Sure.
The mind is a independently existing substance, non-physical in nature and non-extendet, that can not be reduced to the brain nor caused by the brain, or explain in terms of physical properties.
As a identification, I think the mind can be identified with consciousness and self-awareness.
"I think, therefore I am" Rene Descartes
This quote is close, but not quite there- its more like, i am aware that i think, i am beyond my thoughts, emotions, feelings, beliefs, 'story', 'personality', and past, i am beyond perception, i am aware that i am aware, I AM. And this I AM is Love, Oneness, Power, Joy...God.
I really like the way you defined mind
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The brain is not the mind. The brain is a part of the body, another organ.
The body is the projection of the mind. The soul, or spirit, is the vessel for the body. The body is contained within this spiritual aura, and it is the spirit that envelopes and endows this bag of carbon with life. Although the spirit can and frequently leaves the body, the spirit needs to be committed to the body for the body to be 'alive'.
Basicaly we are spirit, and we have mind. In this plane of existance (duality, illusion), we use our mind to project the body and our 'reality' (illusion/delusion). The body is a tool for projection and communication.
The mind is of the Oneness and is spirit, real, and eternal. The body is of matter, and is illusory and temporary. Therefore the mind is beyond the body, and does not require a body to exist. But a body cannot exist without mind.
All matter originates from mind. Mind is independant of matter, it is. Matter is dependant on mind, and only exists because of mind. While we are on this plane of duality, mind can be influenced by matter. However, mind cannot ever be truly harmed or altered by matter, because matter is illusion and does not actually exists outside this plane. Mind originates perception, perception creates matter, and the matter that is percieved effects and shapes the mind within the framework of duality. Therefore the body can effect the mind through this feedback loop, but only in the framework of duality
Basically, since the separation (which never actually occured except in this illusory dream), we have been on a plane of duality and delusion. When we incarnate here, our mind is limited and trapped by the conditions governing this game of duality- body, time, space. This occurs because of 'perception'. Perception only occurs in duality. Outside duality, perception does not exist, because we know all is One, and only Truth can be known. Perception occurs because we believe that we are separate, that we are limited by time, space, and 'ability'. Perception involves continuous judgment, and then using this judgement to predetermine the outcome of situations. When we prejudge a situation, we create that situation. This creates a cycle of karma. We project what we think. When we break this cycle, through forgiveness and At-ONE-ment, we are released from karma.