Erosion as the Ontological Condition of Diachronic Self-Identity: A Deductive Self-Model Theorem of Phenomenological Lack

Any system that persists through time must track its own temporal states, which forces it to form a minimal model of itself. Because the system's relation to itself differs across moments, comparing its present state to the self-model creates a normative standard it never fully meets. This gap—phenomenological lack—is a necessary modal result of temporal self-relation, not an empirical failure. The structural changes caused by temporal indexing are redefined as erosion, independent of decay or empirical assumptions.

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Abstract

Abstract This paper establishes a fully deductive account of phenomenological lack grounded in diachronic self-identity. I demonstrate that any system satisfying diachronic identity necessarily operates under temporal indexation, which analytically entails the formation of a minimal self-model as a structural requirement of maintaining identity across non-coincident temporal states. From this, I derive that self-relation is necessarily non-equivalent across time, and that any internal comparison structure must generate a normative horizon. Phenomenological lack is shown to be the modal consequence of comparing present state to this horizon under conditions of representational non-coincidence. Erosion is redefined as the class of all structural transformations induced by temporal indexation, without appeal to decay or empirical assumptions. Keywords: Diachronic identity, self-model theorem, non-equivalence, temporal indexation, lack, ontology, modality