The shape of the Earth can also be determined from the axiological standpoint. If knowledge of a particular shape of the Earth has many applications we use every day, while the other has none, then we can be sure the one with many applications is the correct shape of the Earth.
There is absolutely no technology that depends on the supposed ‘knowledge’ that the Earth is flat. On the other hand, there is plenty of technology we use every day that depend on the understanding that the Earth is a sphere. And therefore, we can be sure that the Earth is a sphere.