2+2=4+1-1, so if you think 2+2=4, you should feel bad for both overestimating and underestimating the value of 2+2 by 1.
When you say some Nat doesn't correspond to a quantity, do you claim that due to the small size of the universe or the small size of our brains? Are you an ultrafinitist?
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Small size of our brains, though it is also too large for any being which can exist in the universe. We are finite, in a sense I'm an ultrafinitist, but it is at a level deep into the interpretation of the math, not the math itself. The reals in classical logic are still useful.
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Any "resolution" which claims to make 3^^^3 sensible is only making a model of 3^^^3 sensible to a model of some agent in a model of the universe. It cannot be made sensible by the real actual us in the real actual universe.
End of conversation
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