... we cherish Koans in Soto too and Soto folks work with Koans, chew on Koans, penetrate Koans ... but not as an aspect of Shikantaza Zazen, on the cushion, in the way of Rinzai and mixed Soto-Rinzai practitioners. One cannot read Dogen's Shobogenzo and Eihei Koroku without acknowledging that he and his monks danced with Koans as a key part of his Teaching. We do too. However, one actually wants to get the message of the Koan. Koans do present Wisdom and Zen/Mahayana teachings in very poetic and creative fashion, often going beyond ordinary logic but consistent with the logic of the Mahayana (where a mountain is not a flower - yet it is, and there is no birth or death - yet each is so too, and Buddha and ignorant us are not the same - yet we are. The koans help us see beyond ordinary language and the "common sense" logic of daily experiencing the world in order to know such other Truths too.) The koans are not arbitrary, meaningless or illogical in a Mahayana sense.
One cannot read Dogen's Shobogenzo and Eihei Koroku without acknowledging that he and his monks danced and played with the "classic" Koans as a key part of his Teaching. We do too. We also realize the "Genjo Koan" which are the endless Koans of life continuously manifesting here there and everywhere ... in each gesture and moment of life.
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I am not a Koan introspection teacher, so I am perhaps biased. However, I believe that such kind of Koan work is a great distraction often turning into psycho-babble and gobbledygook and hunting for revelations and such, especially in the hands of teachers who just make it up as they go along. ... In the hands of a gifted teacher, a Koan can come alive. But, in the setting of a Dokusan room with students presenting mysterious answers and yelling or jumping around ... and a teacher who thinks he or she can "read minds" ... it is ridiculous and is more likely to lead to blind alleys. It has plagued the Zen world for centuries. There is one fellow teaching Koans to groups online now, and listening to his talks I wonder if he just makes it up on the fly as he goes along. It is like "stream of consciousness" poetry, wherein once in awhile wisdom does appear (but only once one gets through all the mumbo jumbo).