Basic Constructs of a Formal Theory of Reflections

Abstract

In this paper, the reflection, a structural and/or functional change in an entity caused by external or internal influence, is traced in extensive detail across Western philosophy from antiquity to phenomenology, Eastern traditions, Islamic and Late Antique thought, the historical idealist–materialist debate, and modern cognitive science, neuroscience, predictive processing, embodied cognition, and information theory, revealing a single recurring structural pattern beneath vastly different vocabularies: one entity becomes present in another without being identical to it. This pattern is formalized as the category Refl, whose objects are reflections R = (S, X), pairs of a source S and a resulting state X, and whose morphisms are contacts, directed acts of influence. Refl is shown to satisfy the axioms of a category, to support families of reflections of a common source together with comparison morphisms between them, and to admit collective reflections via categorical limits and colimits. Several theorems are established, including the preservation of source consistency under composition and the existence conditions for a consistent collective reflection, each illustrated across physical, biological, neural, cognitive, and social domains. The framework is then extended with functors and natural transformations connecting a hierarchy of six reflection levels and with explicit temporal structure sufficient to express variation, selection, inheritance, and emergence as basic evolutionary processes within Refl. The text is accessible to readers without specialized training in category theory.