Again you are a talking in philosophical terms. Godel's theorem cannot be applied to that, period. There is even a book for it because so many people tried to apply it incorrectly.
Please try to keep up we just went through a long discussion of what is necessary to apply Godel's theorem in the way I have. Af_newbie summed it up immediately above.
If you want to prove that the universe is an incomplete system that has some axioms that are true but cannot be proven, you have to represent the universe as a system of such axioms, then the use of the theorem would be valid.
To apply Godel's theorem in the way that I did requires me to assume that the universe is ultimately logical aka that it is possible to describe every phenomenon in the universe mathematically. This is an assumption I make in my argument.
You can alternatively choose to believe as af_newbie apparently believes that the universe is illogical and thus globally indescribable with mathematics. Then you would reject my first claim as Godel's theorem would not be applicable.
I wish science would work like that. You just state that something must be possible, and boom you have a proof.
Your claim is basically: Arithmetic axioms that describe the universe must be possible to exist, therefore one of them is true but cannot be proven.
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BTW, the world as we know it at the quantum level, near or at singularities (Big Bang or Black Holes) is not intuitive nor logical
You are twisting my words out of context again.
Who said anything about a proof? I have laid out a logical argument and like all logical arguments it rests on some basic assumptions.
I never said that I could prove the universe is logical. I said that
if the universe is logical then it is incomplete. It is a conditional argument not a proof.
Everything in our lives including the reproducibility of science is consistent with a logical universe. Only at the very boundaries of our knowledge with esoteric phenomena such a black holes and quantum effects so poorly understood that their continue to be multiple competing theories explaining what exactly is happening it is more difficult to say things are logical.
Black holes and poorly understood quantum phenomena strike me as shaky ground to rest a belief in an illogical universe upon but to each his own.