Completeness or Incompleteness

Do we live in a world of completeness or incompleteness? Most folks intuitively sense that incompleteness is far more prominent than completeness. Is there anything that is complete, static, unmoving? Probably only very rare things like God and aspects of mathematics, and even those are simply accepted as complete without proof. Everything else is changing, including the mountains whose intensely gradual movement is invisible to us.

Just as we would not refer to a complete mountain, we cannot refer to a complete human being, even though some people assert that spiritual exercises or belief in a supreme being, or even science, can bring this about. Perhaps. But the number of such people, assuming their condition is even verifiable, is vanishingly small.

Of course we can talk about “completions” in a simple sense, such as when we finish a budget, a round of golf, a prayer, a vacation trip, a book, a meditation or often best of all, a drink. But my interest is not in such completions. It is in the Incompleteness Theorems proposed by the great Austrian mathematician, Kurt Godel, and the application of those to our lives.

Both theorems deal with highly complex mathematics. The first Theorem says that all logical systems are likely to have inherent flaws because they are based on unprovable assumptions. The second Theorem says that seeing a system from the inside may indicate that it is consistent and whole. And it may be, but we cannot determine that without going outside the system. The key insight is that internal flaws are not visible from inside any system.

So what? you might say. That’s all about highly sophisticated math and it has no relevance for everyday life. At one level that is certainly true. At another, I think not. Deepak Chopra, in the fine book, War of the Worldviews, says “If I boldly take this out of the realm of numbers, Godel is saying that unprovable things are woven into our explanation of reality.”

For example, most secular humanists believe that God does not exist, but cannot prove it. Religious people believe firmly in God’s existence, but also cannot prove it. Each accepts his own belief as complete, while seeing the other’s belief as not just incomplete, but dead wrong into the bargain. For each the world is workable in his terms, seeing and acting as he does with an insider’s view. But neither can escape the limits imposed by his own system of thought and belief, and this is often a source of often great animosity between the two.

Although the unprovable assumptions are the root from which many of our personal and societal problems grow, it is not always they that cause the trouble in our relations with others. It is that we accept them and their legitimacy at face value, if we are aware of them at all. And this acceptance is accompanied by a great emotional force, a large hindrance to seeing outside our own systems of belief and thought.

Leonard Mlodinow, the other author with Chopra of War of the Worldviews, gives a fine example of contrasting but workable world views. Imagine a goldfish in round bowl. As it looks out of the bowl, an object moving on a straight path is perceived to be moving in a curved path. An observer outside the bowl sees the object’s linear movement and does not see the curved movement. Contrasting views, but they work within each world.

Human society is not so fortunate. Differences in world views would not be the personal or societal problems they are if people holding them did not interact. But we engage constantly with people whose views we do not share or whose behavior we do not like. We have an insider’s view of our own beliefs and thus cannot subject them to a rigorous critique. And we have an outsider’s view of the other’s beliefs and imagine we can subject them to such a critique. But the challenge is that our assumptions and biases usually preclude us from making a fair analysis.

From the last post I repeat George Friedman’s prescient comment from his fine book, Flashpoints, “There is always a price, and nothing is more dangerous than not knowing what the price is, except perhaps not wanting to know.” One of those prices occurs in failing to appreciate the natural incompleteness of one’s views and positions, leading to absolutism of thought and action, anathema to a healthy person, group or society.

A particularly damaging view arising from absolutism is perfectionism, a belief that humans and their systems are perfectible. We can totally solve societal conflict, we can ensure that no one’s feelings will ever be hurt, we can eliminate poverty, we can guarantee total social success by electing only people from my party, we can make everyone equal with enough money and government effort---these are all examples of perfectionism, mainly from the political realm. While admirable in intent, these views are unworkable because those holding them fail utterly to understand the lessons of human history and what we know of human psychology.

Perfectionism obviously implies completeness, that there are definitive Answers to complex societal problems and differences, instead of approximations of answers. Godel confirms that there is no such thing as a perfect or complete system, no matter what humans think or want. This should give us pause in our thinking, and certainly in our acting. Incompleteness is a fact of existence, and may well be the one that matters most in human relations.

The belief that there are Answers that totally resolve an issue is demonstrated by people who think and accept at absolute face value that their ideas are both correct and workable. Their efforts will produce the complete outcome they have in mind, and there will not be any unintended consequences. Further, and much more dangerous, such folks have an unshakable belief in the moral rightness and purity of their thoughts, beliefs and motives---completeness personified in them. Naturally, this absolutism means that people with a different perspective cannot be tolerated, and must be demeaned if not crushed.

There are two ways of looking at completeness. The first may be clear from comments above. It says that humans can be complete (are perfectible) and can have complete views and produce complete systems and positive outcomes, without flaws. Thus, it falls prey to Godel’s Incompleteness Theories---internal flaws very likely exist everywhere and are invisible within the system. Because such folks hold their views and motives in perfect regard, seeing outside the self-contained system is virtually impossible. Why look outside a system or set of views that is accepted at face value as being complete? This perspective has the obvious unintended and undesirable outcome of adding to personal conflict and societal disturbance instead of reducing them, all of which is deniable by those locked in their own system.

The other version is more realistic and more useful in that it accepts both Godel’s Theories and the inherently flawed nature of humanity in the sense that Kant did: “Out of the crooked timber of humanity, no straight thing was ever made.” This does not literally mean that humans cannot produce anything good. It means that our all-too-human predilections, such as unconscious biases, excessive personal needs, and irrationality often get in our way. This view respects the idea that troubling societal problems are not completely solvable, but may be amenable to approximations of improvement---we progress fitfully.

In this view, each success is a struggle against our own “crookedness,” which pushes us into the damaging perfectionist view, so comforting and so wrong. Each success, whether societal or personal, arises because we have, for the moment at least, escaped the prison and falseness of our internal consistency, possible only by seeing our views from outside.

We move toward completeness to the degree that we give up the idea of completeness, of perfection, and act to constantly uncover our desire to see everything from within the framework of our systems of thought, belief and emotion---what might be termed in Eastern thought as incomplete completeness. The Zen cat waits for no one.