Asymmetry as Ontological Augmentation: Two Proofs of the Independence of the World's Directedness from Pure Logic

This paper investigates whether the directedness and irreversibility of the world are derivable from the pure logical structure of possible worlds. A symmetrical conceptual scheme consisting of four notions—Nothing₁, Nothing₂, Infinity₁, and Infinity₂—is introduced and formally articulated within a modal framework. It is shown that in the minimal normal modal logic K, a fully symmetrical cyclic structure is consistent. Two independent arguments are then developed. First, a causal-informational proof of irreversibility demonstrates that strict return becomes impossible once cumulative differentiation is introduced. Second, a modal-structural argument shows that symmetry between openness and concreteness remains consistent unless additional ontological constraints are imposed. The central thesis is that directedness is not a logical necessity but requires ontological augmentation beyond pure modality.