Towards Group Field-Theoretical Linguistics: A Unified Framework for Integrating Linguistic, Sociological, and Cognitive Phenomena

The origins, acquisition, and evolution of language at ontological, structural, and developmental levels, and its relationship to human cognition and social behaviors, remain a fundamental open problem spanning multiple scales: from the ontological basis of language systems to the emergence of structures, and from cognitive development to language system evolution. Progress is hindered by three critical limitations: (1) the absence of frameworks unifying discrete linguistic structures with continuous physical systems such as neural dynamics, (2) the reliance of traditional approaches on prespecifying object-based or pre-interpreted ontological elements, or fixed background structures, which builds substantive content into the starting point and thus blocks account of the emergence of structure, and (3) although relational ontologies and structuralist philosophies offer promising conceptual resources for explaining emergence, they currently lack the mathematical and computational foundations needed for a unified, generative treatment of structure. We propose Group Field Theory (GFT), combined with condensed matter theoretical methods, as a unified framework that addresses these limitations. This combined framework provides four key capabilities: (1) an abstract and pure relational ontological commitment, which enables inquiry into the emergence of structure because the primitive elements are uninterpreted and carry no built-in semantic or object-based content, (2) background independence, requiring no pre-existing spacetime or representational substrate; for structure emerging, (3) a unified treatment of discrete and continuous structure, allowing both symbolic discreteness and continuous structure emergence to be modeled within the same formal machinery, and (4) interpretability and computational implementability, offering a formal, physically grounded, and practically usable framework for modeling language architecture and human cognition. Within this formulation, we model linguistic, cognitive, behavioral, and socio-normative processes within a common GFT-based formalism. These processes include neural dynamics, social practices, and institutional structures. We then use this unified framework to reinterpret linguistic concepts and phenomena and to examine their connections to human cognition, to normative orders such as law, and to emergent patterns of human behavior. As case studies, we discuss language acquisition, computational linguistic, sociolinguistics, jurisprudence, and evidence science. This work provides a unified, interpretable, and formal approach to language, cognition, and social subjects by modeling their emergence through a physical, mathematical, and philosophical-grounded framework.