Categorical versus gradient grammar in phonotactics

Within the past 2 decades, probabilistic grammars have been put forward in the study of phonotactics as a necessary device to model gradient acceptability of lexical forms. This implicitly suggests that categorical grammars cannot even in principle account for such gradience. Most importantly, influential research has proposed that grammatical forms described by categorical grammars could be simply understood as by-products of probabilistic thresholds. Therefore, either implicitly or explicitly, categorical grammars are painted as not only empirically insufficient but also theoretically and formally redundant by this interpretation of probabilistic grammars in the domain of phonotactics. This paper provides a general overview of this recent debate and argues against the standard threshold interpretation for probabilistic grammars based on mathematical results, explicit axiomatic principles, and recent experimental evidence. In its place, I propose an interpretation for gradient grammars that solves apparent inconsistencies, combines the two types of grammar, accommodates previous technical contributions and data, and establishes a clear theoretical role that opens up further research directions.