The paper tries to show, how fallibilism and necessity are related to each other in the philosophy of Ch. S. Peirce. Fallibilism as an epistemological doctrine is grounded in the idea, that there are no definitely valid propositions. Then, however, the approval of the existence of necessary conclusions in mathematics equals claiming that Peirce’s philosophy embodies a contradiction. The author argumentation is, that the latter is illusionary: in fact there does exist such an interpretation of Peirce’s philosophy, which enables fallibilism and necessity to coexist without any contradiction.