Structural Preconditions of Physical Description: A Functional Account of Applicability Conditions

Abstract

Physical theories operate only if their claims can be about determinate targets, range beyond isolated tokens, impose non-trivial rule-governed structure on assignments, relations, transitions, or their weights, and—where change is described—distinguish ordered configurations. This paper develops a goal-relative functional account of the structural preconditions of physical description. It replaces the earlier seven-level linear emergence path with an analysis that separates four distinct questions: which functions are necessary, whether the inventory is complete, which functions depend on which others, and how structural preconditions become assessable claim-level conditions. Relative to world-directed physical representation (G1), cross-instance systematic physical description (G2), and description of physical change (G3), four functions survive adversarial removal tests: discernibility of claim-relevant determinations, re-identifiability across applications, rule-governed constraint structure, and ordering capacity. Their dependency structure is partial rather than linear. On this basis, six claim-level applicability conditions—Addressability, Interface Control, Stability, Traceability, Carrier Adequacy, and Constraint Disclosure—are justified as operational projections through two-component warrants that combine a structural input with an assessability requirement. The account thereby keeps type-level conditions, transition analysis, and token-level verdicts distinct. Finally, a typed self-licensing argument shows, conditional on explicit licensing-coverage and typed same-kind premises, why a framework claiming complete internal derivation of all its non-trivial applicability-licensing conditions must encounter remainder, cycle, frame-exit, or non-termination. Version 3.0 is a substantive rebase of the earlier version. It abandons the seven-level linear architecture as the evidential basis while retaining and re-justifying the six applicability-condition types within a stronger functional framework.