The only way in which we are able to recognize X as a brain state corresponding to mental state Y is in virtue of reports given by those who possessed brain states like X and who reported Y. In fact, what we call "one" brain state is really a set of processes. As in neurons that fire, say, 40 times a second. The very act of calling it one brain state rather than many depends upon a report of this collection of physical events as pertaining to one mental event.
If we take a snapshot of all of the many processes occurring at the same time and compare it with a different set of processes shortly thereafter, we may find that to the mental state correspond many brain states. If (IF!) one can, on the basis of knowing the physical state determine the mental state, THEN it's not a two-way street: that is, from knowing what a mental state is one cannot infer which "snapshot" of the neural state obtains.
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