This is often referred to as the mind-brain question or the question of materialism. In other words, is mind something can can be explained completely as a physical mechanism or is it not possible to reduce mind to brain?
The two main arguments in favour of the materialist account are that mental activity can be observed as electrical activity under an MRI. The second is that no one has conclusively proven the existence of non-physical entities.
On the other hand, to demand proof of the corporeal existence of something described as incorporeal is not entirely reasonable. Also, even if we could know the precise physical nature of all mental activities that would not explain their experiential character. Thus no matter how valuable materialistic explanations may be in terms of improving our ability to surgically correct brain damage, for example, reductionism is of only limited explanatory value.