Fuzzy Questions, Fuzzy Answers

Some of you may have heard Garrison Keillor’s Thanksgiving story in which Unitarians are featured. Somebody needs to find out what Keillor’s experience is with Unitarians. He mentions us frequently and, I might add, usually, his comments (whether complimentary or critical) are right on the money.

In this story, he describes a Lake Wobegon family visiting relatives back East for the holidays, and mentions that the relatives are Unitarians. Then he says something like this:

A lot of folks say that Unitarians have no beliefs. That is not true. Unitarians have very strong beliefs. It is just that what those beliefs are depends upon what book they last read.

We are, it is true, often criticized this way. When it comes to religious belief, it is hard to pin down Unitarian Universalists. Sometimes we are criticized, and rightly so, for having no beliefs. Other times we are criticized, and rightly so, for having too many beliefs—that we believe anything we want. Sometimes those criticisms are appropriate. Sometimes they are not. See what I mean about it being hard to pin us down?

The whole subject of Unitarian Universalist beliefs is a fuzzy one.

The problem with this line of criticism is that, in addition to it being true, it is also mostly misguided and irrelevant. Unitarian Universalism is not a religion that is centered around a common religious belief system. A common religious belief system is sometimes called a “creed,” and has been uniformly resisted and opposed throughout our history. Though we do not have a uniformly held religious belief system, I am convinced that we hold a fairly uniform religious value system—like that expressed in our covenant. Values are quite different from creeds, but that is grist for a different sermon mill, I’m afraid.

To say we don’t hold uniform beliefs does not mean we don’t hold beliefs. On the contrary, most Unitarian Universalists I know, as individuals, have very strong opinions about all manner of subjects, and most are not shy about expressing them. The problem is that our beliefs aren’t consistent from one person to the next. Most Unitarian Universalists I know have not held the exact set of beliefs over the course of their lifetimes, but have shifted and altered and modified their beliefs as time has passed, and most are not embarrassed to admit it.

If the topic of discussion is Unitarian Universalist beliefs, the conversation is bound to be a fuzzy one. Our beliefs change from person to person at any one time, and our beliefs change from time to time for any one person.

I have long seen this fuzziness as a strength, not a weakness. We humans are not omnipotent, and we form our beliefs based on the best information we have. If we are being responsible about our beliefs, they are bound to be altered in light of new information and new insights. We tend to agree with the French existentialist philosopher Simone de Beauvoir, who wrote: “To say that life is ambiguous is to assert that its meaning is never fixed, that it must constantly be won.”

When I say that I have long felt this way—that our fuzziness of belief is a strength and not a weakness—I can prove it. Any honest assessment of human experience must acknowledge its ambiguous nature. There is beauty in ambiguity. The reason we Unitarian Universalists resist the rigidity of religious creed, the reason for honoring tolerance and valuing an open mind, is that so much of experience is ambiguous. Simple answers to difficult questions may be reassuring, but they rarely reflect the complexity of experience. I am naturally suspicious of any answer (especially a religious answer) that is presented as certain, absolute, and simple. I am more open to answers if they are presented as tentative.

Some years ago, when I was a seminary student, I praised ambiguity because it seemed to more accurately reflect human experience as I knew it. I praised it because it seemed to be the only honest way to live. I praised it because, like art, ambiguity lends itself to the aesthetic richness of interpretation. I praised it because its alternatives (various forms of certainties) were unacceptable.

This morning, I can praise ambiguity for all those reasons, but I have a new one to add to the list. In addition to its consistency with the human psyche, in addition to its beauty of interpretation, in addition to it being a cornerstone of the free mind, ambiguity, I have now discovered, has the added value of being true. It is not just that we experience the world ambiguously. The world is ambiguous!

This time, however, I have a new and improved word. I have traded the word “ambiguous” for the word “fuzzy.” It is a much more common-sense expression of the same idea. I encountered this new word, and this new insight, from a member of All Souls who, a few months ago, recommended a book entitled Fuzzy Thinking: The<<em> New Science of Fuzzy Logic. The author is Bart Kosko, a professor of electrical engineering at the University of Southern California. One interesting part of this book that I will not discuss is Kosko’s claim that fuzzy logic makes computers smarter.

But what is new and intriguing in this book, at least for me, is not the justification that our vague opinions are valid simply because the human mind can’t be certain about things, but rather, the conclusion that our vague or fuzzy or ambiguous opinions may be justified because the world itself is a fuzzy world.

Religious fundamentalisms are the natural product of certainty. They are the consequence of a belief that what we know is actually the way things are. But absolutisms of certainty are not limited to religious ideas. One finds absolutists in nearly every field of knowledge, including every branch of the sciences, whenever someone presents an idea as beyond all doubt.

I have long admired John Dewey’s 1929 Gifford Lectures, which were published under the title “The Quest for Certainty.” In those lectures, Dewey questions all absolutisms, religious, philosophical, and scientific, with the argument that the human mind is fallible and subject to all manner of influence that can skew its understanding. Here is one way he says it:

The world as we experience it is a real world. But it is not, in its primary phases, a world that is known, a world that is understood, and is intellectually coherent and secure.

In other words, the human mind can get it wrong, so we can never be content that the ideas and opinions we form about the world are fully certain. Any fundamentalism or absolutism or rigid doctrine about life is only as reliable as the fallible human mind. The quest for knowledge is a legitimate quest, for we can learn new insights and improve our understanding, but the quest for certainty is always ultimately illusory.

This is where I was thirteen years ago on the subject of ambiguity. We can never be absolutely certain about anything because the human mind makes mistakes.

What Bart Kosko adds to this conversation is that the quest for certainty is thwarted not just because the mind is fuzzy, but because the world itself is fuzzy, too.

From the time of the Greeks, we have been misled into believing that statements about the world must be either true or false, right or wrong. Either ocean tides are controlled by the moon, or they aren’t; either an apple is red, or it isn’t; either gravity holds water in a cup, or it doesn’t. We have turned statements of “facts” into idols about which there can be no doubt. “The earth is flat,” we once said with certainty, “and the sun moves around it.” “The earth is round,” we later said with equal certainty, “and it moves around the sun.” “The earth is egg-shaped or pear-shaped,” is a later certain conclusion, “and the sun is not a sun, but a star.”

What all these statements have in common is that they were each propositions that were true or false, right or wrong. They were not just estimates or guesses—they were statements of “fact.”

The prevailing assumption of Western thought is that all statements must be true or false—completely true or completely false, with no degrees in between. Our thinking left no room for something to be partially true or partially false: black and white with no shades of gray.

But it turns out, after many centuries of working with this mistaken notion, that our statements about the world are only approximations—more or less right. All statements fall somewhere on a continuum between true and false, right and wrong. There is still some truth in the statement, “The earth is flat”—it is just that there is not very much truth in it. The earth we plant a garden patch on is flat, but it is only a very small part of the earth. If you connect it to bigger parts of the earth, you see that it is really round. The statement, “The earth is flat” has an extremely small truth-value; the statement, “The earth is round” has a significantly larger truth-value. But there is more truth-value if we say, instead of “round,” that the earth’s shape resembles an egg, or a pear. “Egg-shaped” or “pear-shaped’ seems to have an even larger truth value, which is to say it is “more true,” but it is not absolute or certain truth.

Any statement we make about anything in the world is necessarily fuzzy or vague, though some statements are much fuzzier than others. All statements about reality are statements of degree: Are rocks hard? Well, more or less—but usually more. Some rocks more so than others. Is the sky blue? Well, more or less—but usually more. Is snow cold? Well, more or less—but usually more. Is snow warm? Well, more or less—but usually less. And so on.

Reality is not black and white choices, but always shades of gray. Kosko says it this way: “The fuzzy view says that almost all truth is gray truth, partial truth, fractional truth, fuzzy truth.”

Math, by the way, is the only exception. Math is the only thing that is either true or false, black or white. But, then, math statements have nothing to do with the world. They only tell us about numbers. Kosko quotes Einstein as one of the great prophets of fuzzy thinking when he observed that “So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality.” From this, it would seem that Einstein embraced a very fuzzy reality.

Fuzzy thinking means simply acknowledging that the truth about everything in the world is a matter of degrees—shades of gray.

Kosko describes asking audiences to raise their hands in response to the questions: “How many of you are tall? How many of you are honest? How many of you are rested?” There is no definite answer, only fuzzy answers, to such questions. People are more or less tall, more or less honest, more or less rested. Some are much more and some are much less of each.

Though ancient Greeks like Aristotle taught us to think in terms of certainty, they could also have taught us fuzzy thinking. Kosko notes that Zeno’s great paradoxes were models for fuzzy thinking. Zeno instructs us, for example, to look at a pile of sand and ask ourselves if it is a pile. Yes, it is. Take away one grain of sand. Is it still a pile? Yes. Take away another grain and ask the question—then a third, a fourth, a fifth grain. Take away thousands, each time asking the question. Is there a point at which it is no longer a pile? Will it be a pile of sand when there are two grains left? Or one grain? Or no grains?

The statement, “This is a pile of sand” is a fuzzy statement because there is no way of determining exactly when it is and when it isn’t a pile of sand. Bertrand Russell, whom Kosko identifies as one of the early prophets of fuzz, though he called it “vagueness,” did the same procedure with baldness. Take away one hair from the head. The another. When does one become bald?

Now, I know that all these mind tricks are not everyone’s cup of tea, and I want to assure you before I go any further that there is, in fact, a point I want to make with all of this. For those of you who don’t care to play the word games I’ve been playing, please know that I hope to make this all relevant before I finish. I do know that there are some of you, though, who, like me, enjoy these sorts of games, so I give you one more example to play with. This one comes not from Kosko but from James Gleick in his book, Chaos. It is an example that troubled me for quite a long time before I read about fuzzy thinking.

Gleick tells the story of Benoit Mandelbrot, a mathematician, who asked the very sensible question, “How long is the Coast of Britain?” So he imagined measuring it.

Take a picture from an airplane or satellite and use reference points to measure it, and you’ll get a measurement, but you’ll miss all the subtleties of small inlets. So you’ll need to get closer and measure the inlets, and your measurement will be longer. If you get close enough, you’ll see the water flowing around large boulders that jut out into the bays, so you’ll need to measure around the boulders, and your measurements will be longer. But the coastline includes not just boulders, but also rocks and pebbles, and you’ll need to measure the water flow around them, and your measurement will get longer. And don’t forget the grains of sand. And the grains of sand contain a molecular structure that juts out, just as boulders jut out. They’re much smaller, but they should still be measured.

At each level, the more precise the measurement, the longer the length of the coastline. Gleick says that Mandelbrot found that

…as the scale of measurement becomes smaller, the measured length of a coastline rises without limit, bays and peninsulas revealing ever-smaller sub-bays and sub-peninsulas—at least down to atomic scales, where the process does finally come to an end. Perhaps.

In this imaginary measurement process, each step toward precision reveals how much more still needs to be measured. Each attempt to be precise reveals how imprecise the answer is. In Kosko’s book, he says that “precision increases fuzziness.” He quotes his own teacher, Lofti Zadeh, chair of the engineering department at University of California, Berkeley, who said, “The closer one looks at a real-world problem, the fuzzier becomes its solution.”

It is time now, I suppose, to leave the mind-games that I find intriguing in Kosko’s book and try to find a principle or value that they point to. The reason for presenting these various mental exercises is simply to illustrate Kosko’s thesis: that fuzzy thinking is justified because the world that we seek to understand is a fuzzy world, not a precise and certain one.

There is, I admit, a grave danger in embracing this fuzzy thinking. If all our knowledge is fuzzy because the world that we know is fuzzy, it would be easy, and mistaken, to conclude that it doesn’t matter what we believe. What we believe isn’t going to be precisely certain anyway. And we aren’t going to get it right, no matter what we do.

This is the complaint, you will recall, that is often lodged against Unitarian Universalists. It doesn’t matter what they believe—U.U.s can believe anything they want. Does fuzzy thinking lead us inevitably to such philosophical and theological apathy or nihilism? Does our inability to know anything for certain trivialize what we believe about the human soul, or about the purpose of life, or about the meaning of death, or about right and wrong, good and evil, or about God, or about anything of importance?

This is not, it seems to me, the lesson to be gained from understanding fuzzy thinking. Fuzzy thinking is not about getting things right, but about getting things right, more or less. This is not because fuzzy answers are some kind of consolation prizes to make up for our inability to know things for sure. Rather, we value fuzzy answers because they are the right answers to fuzzy questions. If questions about rocks and coastlines are fuzzy, how much more fuzzy must answers be about questions concerning the meaning of life?

We hold beliefs because we want answers that are right, more or less. The task is to keep working at it until we are more and more right.

Garrison Keillor’s characterization of us was accurate:

A lot of folks say that Unitarians have no beliefs. That is not true. Unitarians have very strong beliefs. It is just that what those beliefs are depends upon what book they last read.

It is both a criticism and a compliment. And it affirms a certain fuzziness (in the positive sense of that word) at the heart of who we are. We usually call it a “search for truth.” We sometimes even call it a “religious journey.” Whatever we call it, we look forward to the next book, the next encounter, the next conversation, expecting our ideas to be more clearly formed and more adequate than before. Our religious values teach an openness to new ideas and views. That value suggests an inherent uncertainty and tentativeness—a fuzziness. If we were certain about our truths, we’d have no use for open-mindedness.

And there is one other aspect worth mentioning. Consider the statement, cited earlier, by the engineering professor Lofti Zadeh: “The closer one looks at a real-world problem, the fuzzier becomes the solution.” This is why I suggest that most Unitarian Universalists are suspicious not only of rigid answers, but simplistic ones.

The religious journey and the search for truth continue, and in the next leg of that journey, I will not be afraid of fuzzy questions or fuzzy answers.