Postmodernism, while supporting epistemologically itself in the poststructuralist theory, has marked its footprint in education with the realities of 'fragmentation', 'incoherence' and 'political chaos'. While there are academics which assert that 'there is not a postmodern theory of education' (Green, 1994), we assist currently to the debate of modern academics versus postmodern theorists that reclaim, respectively, their particular vision of the university in terms of the idea of the university, the teleology, social functions and the epistemology in the university institution. Specially imperative is the analysis of the contributions of the Bolonia Process in the university institution and in the debate modernism-postmodernism, for the educational competency of the European Union has left a footprint in the university educational tradition of the European continent. In sum, among the conclusions of this debate it is essential the promotion of the humanities, in the sense that it belongs to the university the mission of the social and political leadership of Western society. It is the responsibility of the humanities and the social sciences -more than of other practical disciplines currently promoted- the design of the model of man and society of the XXIst century. Without such orientation, the society rests in the dictate of the economy as only social lookout, with all the risks, limitations and impoverishment that this implies.
