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

Summary

A formal philosophical argument demonstrates that phenomenological lack—a sense of deficiency or incompleteness—follows necessarily from the structure of being a self that persists through time. Any system that maintains identity across different times must index itself temporally, which requires forming a minimal self-model. Comparing the present self to this model inevitably generates a normative horizon, and lack arises as the modal result of that comparison under conditions of non-coincidence. Erosion is redefined as all structural changes caused by temporal indexation, without 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

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