In Reason, Truth and History, Hilary Putnam characterized informal rationality as an alternative that allows to overcome limitations evidenced by the formalist conceptions of rationality. Initially, the paper reviews the characterization provided by Putnam, trying to determine what kind of statements may function as principles of rationality within an informal framework. It establishes that, while Putnam denies any universal principle of rationality, he accepts relative, general and vague principles, that remain subject to needs of cognitive interrelationship with the environment. It shows that principles make exceptions, do not have specific contents and do not provide conclusive results; however, this does not prevent us from assessing the adequacy of conflicting principles. If two individuals have different conceptual schemes, this is due to the fact that they have different cognitive purposes, and it can be asserted that the choices of both are rational. From this point, the paper defends and analyzes the possibility of reviewing principles whose denial is currently not conceivable. Finally, it states that both expressing and maintaining beliefs of controversy are historical elements that should be contemplated by an informal conception of rationality.