The error in that assumption is that brain and mind are not the same thing.
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The late 70s philosophy student that still resides in me is forced to ask:
Is electro-chemical activity in the brain the same thing as a thought?
Sorry - couldn’t help myself, but I actually wrote my honors thesis on issues of mind/body dualism (and no, have never taught philosophy, and have never eaten from the public trough - I got a job instead).
I can likewise say that I have never taken a dime from another taxpayer in spite of decades of apparent unemployment. :-)
Is electro-chemical activity in the brain the same thing as a thought?
That is the question ... I think. I would say not. To say what thought is is as difficult as to say, exactly, what mind is. To some there is really no difference. Thought is mind.
Where it really gets difficult is when it is suggested that every perception and, more than just perceptions, everything conceptual is mind. But what else is any perception or concept, whatsoever, no matter how much solidity one might attribute to it, other than a thought?
What is the brain then and what does it have to do with mind and thoughts? IMO it is simply an organ whose function is to control the body and serves as a biological interface and filter between mind and the physical body. But not necessarily the sole physical interface.