Reductive materialism (Identity Theory ) claims that there is no independent, autonomous level of phenomena in the world that would correspond to the level of conscious mental states. It also states that the level of conscious phenomena is indentical with some level of purely neurological description. Conscious phenomena are nothing over and above the neural level, thus it can be reduced to that level.

Similar reductions have taken place in the history of science:
water = H₂O
visible light = EM-radiation at certain wavelengths
temperature = kinetic energy molecules
pain = neural impulses in C-fibers
seeing red = synchronization of neural activity at 40Hz in V4

Yet a main criticism of this theory is that it leaves out qualia--what it is actually like to see red, or feel pain, or experience anything.

See also: The mind-body problem, Monism, Materialism, Physicalism, Eliminative materialism, Emergent materialism