Self referential statements can also invalidate themselves, producing paradox as well as circularity. The classic logical paradox, "This statement is false," for instance, is an example of a self referential statement which produces a paradoxical conclusion. If the statement is true, then it is false; and if it is false, then it is true, and so on. Another good example is the old puzzle about the village barber who shaves all of the men in the village who don't shave themselves. Does the barber shave himself? If he shaves himself, then he is not a member of the class of men who don't shave themselves, and therefore cannot shave himself. But if he doesn't shave himself, then he belongs to the group of men who don't shave themselves, and must therefore shave himself.
A third example of self referential paradox is the question, "If God is all powerful, can he create a rock that is so large that even he could not lift it?"
A "double bind" is a special type of paradox which creates a "no-win" situation; i.e., a situation in which "you are damned if you do, and damned if you don't." Many double binds involve different levels of processes, such that what you must do in order to (survive, be safe, maintain your integrity, etc.) on one level, threatens your (survival, safety, integrity, etc.) on another level. According to anthropologist Gregory Bate-son, who originally defined the notion of the double bind, such conflicts are at the root of both creativity and psychosis (depending upon whether or not one is able to transcend the double bind or stays caught inside of it).
In this sense, double binds are related to what has become known as a "Catch-22." The term "Catch-22" comes from the novel of that name by Joseph Heller (1961; film 1970). The novel, intended to be a dark but humorous satire of military bureaucracy, is set in a U.S. Air Force unit during World War II. The novel chronicles the attempts of airman Yossarian to escape the horrors of war. In his attempts to get out of the fighting, he becomes caught up in "Catch-22", a mysterious regulation that is, in essence, a circular argument. Yossarian discovers that he can be disqualified from flying more missions if he can prove himself insane. In order to be discharged from the military service because of insanity, however, he must request to be discharged. The "catch" is that if one requests to be discharged, it presupposes one is sane because no sane person would want to continue risking his life. By his unwillingness to fly, Yossarian proves that he is sane.
Double binds often share the quality of paradox and circularity illustrated by the "Catch-22," and lead to a similar sense of confusion and helplessness. Consider the reports of the Salem witch trials in which one of the tests to see if a person was a witch was to bind the person and cast her into the water. If the person floated and survived, then she was determined to be a witch, and was put to death. If the person sank and drowned, she was exonerated with respect to being a witch, but was, of course, also dead.
In short, self reference may be a source of either creativity or confusion, depending upon how it is balanced with other processes within a system. It can produce either pathology or wisdom depending on how it is structured and used.
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