Recent developments in aging research have added new urgency to the bioethical debate concerning life and death issues, the value of life, and the reasonable limits of medicine. This paper analyzes the basic structures of the liberal and conservative components of this debate, showing that there has hitherto been inadequate analysis on both sides concerning the nature and implications of the value of life, as well as, and as distinct from the value of life extension. Classic concepts of the intrinsic or extrinsic value of life are argued to be tangential or actually irrelevant to the value of life's continuance and so to the value of life extension. An analysis of personhood is proposed which focuses explicitly upon the value of life extension to persons. This analysis shows that persons may only intelligibly be understood as processes, for whom life extension is an inalienable and fundamental value. It is further proposed that, properly understood, such an analysis may significantly narrow the liberal/conservative divide in bioethics.