Envelope Relative Comparability of Expressive Richness

This paper analyzes envelope-relative comparability as a necessary condition for meaningful comparison between representational systems of differing expressive richness. It shows that comparisons across models, theories, or descriptive frameworks are admissible only relative to a shared envelope that fixes scope, reference, and standing. Within a closed admissibility framework, expressive richness is not an absolute or monotonic quantity. A representation may be richer in one envelope and impoverished in another, with no global ordering available. Apparent conflicts over explanatory power, realism, or completeness arise when representations licensed in distinct envelopes are compared as if a common scope were already given. Such comparisons constitute illicit scope transport. The analysis is eliminative. It introduces no metric of expressiveness and proposes no method for ranking theories. Instead, it establishes a boundary condition: comparative claims are admissible only when the envelope relative to which expressiveness is assessed is explicitly fixed. Absent such fixation, claims of superiority, reduction, or emergence are undefined. By enforcing envelope-relative comparability, the paper dissolves a class of disputes across physics, mathematics, and philosophy in which representational richness is treated as an objective hierarchy. It closes these disputes by showing that their apparent substance derives from unlicensed cross-envelope comparison rather than from genuine theoretical disagreement.