Functionally, you could challenge some assumptions but not all (though you could hypothetically). You say assumptions are embedded in premises, I could further stretch and claim definitions are embedded in assumptions. So, we regress enough until we re-define the event, theory, experience and what have you until an agreeable (or not) definition is found. This leads to not only a rift between political left and right but a major idelogical/phisophical divide in which we will be forced to choose sides at some point.