Very well said but for a more practicle application for, that is a more beneficial understanding to help lay aside sin, understanding the purpose of salvation and judgement the question isn't what is the spirit but what is the flesh. We are told in the book of Romans a servant of God is one who controls his members or body. That informs us of a division of body and spirit. After a life time of study and a relationship with Christ I understand the body has absolutely no intelligence. It is merely a covering for our spirit. A covering that allows us to exist in this heaven that was created in the book of Genesis. If you remove this garment from your spirit you will then see that the senses of the flesh send data to the brain which in turn relays it to our spirit for interputation. Touch, heat, cold, sight, hearing, etc: etc: are all in the spirit. Blink your eyes or move your arms, pinch yourself or kiss your wife or child, they are all in the spirit. Our brain has zero intelligence just an instrument to relay information to the spiritual brain where the breath of life abides.
When our great profet was caught up into the heaven he said " Lord sin is upon my lips" for he had shed the flesh but unschooled in the ways where he was. All people that have had near death events see there lifeless unintelligence body.
Moreover our bodies must abide in this heaven where Satin is the God of this world, Prince of the air.
I can go on and on speaking of how the knowing of spirit and flesh ties to doctrines of casting out devils, laying hold of salvation, entering into the Kingdom of God, the Glory of Jesus Christ, etc:, etc:, but need to cut it short.
In conclusion if you didn't have a spirit you wouldn't exist because you are your spirit.