> Suppose I tell you 3 + 2 = 5 and 2 + 3 = 5. Did you learn anything non-trivial about + from those two examples? Did you learn that x + y = y + x for all x and y or that x + (y + z) = (x + y) + z?

I gained some evidence. Do you refuse to accept the theory of gravity because we've only measured some examples where F Gm_1m_2 / r^2, not proven it from first principles?