The belief that consciousness is identical with activity in certain parts of the brain, so that “you are your brain” is now widely accepted. It is, however, mistaken. While the brain is a necessary condition of every aspect of consciousness, from the slightest tingle of sensation to the most exquisitely constructed sense of self, neural activity is not sufficient by itself to explain consciousness. This is evident from the fact that there is no fundamental difference between that small minority of neural activity correlated with consciousness and that which is not associated with consciousness. The consciousness-neural activity identity theory faces numerous problems, arising from the fact that nerve impulses are material events in a piece of matter (the brain). First, there is no explanation of intentionality – that through which contents of consciousness are about entities other than themselves. Intentionality, which points in the opposite direction to that of the sequence of causes and effects that are supposed to bring about consciousness, is not seen elsewhere in the material world. Second, the development of the scientific notion of matter is associated with the elimination of appearance, beginning with those “secondary qualities” such as color and feelings of warmth that form the content of consciousness. Third, neural activity is unlike the experiences that it is supposed to be identical with. Fourth, there are properties of consciousness – such as simultaneous unity and multiplicity, and explicit temporal depth and tensed time – that are not seen in the material world. Acknowledging that the failure to arrive at a neural account of consciousness is not a temporary problem (which can be resolved by further research) will open the way to a fundamental re-think that will help us toward an understanding of the difference between brains and people.