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…