This is a bit of an unjust to the history of sociology, and science writ large. What Weber does is help establish, axiomatically not experimentally, the base d

This is a bit of an unjust to the history of sociology, and science writ large. What Weber does is help establish, axiomatically not experimentally, the base definitions for the system of sociology. So yes, it is a fiction from another system, but it must be assumed true in that system. This is, ironically given your accusations, a purely mathematical approach to creating a field. It is taught in 101 because it is important when teaching a subject for the learner to be able to answer “And what again are we doing here?”