On the Non-Transferability of Distinctions

Some distinctions, once lost in representation, cannot be recovered—no matter how much analysis is applied within the resulting domain, because the representation itself no longer preserves the differences on which those distinctions depend. This paper develops that claim as a general structural principle. The limitation is therefore not epistemic (a lack of knowledge or data), but structural: it arises from the design of the representation itself. The argument is developed across three domains—statistical physics, artificial intelligence, and behavioural interpretation. Coarse-graining, proxy failure, and the underdetermination of inner states by observable form are shown to share the same underlying structure: many distinct configurations mapped to a single observable outcome. In such cases, reconstruction fails not because we have not yet found the right method, but because the relevant differences were not carried over into the resulting representation. The paper introduces this as the principle of non-transferable distinctions: what is not preserved under representation cannot be reconstructed within the representational domain itself. This gives the principle significance across very different fields, wherever observable results are used to support stronger claims about underlying structure, capacity, or state. A companion formal paper (DOI: 10.5281/zenodo.19547143) develops the categorical expression of this constraint.