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I’ll take the bait. While I’m not sure that the self and the brain are identical, I will let that go and concentrate instead on your first premise (that your brain is a computer because you can do calculations). I think that there are two problems with your inference from the ability to calculate to the conclusion that your brain is, and therefore you are, a computer. First, not everybody can do calculations – e.g., newborn infants, some mentally disabled (including everybody who is severely mathematically challenged), and the comatose. So by your reasoning, we would have to conclude that only some brains/humans are computers and some are not. But this proposition seems to violate the principle that humans are all, at the most fundamental level, type-identical. Second, most brains can perform many functions in addition to calculating, and it is not clear why we should privilege this particular function over the others as its essence or its defining property. I can read out loud, but that doesn’t necessarily make my brain a speaker; I can see, but that doesn’t necessarily make my brain an eye.
The proof only shows that the brains of those who compute are computers–not the brains of mice, lice, and dead men. Computing doesn’t have to be the sole or defining property of brains–they are also made of biological cells and have mass. No one says that the computer on your desk is nothing but a computing device. The question raised by my proof is in what non-trivial sense is the brain a computer (since the sense in which it clearly is a computer is quite trivial, i.e. it realizes my conscious computations).
I agree that the ability to calculate means that the brain is, to some extent, a computer. I thought that you were trying to defend the more substantive thesis that the brain is nothing more than what’s sitting on our desk. This is largely my fault. I was reading your original post through the lens of what I heard recently on Ideas (CBC): that every generation thinks of the brain in terms of current technology. So Freud, who was heavily influenced by the emergence of the railroad, thought of the brain (or the mind) as a collection of energy flows and drives. Then came the car-engine models of the brain. For the past few decades, the computer models have been most popular, the latest version being that the brain is a parallel processor. Now they’re predicting that the next model of the brain will be the internet/world-wide web.
My actual view is that the brain is NOT a computer, except in the trivial sense explained.