Not true. When expressing the equation as 2 + 2 = 4, then it is implied that we are working in a base for which the symbol 4 is defined, which would be base 5 or higher. In any of these defined systems 2 + 2 = 4. To say that 2 + 2 = 4 is false is never logically consistent, because for the systems in which this is so the symbol 4 is undefined, therefore the statement is not provable.
"Not true. When expressing the equation as 2 + 2 = 4, then it is implied that we are working in a base for which the symbol 4 is defined, which would be base 5 or higher. In any of these defined systems 2 + 2 = 4. To say that 2 + 2 = 4 is false is never logically consistent, because for the systems in which this is so the symbol 4 is undefined, therefore the statement is not provable."
Hah! You make a good point. Just as I can definitively say that 2+2=11 means that I'm using base 3, 2+2=4 means I must be using base 5 or higher. You win!