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The three essential ingredients of a logical paradox are:
In paradox, an absolute statement is recursively applied to its own negation, bridging two logical levels. If the statement is true, then it is false, and if it is false, then it is true. This perpetual oscillation between truth and falsity challenges all our ideas about certainty and reality, and this is at least one reason why we find it so difficult to think about paradox.
There are two more very important elements in the word “enough.” “Enough” presupposes some point on a continuum, while the person has been using an absolute either/or (sure/unsure) distinction with no middle ground. No matter how the person answers, if they accept this presupposition, they are agreeing to a frame in which certainty is on an analog continuum rather than an absolute, digital either/or, and consequently other alternative understandings can be considered. Unless they challenge this presupposition, either answer to this question moves them to an experience of partial uncertainty.
There is yet another important element in the word “enough.” It presupposes reaching a threshold, in this case a threshold of certainty. If the person replies “No,” they are saying that their certainty is something less than the threshold. If they reply “Yes,” they are saying that their certainty has reached (or exceeded) the threshold, and is “enough” to be uncertain.
“Are you sure enough to be unsure?” is the question form of the statement, “If you are sure enough, you will be unsure,” and this is presupposed when asked as a question. This presupposition states that great certainty includes within it the ability to be unsure, taking two experiences that have been experienced as polar opposites, and nesting one within the other.
I have already mentioned that it is very difficult for most of us to process logical paradoxes. When we hear this paradox, stated as a question, (with the “enough” presuppositions packed inside it), most people simply give up and respond yes or no.
If a person answers “Yes,” they are agreeing to a state of unsureness (the “unsure”), and if they answer “No,” they are also agreeing to a state of unsureness “not sure enough.” Whichever response is given, they are agreeing to a degree of uncertainty, and consequently the willingness to consider alternative understandings.
This pattern has the same form as a paradoxical challenge that the devil supposedly once offered to God in regard to God's omnipotence. The devil challenged God to create a rock so large that even God could not move it. If God cannot create a very large rock that he cannot move, he is not omniptent in his ability to create rocks, and if he does create such a rock, he is not omnipotent in his ability to move rocks. Either way the absoluteness of God’s omnipotence is destroyed.
To summarize, this pattern is very useful in situations in which a person is very certain about how they understand something, this understanding causes them difficulty, and their certainty results in their being not willing to even consider alternative understandings. Using this pattern can open them to considering other models of the world.
Learning how to sort out levels of experience in this way is a very useful skill that can help us understand the structure of problems, and decide which level of understanding could use some improvement.
This makes it much easier to find our way through the twisting corridors of another person's mind, in order to help them find their way out of their predicaments—and also keeps us from wasting our time solving problems that they don't have!
Confusion about levels of thinking, the recursion which transcends levels, and particularly recursion that includes negation, are present in many human problems. It is a little-explored realm, and one that often creates paradoxical traps for us. Knowing the three essential elements of paradox (absolute statement, recursion, and negation) can help us identify these traps, and avoid them.
We can't avoid logical levels, or recursion, and we wouldn't want to—that would keep us from thinking about thinking, and having feelings about feelings, thinking about feelings, and many other valuable and unique aspects of our humanity.
But we can learn to use positive statements whenever possible, rather than negations, and learn to be very careful when we do use negation. The NLP emphasis on positive outcomes is one example of the value of this, and the benefits that can result from this kind of care in thinking.
And we can be doubly careful when recursion is also present, which is much more often than we usually think. To give only one example, when someone says, “I am a bad person,” they are saying that everything that they do is bad, and one of their behaviors is the sentence that s/he just said to you, so “badness” applies to the sentence about badness.
And finally, we can also learn to be very cautious about making absolute statements, realizing that all knowledge is relative, contextual, and based on our very limited experience and understanding. Paradoxically, that is one thing we can be very certain about!
I think it is truly amazing that with the three pounds of jelly between our ears we can imagine and think about an infinite universe, but it would be useful to have a little humility all the same. Let’s start with some humility about our knowledge and certainty.
In case the reader at this point is still insistent that there is such a thing as absolute certainty, I offer the following quote from Warren S. McCulloch’s 1945 article “Why the Mind is in the Head,” now included in his marvelous book Embodiments of Mind, MIT Press, 1965.
McCulloch was one of the first and the best to apply mathematical analysis to the functioning of the nervous system.
“Accordingly to increase certainty, every lhypothesis should be of minimum logical, or a priori, probability, so that if it be confirmed in experiment, then it shall be because he world is so constructed. Unfortunately for those who quest absolute certainty, a hypothesis of zero logical probability is a contradiction, and hence can never be confirmed. Its neurological equivalent would be a neuron that required infinite coincidence to trip it. This, in a finite world, is the same as though it had no afferents. It never fires.”
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