<p>The paper substantiates the prospects of normativism in law, namely the possibility of using purely logical means to make a judgment as a logical conclusion. The main criticism of normativism is based on the possibility of conflicts of judicial decisions and especially on conflicts of the norms themselves, when a court under similar circumstances can make opposing decisions which are formally valid. Critics of normativism argue that logic is helpless in resolving the conflicts and that higher justice must be guided by the discretion of judges who share common values or a common ideology, especially in the case of totalitarian societies. However, we show that there are two types of logical argumentation in the elimination of these conflicts: (a) Aristotelian, when a more general basis is sought, from which only one of the contradictions follows; (b) non-Aristotelian, when a compromise is reached between two contrary statements. In the second case, this technique is used mainly for civil cases. Moreover, this technique is quite formal and does not require an appeal to paraconsistent or other non-classical logics for eliminating the conflict. Using two recent court cases, we demonstrate how the proposed two types of logical argumentation work.</p>