The class of philosophical theories that postulate both a physical brain and a non-physical mind, both of which influence behavior, is commonly referred to as
"dualism." Dualism is a philosophical position that posits a separation between the mental and physical aspects of reality.
In this context, the physical brain is considered the material or physical component responsible for bodily functions, while the non-physical mind is associated with consciousness, thoughts, and subjective experiences. Dualism suggests that these two aspects interact and influence behavior, with the mind having the ability to modulate or influence brain function.