"To base that argument" means to provide evidence or justification for the argument. It means using facts, information, or reasons to support and strengthen your point of view. Full definition
These posts are a collection of personal experiences and evidence based arguments for reform. (peacenotpas.com)
This isn't a theory - based argument about positions. (sbnation.com)
However they can still attempt a reason - based argument whether or not the faith - based belief is susceptible to such or not. (religion.blogs.cnn.com)