The Non-Mappability of Aristotelian Metaphysics under Conditions of Ontological Comparability

The aim of this paper is to apply the conditions for the comparability of ontological descriptions to a concrete ontological system and to examine its conformity under those conditions. This paper does not evaluate the validity or superiority of a theory; rather, it adopts the standpoint of assessing conformity on the basis of the definability of descriptive functions—identification, change, possibility, comparison, and structural difference—and their structural correspondences. In this framework, an ontological description is formalized as a structure M = (X, H, Φ, V, U), and comparison is defined as the definability of a mapping that preserves the distinctions among these descriptive functions. It is further shown that these functions form a hierarchical dependency with respect to definability: if any stage in this chain fails, the subsequent functions are not defined. On the basis of this framework, the major components of Aristotelian metaphysics—categories, syllogistic inference and motion, potentiality/actuality, and the four causes—are examined in terms of their correspondence to these descriptive functions. The analysis shows that while categories provide a structure corresponding to identification, syllogistic inference and motion are not definable as transition relations; potentiality, not presupposing a set of transitions, is not definable as a constraint operation; and the four causes are not formulated as mappings that represent structural transformation. Accordingly, these functions do not simultaneously hold as a chain of definability, and no mapping that preserves them is definable. Therefore, Aristotelian metaphysics does not satisfy the conditions for the comparability of ontological descriptions in the sense defined in this paper. This conclusion concerns structural conformity under the given descriptive conditions and does not constitute an evaluation of the historical significance or systematic value of the theory.