- July 6th, 2017, 12:57 pm
#290945
It's not word games at all, it's the nature of mathematics. It is impossible to ever refute any mathematical statement regarding "1 + 1 = 2" by referencing empirical evidence. Adding two integers is governed by the axioms of the system. In a certain system "1 + 1 = 2," in a certain system, "1 + 1 = 0," and these systems will not change even if every time someone added one orange to another orange and mysteriously ended up with 5 oranges. This is because the systems of math are based on their axioms and are independent of external evidence. Different mathematical systems, however, can be devised where the "addition" does not involve distinct integers, so that the math can better reflect what is empirically being discussed. However, math will always exist independently of any empirical evidence. This is why Einstein could not refute Euclidean geometry, despite showing spacetime was curved, because Euclidean geometry is based on a specific set of axioms, not on empirical evidence.