Metastructural Theory in GGM: Prior Conditions of Structure Formation, Posterior Evaluation, and Recursive Transition

In GGM, the meta is not a single transcendent level fixed outside Structure. Functions that mediate the formation of Structure and functions that evaluate an already formed Structure are both meta-level in role, yet they occupy different positions in the generative order and run in different logical directions. This paper sets out that distinction under two interpretive names: prior formative meta and posterior evaluative meta. The two positions are not reducible to each other, yet they are recursively linked, so that the evaluative result of one phase may be converted into a condition of the next. Even that conversion, however, does not license the circle that would return Necessity to the status of a cause of Structure. This arrangement calls for a distinction that ordinary usage conflates: between inclusion, whereby a broader category subsumes narrower items, and objectification, whereby something is taken as an object of description and evaluation. It is the latter that constitutes a meta position, and since an object must already stand before it can be taken as one, evaluative meta is necessarily posterior. Hilbert's proof theory illustrates from outside the system that the same point is not peculiar to GGM, since its metamathematics reasons by more restricted finitary means than the object mathematics it studies. Tarski's result points the other way, since for sufficiently expressive formalized languages a truth definition succeeds only where the metalanguage is of higher order than the object language. That metahood falls on either side is itself evidence that it is not defined by breadth of inclusion. This paper is a conceptual introduction for entering GGM Volume I: an interpretive guide for readers that registers no new official concept or formula. This record contains both the English and the Korean edition.