3.12 Possible and impossible language worlds

Moro’s impossible languages provide a particularly sharp instance of a prior-relative hypothesis class [ Moro , 2023 ] . A purely formal learner may range over all coalgebras of a language endofunctor, \(\mathbf{Coalg}(F_{\mathrm{lang}})\). A humanly structured ORACLE instead ranges over the declared subcategory

The prior does not tell the learner which human language is present. It says which formally describable continuations are admissible candidates for human language at all.

This restriction has two effects. First, it can turn an otherwise nonidentifiable presentation into an identifiable one by deleting formal competitors that violate the universal-grammar doctrine. Second, it creates a diagnostic obligation: if sustained evidence can be modeled only outside the admissible subcategory, ORACLE must decide whether the evidence was mistyped, the current language model was wrong, or the doctrine itself needs revision. The slogan “the brain is a sieve” becomes categorical: the sieve is an admissibility subcategory together with the observers through which its objects are presented.

Language also demonstrates why overlaps matter. Acquisition is not only identification internal to the language coalgebra. Reference links language to objects; spatial expressions link it to geometry; numerals link it to magnitude; imperatives and explanations link it to agency; conversation links it to indexed social state. An impossible world model can arise from individually admissible fragments glued by inadmissible cross-fragment warrants.