The question of morality is indispensable to postmodernist thought. Postmodernism, often described as a form of anti-foundationalism, provides answers to this question that raise  further questions and objections. This paper asks if morality can be established without a foundation. In answering this, the paper discusses the thought of two prominent postmodernist philosophers, Richard Rorty and Gianni Vattimo. For conceptual and historical perspective, the study explores the meaning of foundationalism before tracing the transition from foundationalism to anti-foundationalism. It examines the main ideas of Hans-Georg Gadamer, as a pioneer of twentieth century Hermeneutics, at the core of which is the concept of the finitude of man. The article argues the importance of this concept to the domain of morality, ultimately concluding that morality can't be established without a solid foundation.