Closing the Loop: How Semantic Closure Enables Open-Ended Evolution?

This manuscript explores the evolutionary emergence of semantic closure -- the self-referential mechanism through which symbols actively construct and interpret their own functional contexts -- by integrating concepts from relational biology, physical biosemiotics, and ecological psychology into a unified computational enactivist framework. By extending Hofmeyr's (Fabrication, Assembly)-systems -- a continuation of Rosen's (Metabolism, Repair)-systems -- with a temporal parametrization, we develop a model capable of capturing critical properties of life, including autopoiesis, anticipation, and adaptation. Our stepwise model traces the evolution of semantic closure from simple reaction networks that recognize regular languages to self-constructing chemical systems with anticipatory capabilities, identifying self-reference as necessary for robust self-replication and open-ended evolution. Such a computational enactivist perspective underscores the essential necessity of implementing syntax-pragmatic transformations into realizations of life, providing a cohesive theoretical basis for a recently proposed trialectic between autopoiesis, anticipation, and adaptation to solve the problem of relevance realization. Thus, our work opens avenues for new models of computation that can better capture the dynamics of life, naturalize agency and cognition, and provide fundamental principles underlying biological information processing.