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Decius comments on Natural Laws Are Descriptions, not Rules - Less Wrong
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Specifically, he proved that there is a true statement in a formal system that cannot be proven by the formal system. There is an additional option: that of a formal system which is incapable of self-reference or self-description.
That would be a system in which "There does not exist a valid proof that "There does not exist a valid proof that the statement "There does not exist a valid proof that the statement ""There does not exist a valid proof that the statement... ...is true" is true" is true" cannot even be constructed.
I should have been more careful when I said "arithmetic" too, because if I recall correctly a system that has only addition and not multiplication is insufficient to construct a self referencing statement.
I guess I am making the assumption that if the rules of the universe exist, they at least contain addition and multiplication since we can construct both of them.