I think his intentions are pure but his thinking is slightly too inclusive
What exactly do you mean by "show"? You can make a proof? That means that you are using a computational language? But you will be more defensible than the idea of information?
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I might be able to get to a meta proof of the incompleteness of computational proof. I would start by seeing quantum uncertainty, entropy, and incompleteness as aspects of universal overfitting. Nature uses these buffers to cheat and blur the seams of realism (I have observed).
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This is too fanciful for me! You are not reasoning, you are quite freely associating?
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That X is informative to some conscious agenda doesn't prove that X can be defined solely as 'information'. I think that this is a pervasive and profound oversight. Yes it is informative that the sky appears blue, but that doesn't explain why blue isnt just unexperienced numbers
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