Karl Popper believes that science does not necessarily seek to unveil the truth. He does not assert that the unending formulations and testing of hypothesis or theories will ultimately generate truth or certainty. On the other hand, the image that science likes to project of itself is that of rationality per excellence. Armed with a special tool called the scientific method, the institution of science believes it now possess the tool with which it could now generate logic of justification and certainty. This tool or method is what Magee calls the Hallmark of science. This study examines the rationality of the claims of the scientific enterprise in the light of Kuhns, Feyerabends and Poppers conception of Verisimilitude with the view to showing how problematic the whole idea is. In all, we shall present Poppers verisimilitude concept as a more rational ideology that the scientific enterprise should adopt in place of what is presently conceived as the hallmark of science.