Transdual & Dual Reason
In Zen, they often say that you can't resolve a koan through reason. You have to become the koan, and find a way to express it (and express it from the absolute or relative depending on what they are looking for).
In my own experience, this is true - but there is also a fuller picture.
Dualistic reason
When we are mostly or exclusively identified as any subset of what is - most typically a human being - our view is necessarily dualistic. We separate what is into seer and seen, me and other and so on.
And since our view splits the world up, our reason will as well. We reason through polarities, but often only see only the poles and miss the whole of the polarity. We get caught up in the differences between the poles, and miss the larger whole they are embedded in.
In areas where our exclusive identity does not come into play so strongly, we may be able to see the whole of the polarity. But in areas where our identity comes into play, it will be far more difficult for us to transcend the poles and come to the polarity.
For instance, if I am exclusively identified as my human self, I will experience a separation between myself and other selves. And in some cases, especially when I experience being threatened by a particular other, I won't be able to find our shared humanity and characteristics. The other becomes fully "other".
Or I may be identified as the Witness and see the world of form as "other". In this case too, I am not able to see - or find myself as - the larger whole that embraces both.
So in the case of koans, it is true that as long as we have an exclusive identity, we may not be able to use our (dualistic) reason to resolve a koan. We have to drop our familiar way or reasoning and experiencing the world, and fully become the koan. That is the only way to find any resolution. And when we find ourselves as the koan, our reasons follows and finds a way to express it.
Transdual reason
So here, when we find ourselves beyond and including all polarities, we also find a more transdual reason.
As I become more familiar with myself as Big Mind, my view and reason becomes more deeply transdual. And as my familiarity deepens, this view deepens and becomes more stable.
Deepening & Clarification
Of course, it is possible to develop a more transdual reason even before all duality is dropped from our immediate experience. A simple trick is to use the both/and guideline. For any polarity, both ends have validity. It is all included, and the only question is how.
And this how is the incentive to clarify, deepen and become more intimate and familiar with myself as the absolute, as Big Mind, as that which is beyond and includes all polarities.
The only way to clarify the how is to dip into the absolute again and again, and bring it back into my human life. To deepen my familiarity and intimacy with myself as the absolute and relative - as Big Mind and my human self - and the integration of the two in my daily life.