This is a term used by Gurdjieff referring to thinking beyond the passive associative mechanism of the brain by the effort of the will. Being-mentation is not just thinking with the brain but it is thinking with one's entire presence.
Being-mentation cannot be done theoretically, it must be done actively by the use of one's will. This activity puts the thinker into a proper relationship with his own thoughts. The thinker now becomes the active participant in this relationship rather then just a passive instrument. It puts the thinker more in touch with who he is, his essential nature. It allows the thinker to think beyond the automatic associative thinking mechanism of the physical brain allowing for spontaneous or creative thinking.
Active being-mentation allows for the proper digestion and assimilation of experience. This is comparable to the digestion of food. Food may enter the organism but a long digestive process goes on before this food is sufficiently refined to enter the bloodstream and thus become inseparably absorbed into the organism. Until this happens the food is not part of the eater: He may lose it altogether by getting sick. Active being mentation is the process which facilitates the digestion of experience and allows it to become part of one's own essence.
Being-mentation is the thinker thinking with the brain rather then the brain thinking for the thinker. It is thinking as thinking would be in man if he were as he ought to be. An example of active being-mentation is the type of thinking that was used by those who passed on information through the use of allegories, myths, and fairy tales.