Penelope Maddy Department of Philosophy, University of California, Irvine, California 92717 pmaddy@benfranklin.hnet.uci.edu Title: Methodology for the Naturalist Abstract: Among the outstanding methodological questions of contemporary set theory are these: do statements independent of the standard set theoretic axioms remain genuine mathematical problems? and if so, what means are appropriate for answering them? In this talk, I explore a naturalistic approach to these questions.