Philosophy is a radical inquiry whose task is to interrogate the fundamental assumptions of some given activity, discipline, or set of beliefs. In doing so, philosophical inquiry must attempt to delineate a problem and to develop a method for resolving that problem. However, to be true to its intention, philosophy must be able to examine not only the object of its inquiry but also its own method of interrogation. To accomplish this task, philosophical inquiry must be able to create a distance not only from the assumptions under investigation but also from its own assumptions, which is to say, that it must be able to raise questions about its own method. This self-reflexivity requires that any given philosophical investigation must be examined from an alternative vantage point. Since the assumptions which inform the inquiry are deeply imbedded within a given culture, immanent critique is insufficient. The only way to step outside the boundaries of these cultural presuppositions is to reflect on the given problem from the vantage point of another culture's philosophical tradition. Thus, I argue that philosophical inquiry is unable to go beyond certain limits without being cross-cultural philosophy. I illustrate the way in which cross-cultural philosophy does this with respect to the problem of the self by placing the Western philosophical approach to this problem in dialogue with the Indian Hindu-Buddhist narrative.