If mental states are identical to brain states, then they must share all their properties in common. This is Leibniz’s principle of the indiscernibility of identicals: if ‘two’ things are really ‘one’ thing, then the ‘two’ things must be indiscernible, i.e. you cannot have quantitative identity without qualitative identity - Leibniz law. Second, a brain state, understood as the firing of particular neurons in the brain or the existence of certain neural connections, has certain spatial properties. In particular, it has a precise location in space, occurring in a certain part of the brain or as a certain pattern or shape across many parts of the brain. We can also talk about the spatial relations (up, down, left, right) between the neurons involved and therefore between ‘parts’ of the brain state. We can also talk about the spatial relations between one brain state and another. Brain states of the prefontal and frontal cortices occur a few inches closer to your forehead that brain states of the visual cortex. However, mental states do not have such spatial locations. For example, neuroscientists have associated activity in the prefontal and frontal cortices with thoughts and activity in the visual cortex with visual experience. But my thoughts are not literally a few inches closer to my forehead than my visual experience. Or again, my hopes are not literally about 18 inches above my heart. Mental states are not spatially located in the same sense that brain states are. Therefore, mental states cannot be identical with brain states.