Traditionally, the koan in the Buddhist tradition was designed as a statement which circumvented conscious understanding and logical interpretation by intentionally being impossible or paradoxical. In this way one could move past what was seen as a superficial perception of the world and the self. In euro-religious traditions, such as as Christianity, the koan exists in a different form, that of affirmation of the mystery of God (i.e. doctrines such as the Trinity or Hypostatic Union). Both of these predicate on the notion that an ultimate understanding of reality and existence lie beyond the realm of logical extrapolation. One must use other means to ascend the path of realization and, ideally, enlightenment.
However, where does this idea gain credence? What on the planet has even suggested that anything other than logical transition from cause to effect and inerrant rules of description, premise, and argument is valid? It would seem to require a leap of faith to be able to even consider the rejection of logic in favor of another method of interpretation, right?
I don't know.
It would seem to me that logic is a man made construct. It derives its basic principles from Nature. Nature is consistent, and logic aims for that same consistency. This is not to say that Nature is logical. In fact, I believe it is not logical (intrinsically). To say that Nature is logical is to make a value judgment post facto. Similarly, think of a situation where one has never seen a chair before in his life, and then at age 50 sees a chair for the first time. From there he proceeds to declare all the qualities that chairs are allowed to have from his observation of this one chair. All chairs are wooden, with a back support that has two horizontal bracers placed above a grooved plate with four legs beneath. Obviously, we know that many chairs do not fit this description. What the man has done is used one example to try and extrapolate a rule system to apply to the entirety of a category. Another way of putting it: he has confused an element of a set with the set itself. To me this seems along the same veins of a circular argument, where the conclusion is entailed in the premise. Also think of the occasionally used Christian argument for the divinity of Jesus: Jesus is divine because he exhibits all of the qualities of godhood, which ignores the fact that the argument defines what constitutes 'godhood' on their preconceived notions about Jesus. Another view is to consider the use-mention distinction
Now, it is perfectly acceptable to say that Nature is logical in the same sense that one says that one thing or another is beautiful. It merely affirms that the discussed object has qualities that line up with the given word ('logic,' or 'beauty') However, to say that Nature is logical seems erroneous to me. Logic is merely a human construct, a language for interpreting and interacting with the perceived exterior world. And this brings me around to the original topic at hand: the (in)validity of the koan.
The main challenge to the validity of the koan lies in its non-logic; however, challenging it on the basis that it doesn't conform to the standards of logic only functions under the premise that logic is the only valid system for synthesis of external experience. Several elements of the human experience cannot be equated with logical interpretation, such as aesthetic and emotional response.
Some argue that merely stating what 'is' is 'natural' is a fallacy. In this case I think it is instead entirely appropriate. By the fact of our birth we have an intuitive aspect that should not be denied - it constitutes an essential element of our humanity. Am I saying that we should not be logical? No. I merely suggest that logic is not the end-all to deriving understanding (I'll stay away from the thorny word 'knowledge,' which broaches another sprawling web of arguments not related to what I'm discussing here).
It is the play between logic and intuition that grants true insight.
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