I find it funny that so many people drag Gödel's proof into the domains of physics and philosophy of mind in the hope that they can show that some of reality is too broken to be represented in mathematics, instead that some of mathematics was too broken to represent reality.
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A re-presentation can only occur through another presentation. Mathematics can only be used to present itself. To get sights, sounds, feelings, thoughts - even geometric shapes requires a non-mathematical, non-representational aesthetic. Math only gives the 're-'.
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Even to say 'expressed by your mind' has no mathematical or physical meaning. Neither of those domains has any use for expression.
End of conversation
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