@platorepublic,
The word Koan actually means 'Public Case' or 'Public Record'. They are deliberately paradoxical statements, questions, anecdotes or epigrams which are given to Zen students during the course of meditation training. The aim is to provoke 'satori' or Zen enlightenment which requires stepping outside the normal 'discursive' consciousness or stream of ordinary thinking.
There is a traditional text called the Blue Cliff Records which contain several hundred Koans.
Koans often seem meaningless, paradoxical or baffling, but this is deliberate. Their aim is soteriological rather than rhetorical or logical. The student is 'given' a koan and sent back to the meditation hall (dojo). After some time the student will have a formal interview (dokusan) with the Zen Master. This does not follow a set pattern, but frequently the master will allude to the Koan, and the student will respond. The master is thought to be able to gauge the level of the student's 'attainment' on the basis of this response.
---------- Post added 04-29-2010 at 04:11 PM ----------
Zen, and Buddhism generally, are anti-philosophical in the sense of discouraging philosophical speculation and idle chatter. Zen is actually derived from the Indian word 'Dhyana' which is usually translated as 'meditation', but there is really no word for it in English. Dhyana is entering into states of profound stillness and quietness culminating in 'samadhi' wherein normal cogitation is suspended. There is nothing like that much in modern philosophy although there are some comparable practises, arguably, amongst the pre-Socratics, and Socrates himself was known to fall into trance while contemplating.