The Galileo Affair has received considerable attention in recent years, particularly on account of the establishment of a study commission by the Holy See. New interpretations have been offerred, including some which assert that the case is now closed and may be forgotten. This interpretation can be traced back to the well-known thesis of P. Duhem, who considers Galileo's epistemological outlook to be incorrect, and sees in this the source of conflict. However, an analysis of the epistemological content of this thesis, and in particular of the value of the galilean proofs and of the diverse conceptions of science maintained by Galileo and R. Bellarmine, shows that this view is inexact. Galilean science, even though it lacked a precise understantding of itself, constitued a new form of knowledge, which at the time was not adequately recognized. The Galileo Affair leads us to acknowledge that the correct attitude for dealing with possible conflicts, at the epistemological level, between science and faith, especially when faced with the appearance of new scientific areas, necessarily includes a profound reflection upon the scope and value of the various forms of rationality.