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Banality and Unresolvedness

This monograph develops a field-theoretic theory of meaning grounded in the analysis of banality, repetition, and semantic instability. Departing from classical functional approaches—where meaning is modeled as a mapping—the work proposes that meaning is not a static value but a geometric property of a cognitive field. The central object of the theory is a scalar potential , defined over a semantic space. Within this framework, meaning is identified with the magnitude of the gradient: while instability (unresolvedness) is associated with curvature: Banality is formally defined as the degenerate phase in which both gradient and curvature vanish, leading to a flat field with no differentiation or interpretive structure. In contrast, unresolvedness corresponds to regimes of excessive curvature and instability, where no stable semantic attractors exist. The theory establishes a fundamental duality between banality and unresolvedness, showing that they constitute opposing limits of a single dynamical system. Meaning emerges only in the intermediate regime, characterized by controlled tension—non-zero gradient and bounded curvature. To parameterize the space of semantic fields, the monograph introduces the signature space Syg (a, b, c).