Rough statements and fuzzy logic.

THE WORDS "FUZZY" and "understanding" don't seem to go together. Yet in the article "Fuzzy Logic and General Semantics," Milton Rosenstein shows us that "fuzzy logic" enhances our understanding. (1) How can this possibly be? Even though there is an apparent disagreement, Rosenstein explains the value of fuzzy logic in understanding reality.

To understand fuzzy logic, one must learn about its opposite, Aristotelian logic. "A-logic" has an "is or is not" basis. Something is either white or black; there is no gray matter in between. "A-logic" confines itself to short statements, not "to extended locutions." (1)

Understanding the fundamental flaws of A-logic highlights the coherence of fuzzy logic. A-logic depends heavily on crisp statements, which are so precisely exact that everything is either so or not so. For example, I say it is 70 degrees outside, even though I do not mean it is 70 degrees exactly; the temperature is approximately 70 degrees. A-logic has forced me to make a false crisp statement, since A-logic cannot handle the "approximate" value.

"The temperature is around 70 degrees" is considered a rough statement. Rough statements are more relevant than crisp statements. "'The bus should go faster', 'the room should be warmer', and 'the computer has insufficient storage,'" are rough statements. We do not say the bus should increase its speed by 17.5 M.P.H, nor the room temperature should increase 11.3 degrees. We need a language and a logic that employs these rough statements, and that's were fuzzy logic clearly comes into the picture.

Fuzzy logic's description of reality is much "truer" when compared to a crisp statement. Fuzzy logic accepts the "gray areas" in between the black and the white; "the world is expressed through shades of gray": "The world we inhabit, plan in, try to control and understand, can seldom be matched by crisp statements." (1) Through our experiences we know that most events fall within intermediate ranges. For example, even though there are only two political parties in America, many Americans would consider themselves "moderates."

With that definition in mind, how does fuzzy logic relate to general semantics? It's simple: the map doesn't match the territory. Fuzzy logic helps us create better maps for understanding the world, the territory. Crisp statements don't fit with our actual perceptions of the world. A-logic makes the world bipolar, and we know from experience that there are many different parts of the world.

Crisp statements can and have led to disaster. Recently, the Bush administration made infamous crisp statements about weapons of mass destruction. President Bush said, "We found the weapons of mass destruction. We found biological laboratories." And Vice President Cheney stated, "Simply stated, there is no doubt that Saddam Hussein now has weapons of mass destruction." (2) We know today that there were no weapons of mass destruction. If the Bush administration had used rough statements, such as "Saddam has used biological weapons against his people, and yet there are people stating he won't develop and use weapons of mass destruction." we might be in a much different situation today.

When this is applied to my life, I think of the conflicts that I have waged. In my elementary school years there was no such thing as "gray area." Everything was either right or wrong, and conflict ensued like a wildfire. But as I aged and matured, I realized that nothing was either black or white, and thus my conflicts began to deflate and burn themselves out.

In my personal experience, the academic grading systems between different countries demonstrate the distinction between A-logic and fuzzy logic. I attended a private high school in Quebec for three years. A grade of 85% was considered an absolute honor; an achievement that only a few can achieve. Anything above 90% was impossible; the highest average in the school's history was 89%, and the student who achieved it is currently a Page in the Canadian House of Commons. Pages undergo a rigorous screening and interview process, and only 40 graduates a year across Canada are selected.

Yet in the United States, 90% average is almost expected for the top 15% of a school's population. Can you imagine a B or B+ student, one of forty from across the country, being selected to a similar page program for the Senate? A B or B+ student isn't even qualified for that! When I returned to Vermont Academy, my average went from 78% (B plus in Canada) to 87%; only 2% off the highest grade average record at my old school.

A-logic cannot explain the gap between the American grading system and the Canadian, yet fuzzy logic can. Fuzzy logic says "He is one of top students who ever attended here", and both American and Canadian grading systems would correlate that. A-logic would say he was the greatest, or he was not.

In grade 10, I joined the Public Speaking and Debating Team at Stanstead College. I wrote and presented many persuasive speeches, but now I see I wrote them all with A-logic. Since I did not allow any gray areas in my speeches, I was disconnected from reality. Because of this my speeches did not apply to the real world; they were either black or white in a world of gray.

This idea is also apparent in Freud's theory of the human psyche. According to Freud, our psyche consists of the super-ego, the ego, and the id. The super-ego is described as our consciousness (conscience?) and regulates our morals, prohibiting us from violating our own rules. The id is our "pleasure principle" or the driving force that wants immediate satisfaction. The id does not care about the external effects, just as long it achieves satisfaction. Finally, the ego regulates the id and super-ego; it will make a decision to both fit the current environment and satisfy both id and super-ego.

The ego has to use rough solutions as it deals with both crisp aspects of the mind, the super-ego and the id. The ego has to satisfy both polar opposites. Our ego cannot use A-logic since it works on an "either-or" dichotomy. Instead, it must work on a "both-and" basis--a fuzzy solution to the psychic conflict. Fuzzy logic fits wonderfully with this theory. The three-part structure of the psyche, with human beings relating to their needs and their environment, represent the perfect example of fuzzy logic at work.

The ETC article, "General Semantics and Fuzzy Logic," helps explain an important source of conflict within our lives. Rough statements are more logical for the real world because this is a world in shades of gray--who ever said that we live in a black and white world?

REFERENCES

1. Rosenstein, Milton. "Fuzzy Logic and General Semantics." ETC.: A Review of General Semantics October 2004:

2. Stoft, Steve. "'Weapons of Mass Destruction' Quotes." zFacts.com. 17 April 2006. zFacts. <http://zfacts.com/p/581.html>.

ROB WELSH *

* Rob Welsh is a senior at Vermont Academy and currently resides in Springfield, Vermont. He is originally from Mystic, Connecticut. Rob plans to attend a college of the liberal arts in the fall.