Beyond Shared Premises: Generative Procedures and Inferential Connectivity in Mathematical and Physical Theories

Source abstract

Accounts of theoretical unity often emphasize shared axioms, common laws, or the derivation of many conclusions from a small stock of principles. Yet the connectivity of a theory may also depend on how its results are produced. Distinct claims or branches can be closely related because they are generated, transformed, or reconstructed through recurring procedures: a diagrammatic expansion, a functional derivative, a change of representation, a proof schema, or a heuristic that suggests a conjecture later established by rigorous derivation. This paper develops a procedural account of theoretical connectivity that supplements, rather than replaces, premise-based accounts. It distinguishes foundational dependence, generativeprocedural dependence, formal inferential dependence, representational translation, and evidential constraint. The proposal is illustrated by quantum field theory, where generating functionals, correlation functions, Feynman-diagram expansions, LSZ reduction, and scattering observables are connected by a network of reusable procedures, and by mathematical practice, where generating functions convert recurrences into functional equations and support further analysis. The paper also clarifies the role of analogy: procedural similarity can guide discovery and extension, but does not by itself establish validity. Existing work on explanatory unification, mathematical analogy, and mechanisms already addresses important parts of this terrain, especially the reuse of argument patterns. The contribution advanced here is a more explicit account of how premise structure and procedural reuse jointly shape a theory' s inferential network, together with distinctions that make this account testable in case studies. The proposal is conceptual and programmatic; its originality and reach require further comparison with the literature and systematic historical analysis.