I cannot conceive of a possible world where “making XX and XX come out to XXXX required an extra X to appear from nowhere, and was, moreover, inconsistent with other arithmetic I visualized, since subtracting XX from XXX left XX, but subtracting XX from XXXX left XXX.” Unless, in that possible world I did not know how to reason.
If 2 + 2 really was 3, what would 1 + 2 be? Not 4, since then 2+2 = 2+1 and since subtraction is defined as the inverse of addition (if its not, its not subtraction) we would have 0 = 1. Not 3, since in the world you’re imagining ... (read more)

I cannot conceive of a possible world where “making XX and XX come out to XXXX required an extra X to appear from nowhere, and was, moreover, inconsistent with other arithmetic I visualized, since subtracting XX from XXX left XX, but subtracting XX from XXXX left XXX.” Unless, in that possible world I did not know how to reason. If 2 + 2 really was 3, what would 1 + 2 be? Not 4, since then 2+2 = 2+1 and since subtraction is defined as the inverse of addition (if its not, its not subtraction) we would have 0 = 1. Not 3, since in the world you’re imagining ... (read more)