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>Sure, we can say 1 + 1 = 2, and that's objectively correct

even that can't be objectively correct because it based on agreed upon the definition of 1, definition of 2, definition of + and the axiom.




Agreed. A couple of examples to illustrate this: in boolean arithmetic, 1+1=1, in modular (2) arithmetic, 1+1=0.




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