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That's a loaded argument. Human biology, and by extension human minds, follow a myriad of rules that are a result of biological processes being played out. Lik
by Udo 9y ago
That's a loaded argument.
Human biology, and by extension human minds, follow a myriad of rules that are a result of biological processes being played out. Likewise "machines" also follow the rules laid out by their physical design. There is no fundamental difference in this regard, there is no new set of information-theoretical rules that comes into play when you switch to a carbon-based machinery.
> What formalism, if any, is the human mind subject to?
In the context of this argument, the mind of the human mathematician would be subject to the rules of the formal system. Since Gödel we know that such a formal system cannot be proven true inside the system itself. However, an entity that views the system from the outside can potentially see it's true. There is no fundamental difference between a human mind and a hypothetical machine mind as far as the capability to come to the same conclusion is concerned. That's why Lucas took special care to specify upfront that the machine mind is prohibited from coming to that conclusion, by confining it to live within the formal system only. Yes, their argument is really that circular.
> Isn't our current conception of a machine that it will bound to some formalism in terms of reasoning? Are we so bound?
We are not, and neither would a generally intelligent machine. The burden of proof is on Lucas/Penrose to show that a generally intelligent machine would still be bound to that formalism, at which point it would cease to be considered generally intelligent. They seem to argue that their postulate is true because the individual components of such a machine are bound by those rules, but then again so are the individual components of our brains.
- scandox 9y agoWell I wasn't intending it as an argument. I was actually just interested to see what someone who had actually thought about it would say.
- manyoso 9y agoSo your claim is that the Human mind is a physical machine and that computers are also physical machines and thus both are bound to physical laws... and this negates Penrose how? Do you think Penrose disagrees that the Human mind is bound by physical laws??
- Analemma_ 9y agoI think Penrose is handwaving to try and have it both ways: he's saying the brain obeys physical laws, but that it does not embed a formal computational model. But that's impossible: the second is a logical consequence of the first.
- manyoso 9y ago"But that's impossible: the second is a logical consequence of the first." No, it is not. It is far from proven that universal physical law can everywhere be simulated by a Turing machine. If you had proof of that you'd be up for a Nobel. So publish your paper or perhaps consider that Roger Penrose is not an idiot and you might not know what you are talking about.
- deleted 9y ago[deleted]
- gpderetta 9y agoIt is not proven and possibly it can never be proven. But it can be disproven, and given the success of the Church-Turing thesis, I would say that the burden of proof rest on those that claim that a system more powerful than a Turing machine exist.
- manyoso 9y agoFair enough, but that is a far cry from 'logically impossible' which the parent comment explicitly stated.
- Udo 9y agoI'm not making a claim, I argue based on what we already know. Penrose is the one claiming something here. > Do you think Penrose disagrees that the Human mind is bound by physical laws?? Yes. Having read his work in the past, I know that he disagrees the human mind is bound by physical laws. This is the whole reason behind the argument they're putting forth to begin with: they postulate that humans are capable of making an inference that could not possibly be made by a machine intelligence. However, it has never been shown that we are not a machine intelligence.
- tlb 9y agoAlso, humans often believe things that aren't provable in any formal system S because they're not true. Even good mathematicians believe (hopefully temporarily) false propositions. So the argument "some true things are not provable by formal logic in S, therefore if a human can believe something not provable in S, they must not be a formal system" is valid, but does not imply "no machine can be constructed that believes something not provable in S" since a little sprinkling of randomization can make anything possible. A machine that can prove any true proposition with p>2/3 and only believes false propositions with p<1/3 would be pretty useful.