 Horn sometimes describes Q and R as “antinomic forces” (e.g., Horn 2004: 14), which would be appropriate if the bracketed conditions were omitted. Without the conditions, Horn’s principles would clash as often as  Grice’s.[48]  Without independent means of determining antecedently which force will “prevail” in a given case, Horn’s principles would lack predictive or explanatory value. Lepore &amp; Stone (2015: §3.1) suggest treating Horn’s principles as “simultaneous equations”, constraining but not determining the conversational implicatures. But this assumes the equations have a solution. Not all simultaneous equations do.