This paper clarifies the functions and roles of the Numeration assumed in Minimalism and what categories are included in the elements of the Numeration. A numeration is a set of LIs’ as an array at worktable for CHL in which only those necessary for the operation of syntax to derive a correct structure are selected. It participates in CHL sometimes with an integration of features, sometimes with separated features. This operation is ultimately intended to act as a suitable interpretation that converges in the PF and LF. An element of (N) consists of a pair of (LI, i) in which LI refers to a lexeme and i refers to the index of how many times the LI is used to participate in CHL. The process of operation generating a syntactic object at each level of CHL will not stop until the index becomes zero. The (N) provides the LIs’ for a deriving structure determining the reference set, and the cause of the features’ check. This paper explained it with some examples of Korean that the (N) also worked as a criterion for determining which was the correct or not among competitive derivations. This set of (N) is used as materials for the minimal computation of derivation and prepares the basis for a very limited basic operation in the external and internal movements of the syntax. Examples The operation of the (N) include Select, Merge, Move, and Agree. Next, it was argued that the functional category should be arrayed in a separate space called discourse numeration((DN)) because it serves as a discourse-level information structure rather than as the (N) for syntactic CHL. For example, in Korean, the functional categories ‘Top, Foc’ in the information structure level such as ‘topic’ and ‘focus’ should be checked at the information structure level. These categories correspond to the phases of “discourse model, situational knowledge, encyclopedia knowledge, etc.” This can be seen as similar to the (N), which is the space of an operating system for the working LIs’ selected from the lexicon before a syntactic object enters the computational process.
Since functional categories, such as C, T, and I, have a check relationship in a phase beyond the sentence dimension, the possibility of expanding these functional categories to elements of the discourse selection set was also carefully presented. With this assumption, the discourse selection set should be constructed before (N) is constructed. Functional categories such as C, T, and I have a checking chain in the phase beyond the syntactic level. Therefore, it was suggested that these functional categories should also be incorporated as elements of the (DN). With this assumption, the (DN) must exist independently before the (N) is constructed.