MetaStructure and Iterated MetaStructure: MetaCognition, MetaLaerning, MetaAnalysis, MetaScience, MetaPhilosophy, and More

A MetaStructure is a higher-level framework that treats entire collections of structures as single objects, equipped with natural operations that preserve isomorphisms across different domains. The term “Structure” here refers broadly to mathematical systems as well as real-world models. An Iterated MetaStructure generalizes this idea recursively, generating successive layers in which structures of structures form deeper hierarchical meta-levels. In this paper, we investigate whether well-known meta-concepts such as MetaCognition, Meta-Learning, MetaAnalysis, MetaScience, and Metaphilosophy can be extended by means of Iterated MetaStructures. While some of these meta-concepts are primarily conceptual in nature and lack precise mathematical definitions, we deliberately attempt to formalize them as rigorously as possible and examine whether such formalizations can be systematically extended.