Relation-Generated Structuralism: A Formal Theory for Theory Formation Beyond Object-First Ontology

This paper proposes a relation-generated structuralist theory for theory formation in mathematics and the sciences. The central thesis is that a theory is not fundamentally an inventory of objects and their intrinsic properties, but a structured system in which objects are first located in order to make relations expressible, testable, composable, and generative. Objects are not eliminated; rather, they are subordinated to relation-structure as the primary source of mathematical and scientific content. We formalize this idea through a hierarchy of relational signatures, axioms, closure rules, and higher-order relation transformations. The theory explains why modern structural thinking naturally emphasizes morphisms, maps, transitions, interactions, equivalences, invariants, and compositional laws. We prove several basic propositions showing that relation-based specifications determine object identity up to structural equivalence, that theoretical content can be reconstructed from relational closure, and that category theory is a special case of the proposed scheme. The resulting view yields a unified philosophy of theory generation applicable to mathematics, physics, computer science, network science, and other domains where structure rather than substance is primary.