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Theory of everything vs Godel's incompleteness theorem. 
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#19
Mar1412, 03:37 AM

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#20
Mar1512, 01:02 AM

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So similarly, you can imagine some weird hypothetical TOE in which integers are represented not as themselves, which would be hohum physics wise, but rather in terms of he physical content of the theory. For instance, you can have an infinite number of particle types, each type corresponding to one natural number. Then various properties of numbers would correspond to various properties a particle can possess, and Godel's theorem would tell us that there is some particle property such that the proposed TOE cannot tell which particles possess it and which don't. But this is a rather farfetched scenario, and it would only become an issue if the theory proved enough facts about the natural numbers for Godel's theorem to apply, and depended strongly enough on all knowing all the truths of number theory, both of which are very unlikely possibilities. 


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