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ORIGINAL: http://vserver1.cscs.lsa.umich.edu/~crshalizi/notabene/godels-theorem.html
Gödel's Theorem

A much-abused result in mathematical logic, supposed by many authors who don't understand it to support their own favored brand of rubbish, and even subjected to surprisingly rough handling by some who really should know better...

There are two very common but fallacious conclusions people make from this, and an immense number of uncommon but equally fallacious errors I shan't bother with. The first is that Gödel's theorem imposes some some of profound limitation on knowledge, science, mathematics. Now, as to science, this ignores in the first place that Gödel's theorem applies to deduction from axioms, a useful and important sort of reasoning, but one so far from being our only source of knowledge it's not even funny. It's not even a very common mode of reasoning in the sciences, though there are axiomatic formulations of some parts of physics. Even within this comparatively small circle, we have at most established that there are some propositions about numbers which we can't prove formally. As Hintikka says, "Gödel's incompleteness result does not touch directly on the most important sense of completeness and incompleteness, namely, descriptive completeness and incompleteness," the sense in which an axiom systems describes a given field. In particular, the result "casts absolutely no shadow on the notion of truth. All that it says is that the whole set of arithmetical truths cannot be listed, one by one, by a Turing machine." Equivalently, there is no algorithm which can decide the truth of all arithmetical propositions. And that is all.

This brings us to the other, and possibly even more common fallacy, that Gödel's theorem says artificial intelligence is impossible, or that machines cannot think. The argument, so far as there is one, usually runs as follows. Axiomatic systems are equivalent to abstract computers, to Turing machines, of which our computers are (approximate) realizations. (True.) Since there are true propositions which cannot be deduced by interesting axiomatic systems, there are results which cannot be obtained by computers, either. (True.) But we can obtain those results, so our thinking cannot be adequately represented by a computer, or an axiomatic system. Therefore, we are not computational machines, and none of them could be as intelligent as we are; quod erat demonstrandum. This would actually be a valid demonstration, were only the pentultimate sentence true; but no one has ever presented any evidence that it is true, only vigorous hand-waving and the occasional heartfelt assertion.

Gödel's result is of course quite interesting, if you're doing mathematical logic, and it even has some importance for that odd little specialization of logic, the theory of computation. (It is intimately related to the halting problem, for instance.) It also makes a fine piece of general mathematical culture; but it doesn't shake the foundations of the house of intellect, or exalt us above all else that greps.

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ORIGINAL: GotSteel

A much-abused result in mathematical logic, supposed by ..... [snip]

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ORIGINAL: tweakabelle
Perhaps the error is insisting that the only possible way to answer philosophical questions is through scientific investigation. I am unaware of any scientist of note who would make this claim. After all, such dogmatism is antithesis of proper science.

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Well the comment you responded to asserted that the relationship between consciousness and the brain is interactional, with agency on both sides. I don't know what you mean by "outside the brain" in that context. Where does the 'inside/outside' question arise in this?

Edited to add: On reflection, "agency" is probably the wrong word. What I mean to be saying, or at least closer to it, is that the arrow of cause and effect can point in both directions.

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The idea that the action of a single tiny particle is responsible for generating mass in all the particles around it, and then disappearing is counter intuitive to say the least. Yet it was proposed, and generally accepted as part of our understanding of the quantam world for over half a century until its existence was demonstrated recently.

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The notion that consciousness may depend, at least partially, on an external force or energy doesn't strike me as any more far fetched. Especially when we recall that a complete explanation of consciousness will be impossible as long as we remain entirely in the realm of the physical.

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ORIGINAL: tweakabelle
* Anyone interested in a more detailed examination of this vitally important question is invited to read:
The Origins of Knowledge and Imagination
by Prof. Jacob Bronowski 1979 Yale University Press
While maintaining academic rigour, this text will is easily absorbed by any educated person.

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ORIGINAL: tweakabelle
GS, we can throw this issue back and forwards as much as you like*. Our previous discussion got as far this challenge, which was put to you in post#319:
"We just cannot have a Theory of Everything, a theory that describes all the data without either internal contradiction or external invalidation. If you still wish to contest this point, please demonstrate how such a theory is possible.

Thus far, I haven't seen any response from you to this question. Continuing uwillingness or inability to answer this question will amount to de facto concession of the point. If you will excuse my bluntness, it's time to either put up or shut up.

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ORIGINAL: GotSteel

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ORIGINAL: tweakabelle
Perhaps the error is insisting that the only possible way to answer philosophical questions is through scientific investigation. I am unaware of any scientist of note who would make this claim. After all, such dogmatism is antithesis of proper science.

Of course they wouldn't philosophical questions would be within the realm of philosophy ergo outside their area of expertise.

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ORIGINAL: GotSteel

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ORIGINAL: tweakabelle
* Anyone interested in a more detailed examination of this vitally important question is invited to read:
The Origins of Knowledge and Imagination
by Prof. Jacob Bronowski 1979 Yale University Press
While maintaining academic rigour, this text will is easily absorbed by any educated person.

1979?.....really?.....19 your fucking kidding me 79. You really might want to brush up on what's happened on this topic in the last MY ENTIRE LIFETIME.

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ORIGINAL: GotSteel

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ORIGINAL: tweakabelle
GS, we can throw this issue back and forwards as much as you like*. Our previous discussion got as far this challenge, which was put to you in post#319:
"We just cannot have a Theory of Everything, a theory that describes all the data without either internal contradiction or external invalidation. If you still wish to contest this point, please demonstrate how such a theory is possible.

Thus far, I haven't seen any response from you to this question. Continuing uwillingness or inability to answer this question will amount to de facto concession of the point. If you will excuse my bluntness, it's time to either put up or shut up.

Tweak, your the only one making positive claims regarding whether this red herring is possible. I'm not aware of any way to demonstrate that we'll ever discover such a theory short of discovering it. We certainly aren't there yet, will we ever be *shrug* I don't know. So what?

What I have been pointing out is that your Godel argument is intelligent sounding jibberish fit only for creationist websites (where it frequently appears).

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ORIGINAL: vincentML

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The idea that the action of a single tiny particle is responsible for generating mass in all the particles around it, and then disappearing is counter intuitive to say the least. Yet it was proposed, and generally accepted as part of our understanding of the quantam world for over half a century until its existence was demonstrated recently.

Very often woo woo mystics make the leap from quantum mechanics to consciousness as energy. I take it that is not your intent here but you are trying to demonstrate an instance where understanding of a phenomenon may eventually turn on the appearance of something previously unknown. But, isn't that true of all advances in human knowledge?

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The notion that consciousness may depend, at least partially, on an external force or energy doesn't strike me as any more far fetched. Especially when we recall that a complete explanation of consciousness will be impossible as long as we remain entirely in the realm of the physical.

two things strike me here. 1. I don't understand why you think a complete explanation of anything is a worthy or necessary goal. Maybe only a functional understanding will suffice. 2. I don't see how your point is any different from someone saying we will never have a complete understanding of the universe as long as we remain completely in the realm of the physical . . . so let's seek out something that is greater than the physical universe. Where does science end and mysticism begin?

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ORIGINAL: tweakabelle

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ORIGINAL: GotSteel

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ORIGINAL: tweakabelle
GS, we can throw this issue back and forwards as much as you like*. Our previous discussion got as far this challenge, which was put to you in post#319:
"We just cannot have a Theory of Everything, a theory that describes all the data without either internal contradiction or external invalidation. If you still wish to contest this point, please demonstrate how such a theory is possible.

Thus far, I haven't seen any response from you to this question. Continuing uwillingness or inability to answer this question will amount to de facto concession of the point. If you will excuse my bluntness, it's time to either put up or shut up.

Tweak, your the only one making positive claims regarding whether this red herring is possible. I'm not aware of any way to demonstrate that we'll ever discover such a theory short of discovering it. We certainly aren't there yet, will we ever be *shrug* I don't know. So what?

What I have been pointing out is that your Godel argument is intelligent sounding jibberish fit only for creationist websites (where it frequently appears).

Your continual attempts to link my position to creationist and creationism nonsense are sad and tiresome. Such cheap shots do nothing to further your position, and just lower the tone of the thread. This has been a reasonably civilised thread thus far. Please try to respect that.

As has been pointed out to you previously the Godel argument is not the only way of supporting my position. However sticking with it for a moment, please reconcile your claim that " your Godel argument is intelligent sounding jibberish[sic] fit only for creationist websites" with this paper by Stephen Hawking titled "Godel and the end of Physics".

Hawking sets to examine whether "we ever find a complete form of the laws of nature" and concludes that any attempt to do is doomed to failure. Which is more or less what I have been arguing all along.

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I mean a set of rules, that in principle at least, enable us to predict the future to an arbitrary accuracy, knowing the state of the universe at one time.

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Please rest assured I'm totally uninterested in anything you have to say on any topic and have no wish to receive any communication from you unless it is to apologise for your past repulsive utterly unfounded abuse and generally obnoxious behaviour.

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ORIGINAL: Kirata

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ORIGINAL: vincentML

My point would be that the brain creates consciousness and will as emergent out of memories and neurochemical synaptic networks.

And I'm not saying that view is wrong. I don't know. I'm only saying that this conclusion goes beyond the evidence, which so far is purely correlational.

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ORIGINAL: vincentML

the universe might be the lesser of the two if it does not have some sort of cosmic-neuro connections and is otherwise a process of random events.

And if the universe does have some sort of cosmic-neuro connections, might the universe function like a "brain" (in effect) and therefore be conscious?

K.

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The main thing I hoped to achieve was to demonstrate that the idea
that consciousness had an external dependency or relation of some kind was not as far fetched as it might initially sound. It is not an explanation that can be eliminated as unprecedented or without parallel in the natural world.
I'm not stating that this is what happens merely that it is a possibility along with many others.

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Surely understanding this phenomenon is a worthy goal in itself. While functional explanations might suffice for more mundane phenomena, for a matter of this importance, a more profound understanding is necessary IMHO.

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What is the demarcation point between science and mysticism? I'm not sure that there an absolute one. Evidence based explanations seem to me to be far superior to those that lack supporting evidence. But all that hangs on what is allowed as admissible evidence, who gets to make those definitions, and on what basis the decisions are made doesn't it?