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Originally Posted by qiflow What Godel proved is that each there are statements in a formal axiomatic system that are true but not proveable. A theory does not have to be proven true. That is why it is a theory. |
It isn't about whether you can prove the theory. It is about whether the theory says something about the statement.
Whether the theory says (Prove means the theory "says") the statement is true or false.
But every theory after Gödel has statement, with are inside the theory neither true or false (or the theory says that the statement is both true and false).
But outside the theory, in the "real world", the statement can be true or false.
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So even if you can't prove something about the theory, that doesn't mean the statement is not true.
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There are two things in a theory.
The "rules of the theory".
Then you take a statement and put it into the theory. The theory either the statement is true, it is false, that the statement is neither true or false or that the statement is both false and true.
Now you have for every theory a statement A that the theory either answers with both true and false or neither true nor false. But in reality the statement is true (Statements like: "This statement is false" are also in reality neither true or false).
So you would need an additional rule in your theory that says A is true or that says A is false. But that creates a new statement B that has the same problem.
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Good points. Are you saying that the theory can't exist because it would need an infinite number of statements? There are nonsensical and inconsistent theories of everything that don't need an infinite number of statements. The answer to any question would be "Yes".
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So the question "Does every question has to be answered with "No"" will be answered with "Yes".
That means that every Question is answered with "Yes" and "No" at the same time with conflicts with the concepts of logic. Something is either True, False or something in between but it can't be both True and False.
So your theory is false (by the definition of false).
So there are theories of everything that are false.
When I said their isn't a theory of everything, I meaned right theories or maybe right theories.
Maybe something like: "42" or " " could be a theory of everything but a meaning full theory that does actually say something is no true theory of everything.
At the moment you have an infinite amount of statements Gödels theorem comes into play.
Another question, which is a bit more on Topic:
Is Chaos Theroy offensive?
I mean the butterfly surely can't be made responsible for creating that hurricane, isn't Chaos theory unmoral when it makes the butterfly responsible?