I have heard that Gödel Proved that Arithmetic cannot be reduced to logic or formal logic. Although I have read explanations which basically state that arithmetic is not complete and thus not definitional like in formal logic, I cannot get my head around how 1+1=2 is NOT reducible to formal logic. This seems like an obvious analytic statement in which "one and one" is the same as saying "two". Can anyone shed light on this?
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