In this article, I engage in a discussion of the approaches of the normativists postulating the absence of a linguistic norm and assuming the identification of the norm with usus. I have made an attempt to prove the existence of the norm as a level of internal organisation of language, based on linguistic and mathematical-computational considerations. I accept the need for separate models of language: linguistic and mathematical, which serve different purposes and have different properties. I ponder the dual nature of language manifested by its finite infinity, assuming that only the usus is infinite. I postulate the adoption of a theory (formulated by K. Kłosińska) assuming the existence of an invariant norm together with ‘allonorms’. I also propose the introduction of the probabilistic Gaussian model into the codification procedures of the linguistic norm as a method objectifying the procedure and removing the (qualitative and quantitative) arbitrariness of codifiers.