A note on invariance of grammatical categories

This squib aims to further our understanding of the relation between invariants of grammar and grammatical categories. Keenan and Stabler (2003) propose to formalize of the notion of ‘structural/ grammatical’ in terms of automorphism invariance, based on a very general notion of formal grammars (Bare Grammars). It is natural to think that category labels (more precisely: sets of language expressions that bear a given category label) are flesh and blood of grammatical structure and should be invariant. Indeed, categories are invariant (under stable automorphisms) in all of Keenan and Stabler’s example grammars. But in fact it is possible to construe several types of counterexamples where grammatical categories fail to be invariant. I conjecture that automorphism invariance characterizes only categories whose content is properly syntactic, excluding e.g. morphological properties, which are traditionally also considered grammatical.