Adaptive logicians have long treated mathematical theories using non-monotonic logical techniques. Other non-classical logicians are just starting to come around to this idea. In order to have a set theory that is powerful enough, for example, to act as a basis for model theory, we need to be able to prove a lot of standard classical theorems. To capture these classical theorems within the context of relevant logic, I have previously suggested using conditionals of a sort in order to provide surgical applications of classical rules like disjunctive syllogism. This paper will explore this technique further and discuss certain of its epistemological consequences.