The article argues that, while Quentin Meillassoux‘s project, undertaken in After Finitude, merits attention, since the French philosopher is right that faith in sciences‘ capacity to open up new domains to thought must be restored, the solutions he offers have two serious shortcomings. 1) His depiction of science as the producer of ancestral statements does not capture satisfactorily the essence of scientific creativity. 2) The claim that everything is necessarily contingent is fundamentally incompatible with scientific knowledge. The article, then, contrasts Meillassoux‘s principle of the necessity of contingency with a principle that is extracted from the historical epistemology of Léon Brunschvicg and Antoine-Augustin Cournot. Instead of a principle of unreason, the article defends a principle of a metamorphosing reason founded on the practical impossibility of irreducible contingency.