We analyze the syntax of Genitive to argue that all the definitions proposed to partition the category of Case into grammatically relevant subclasses can be eliminated in favor of only one distinction: that between interpretable and uninterpretable Case features. Combined with other minimalist assumptions and some Case-checking hypotheses, the reduction of Case types to [±interpretable] nearly exhausts the core grammar of Genitive, resolving certain ambiguities that date back to Dionysius Thrax. We claim that Genitive covers interpretable and uninterpretable instantiations, deriving correlated consequences both on their form and distribution, and a number of previously unnoticed generalizations. In certain languages the two types of instantiations are distinguishable, in others they display systematically ambiguous forms. The mapping of Genitive syntax to the Conceptual-Intentional system in terms of just [±interpretable] is always straightforward. Instead, the mapping to the Sensory-Motor system is more articulate and partly idiosyncratic: still, it turns out to be governed by a principled and deductive parametric structure, settable from positive evidence and guided by a number of independently plausible Third Factor conditions.
