On the Non-Transferability of Distinctions

This paper examines a general problem of domain transition: why distinctions that are operative in one domain often fail to remain available in another. It argues that this failure reflects a structural limit of representation. When a representation collapses distinctions, those distinctions are not merely difficult to recover; they are absent from the target domain. The paper formulates this as the principle of non-transferable distinctions: what is not preserved under representation cannot be reconstructed within the representational domain itself. The resulting limitation is therefore structural rather than merely epistemic. The argument is developed across three domains: statistical physics, artificial intelligence, and the interpretation of behaviour. Coarse-graining, proxy failure, and the underdetermination of inner states by observable form are analysed as instances of the same many-to-one representational structure. On this basis, the paper reframes such failures not as defects of knowledge, data, or inference, but as consequences of the design and limits of representation itself. It thereby clarifies why invariant reconstruction fails in such cases and shows that what can be recovered within a target domain is strictly bounded by what was preserved in the original mapping. A companion formal paper (DOI: 10.5281/zenodo.19547143) develops the categorical expression of this structural constraint.