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 Originally Posted by MadMojoMonkey
I don't think that's what the Godel's Incompleteness Theories say about physics.
Yes I wasn't trying to imply that GIT had anything to say about physics. What I was mainly saying was, physics doesn't concern itself with rigorous proof.
So in a sense, there are two ways to answer "even a mathematical model that explains every known thing perfectly may still be false?" - firstly, the physics answer: "how could we ever know it explained every known thing perfectly? we could arbitrarily approach "perfectly" as our measurements got more and more accurate, but we could never reach a perfect standard of measurement", and secondly the maths answer: "assuming the human mind is equivalent to a turing machine, no-one could ever prove that our systems of mathematics are consistent, the model itself may be inconsistent and we couldn't know it anyway"
The GIT's say that no matter how many axioms we put into the system, there will always be statements within the framework of the system which cannot be proven true or false by the axioms, and no finite number of axioms can relieve this property.
Yeah, and further than that, it also says that, in any system we might devise which is at least as complex as basic arithmetic (peanos axioms and the natural numbers), that it is impossible (algorithmically) to prove a systems consistency within that system.
It's possible (but now we're really going down the rabbit hole) that human mathematical creativity is not algorithmic - ie. the mind is not equivalent to a turing machine, in which case Godels theorem doesn't apply to us.
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