The nature of paradigm and paradigm shift is such that existing sciences cannot be overcome exclusively via logic, reason, and experimentation. The reason being is simple; both paradigms define themselves as good science. There are no neutral criteria by which you can actually compare two sciences. Aristotelian astronomy defined the universe at this point and was (locally speaking) the best explanatory model. In order to actually overturn a prevailing theory, other factors must be taken into account. For some, that might be waiting until the old guard dies off, and the paradigm goes with them. For others, all that's needed is a strongly passionate argument.