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 3 – 2 = 2 so than if 2+1 = 3 we can substitute it for 3 (because it ‘is the very same thing as 3’) and get 2+1-2=2 and since addition is commutative (its just putting 2 things together and I can’t conceive of the order mattering) we would again have 1 = 0.
Now, you can write a post about an imaginary world where addition is not commutative or where things have different properties than themselves (so I can’t substitute 2+1 for 3) or where the set of integers is not closed under addition but they wouldn’t be conceivable.
Yes I can conceive of putting 2 ear plugs next to 2 ear plugs and being left with 3 but even if that happened I would still believe that 2+2 = 4
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 3 – 2 = 2 so than if 2+1 = 3 we can substitute it for 3 (because it ‘is the very same thing as 3’) and get 2+1-2=2 and since addition is commutative (its just putting 2 things together and I can’t conceive of the order mattering) we would again have 1 = 0. Now, you can write a post about an imaginary world where addition is not commutative or where things have different properties than themselves (so I can’t substitute 2+1 for 3) or where the set of integers is not closed under addition but they wouldn’t be conceivable. Yes I can conceive of putting 2 ear plugs next to 2 ear plugs and being left with 3 but even if that happened I would still believe that 2+2 = 4