Is it possible to formally prove that the human mind is equivalent in computational capacity to a Turing machine?

Some papers that were helpful to me in understanding this issue:

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    My dad's a shrink. I once put a similar question to him. He replied that for a long time people have likened the mind to the most advanced technology of their time. He supported his claim with an example: In the 19th century, psychxists likened the mind to a steam engine - with impulses to act that built-up pressure until they compelled the person to act on them. I don't think he was suggesting that the mind-technology analogies be discarded, but rather that we be be suspect of their completeness, and to a lesser extent, their accuracy. Food for thought. – Hal Jun 6 '13 at 11:16
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    The definition of a Turing machine includes an infinite memory size and the capability of working on a computation for an unlimited time. In both of these senses, the computational capacity of a Turing machine is infinite. The human mind is finite in storage capacity and is not immortal, so its computational capacity is finite. (The human mind may also have nondeterministic features, whereas a Turing machine is deterministic.) – Ben Crowell Jun 6 '13 at 17:10
  • I think, even though the brain almost certainly doesn't use quantum effects, it is still subject to them, and so we should probably consider it as a quantum TM if our goal is a maximally accurate description (en.wikipedia.org/wiki/Quantum_Turing_machine). – user2429920 Sep 12 '15 at 20:03

We cannot meaningfully prove that the mind is not Turing-computable, since we cannot enumerate the computations of the mind (so that we could show that each is Turing-computable by constructing a Turing machine that performs the same computation).

We can defer to the simple mathematical laws that the universe seems to run by and note that those are Turing computable, and therefore our minds ought to be, but this falls rather shy of a formal proof (or if made formal it's a very unsatisfying one as it takes as axiomatic the Turing computability of the unverse and that our minds are implemented by our brains which are wholly products of the universe).

  • Yes that's what I mean. Edited my question to reflect this. – lk145 Jun 5 '13 at 22:02

the only 'proof' I know, is by essentially assuming it, which is just circular reasoning and unsatisfying.

I rather suspect that physical laws only look turing computable at the scales we look at - and at their own scale, ie below or around planks distance they aren't.

It would surprise me very much if nature didn't make use of quantum effects in the biology of a human being as nature is subtil.

Finally the human mind in itself is not about computability.

  • Are you making a normative claim here about how we should approach understanding the mind: "Finally the human mind in itself is not about computability."? I'm not sure what you mean here. – lk145 Jun 5 '13 at 23:44
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    its a normative claim about consciousness - which most people would say human minds are. Or at least we are. – Mozibur Ullah Jun 5 '13 at 23:47

Your mind is a Turing machine. The translation table is your cognitive ability to convert sounds into English syntax. The tape is your aural environment existing in time. What you do once you interpret those symbols depends on your training, thus far which has been written indelibly in your memory.

Now report to your commandor.

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