Is Mankind Smart Enough?

[flatline]

I think we'll have to think of some different word. I imagine Ray Kurzweil (futurist author) has already thought of something.

[Piers]

Clearly No. Gödel’s incompleteness theorem shows that any universe model we construct will not cover everything. I really don’t think there is room for debate.

[Cooker]

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Clearly No. Gödel’s incompleteness theorem shows that any universe model we construct will not cover everything. I really don’t think there is room for debate.

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I am not an expert on Gödel’s incompleteness theorem, but I am fairly sure that it is not far reaching enough to make such statements. Certainly, euclidean geometry is a complete theory, so complete theories do exist. The existence of complete theories is enough to allow for the possibility that there may exist a complete final theory of the universe (although it could not be based on a recursive scheme I believe).

[Lestat]

<font color="red">The existence of complete theories is enough to allow for the possibility that there may exist a complete final theory of the universe (although it could not be based on a recursive scheme I believe). </font>

I don't think there's much question that a complete theory of the universe exists. The question is will man ever figure it out?

[Piers]

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I don't think there's much question that a complete theory of the universe exists. The question is will man ever figure it out?

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You are correct in the sense that the universe is its own model.

What I am saying is that it is not possable for us create a complete model of the universe using a set of axioms plus logic. which is what mankind will have done if it created the OP's "Theory of everything".

The reason Man can not understand everything is not that we are not cleaver enought, but that its not logical possable for us to.

[Piers]

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I am not an expert on Gödel’s incompleteness theorem, but I am fairly sure that it is not far reaching enough to make such statements. Certainly, euclidean geometry is a complete theory, so complete theories do exist. The existence of complete theories is enough to allow for the possibility that there may exist a complete final theory of the universe (although it could not be based on a recursive scheme I believe).

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Basically my understanding of Gödel’s theorem (its about twenty years since I worked my way thorough it) is that you take a sufficiently complicate theory, anything that includes the natural numbers should do.

Then you encode the theory within itself. What this means is that you have a well-formed statements within the theory which have a meanings on two levels:

There is the up front meaning, as given by the logical system itself.
An indirect meaning that you get by decoding the statement.

If the statement is a theorem then both meanings are valid.

You now show it is possible to construct a statement that when decoded has the indirect meaning “This statement is not a theorem of the logical system”.

Clearly the statement is not a theorem, because if it was a theorem that its indirect meaning would be true and hence it would not be a theorem. For much the same reason its negation is also not be a theorem.

So we have a statement that is in a sense ‘true’ but not contained within the system.

Now imagine that we have devised a model of the universe. This will consider a set of rules by which the universe is governed. By their nature it will be possible to express these rules in such a way that Gödel’s theorem can be applied to them.

Statements using the language of our universe model become statements about the real world that can be either true or false.

So what can you say about the statement “I can not be explained using this model”. Both it and its negation map on to a meaningful statement about reality, one of which is true but neither are contained within our theory.

(Or things are really weird, and logic breaks down in some way, which would negate the above argument, but that would also negate any theory we would have knocked up as well.)

[Cooker]

But the one key point of Godel's theorem is the type of system. I believe it must have an infinite recursive structure to fall into the class of theories that must be incomplete. If the final theory doesn't have such a structure, then it is possible that it could be complete (like euclidean geometry).

I personally feel as though physics is being overly dominated by a search for a final theory, but I think a final theory is still a possibility (although I entertain many ideas about possibilities here as well). If it is to be complete, then it will have to be much simpiler than the arithmetic of the natural numbers I agree. However, I do not agree that a final theory must be more complex than the arithmetic of the natural numbers, so I think completeness is still a perfectly possible choice. I think this would suggest that the natural numbers are an invention of man and not of nature.

[Piers]

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But the one key point of Godel's theorem is the type of system. I believe it must have an infinite recursive structure to fall into the class of theories that must be incomplete. If the final theory doesn't have such a structure, then it is possible that it could be complete (like euclidean geometry).

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Do you really believe that a complete theory of the universe might not conatin an infinitive recursive structure (such as the natural numbers)? The possibly of the universe not haveing such a recursive structure goes so against my intuition that I really cannot imagine it.

[hmkpoker]

I think it's pretty foolish to say that our brains will ever be able to comprehend all the complexities of existence...

...but perhaps we can build something that can.

[hurlyburly]

I said yes, I can't see how it won't happen at some point in the future. Every few generations adds something significant to the general knowledge pool. I doubt humnan nature will allow for everyone to prove mathematically that it's correct, but several people will, and all it takes is one to figure it out, and then many can understand it.

Discovery is the key, mankind is keen on discovery and there is a lot of incomplete information.