On the Theoretically Possible Number of Cases in Natural Language

 Introduction. The case, which is a semantic and grammatical category, appears in natural  languages in the most unexpected way. A word or phrase that has a substantive unit at its  core receives an inflection (internal or external) in one case or another, which can be  expressed both explicitly and implicitly, and has a grammatical meaning. In this case,  inflection can be accompanied by a preposition that has a lexical meaning. These case  indicators, morphological and syntactic, organize the main or secondary substantive part of  the sentence, i.e. are related to the category of space. The number of cases today is still the  subject of scientific debate. Methodology and sources. The present study is based on analizing the views of various  scientists on the category of case, with special attention to the theory of L. Hjelmslev.  According to this theory, the maximum possible number of cases in natural language is 216.  In order to provide a purely formal calculation of the possible number of cases, which would  be at the same time independent on the earlier views, the article represents the substantive  part of the sentence as a semifinitive multiplied by a specifier (proto-specifier). These  statements are prescribed by the binomiality idea, having been developed since 1993 at ETU. Results and discussion. The generally accepted division of sentence parts into main and  secondary ones leads us to dividing all possible cases into direct cases (for subject) and indirect  cases (for secondary substantive parts). Thus, the direct case can be obtained by a simple  transformation from any indirect case, i.e. the space specifier goes back to the spatial proto-specifier. The space proto-specifier represents external space added to substantive mass. The  substantive semifinitive is a substantive mass multiplied by internal space. As the binomiality  idea prescribes, substantive masses can be in four states, while substantive semifinitives can be  in six states. Thus, the number of possible case forms should be equal to 24. Conclusion. According to classical physics, space is three-dimensional, so grammatical  space, both external and internal, should also, obviously, be considered three-dimensional.  This means that four states of substantive mass and six states of substantive semifinitives  can be in each of the three dimensions. Thus, the maximum possible number of cases may indeed reach 216. It should be noted that L. Hjelmslev derived the number 216 in a  completely different way, by dint of much deeper reasoning. In the future, it would be  interesting to compare L. Hjelmslev’s binary oppositions with the constituents of substantive  parts of sentence.