This chapter explains the motivation for Conceptual Nonnaturalism. The upshot is pessimistic and skeptical about the prospects for Conceptual Nonnaturalism. Importantly and characteristically, nonnaturalism rejects the thesis of normative naturalism that moral and other normative properties are natural ones. Conceptual Nonnaturalism is compatible with metaphysical naturalism, according to which the natural exhausts reality. The chapter describes the familiar, standard, metaphysical and epistemological challenges to orthodox nonnaturalism and then discusses how Conceptual Nonnaturalism seeks to avoid these challenges. It criticizes Terence Cuneo and Russ Shafer-Landau's theory of conceptual truth and argues that their theory of concepts faces challenges that are similar to those faced by orthodox nonnaturalism. The chapter also criticizes Cuneo and Shafer-Landau's claim that there are substantive moral claims that are conceptual truths. Cuneo and Shafer-Landau make a number of claims in arguing for their thesis that the fixed point propositions are conceptual truths.