Abstract. The purpose of this article is studying the properties of both arbitrary tuples and the individual N-ary tuple , as well as the properties of the relevantly named objects comprising this tuple. It is proposed to reconsider and offer a clearer view of the basic concepts in the collective subject related field, as well as to implement emerging new opportunities for their analysis. 2 postulates, 10 assumptions, and one hypothesis are introduced to accomplish this. The new concepts of "intelligent tuple" and "conceptual field" are introduced, and the properties of the relevantly named objects are examined. The possibility of tuple operations is considered. The necessary and sufficient collective subject properties are proposed and discussed.