in Everyday Life
Kosko, B. 1993. Fuzzy Thinking. The New Science of Fuzzy Logic. New York: Hyperion.
Kosko, B. 1999. The Fuzzy Future. New York: Harmony Books.
Sattler, R.: Wilber's AQAL Map and Beyond
Continue with Chapter 3 on Healing Thinking through Both/and Logic, Buddhist and Jain Logic, or return to Table of Contents of this book ms on Healing Thinking and Being.