While in non-legal texts linguistic uncertainty either does not hinder normal linguistic practices or can be removed by clarifications, the elimination of uncertainty in legal texts is complicated since peculiarities of legal language precludes its complete exclusion. Accordingly, the task of overcoming legal uncertainty is delegated to the judge and the question arises as to what methods of dealing with the legal text are applicable. The article examines the approaches distinguished in the theory of legal argumentation to assess whether they can offer a methodology which will be able to overcome the policy consequences of the language “open texture” as a characteristic of uncertainty of the natural language in which legal texts are presented by formalizing the process of choosing one of the possible options of the legal text interpretation in judicial decisions. The author concludes that the methods to deal with an uncertain legal text offered by the topical-rhetorical and dialectical approach are limited to the formulation of requirements for the process of argumentation (which do not guarantee absolute predictability of the decision to be made), as well as criteria to evaluate the justification of the decision retrospectively. In turn, the possibility to critically assess the arguments limits the arbitrariness, forcing the judge to follow standards of acceptability and sufficiency of the reasoning to justify their decision.