Keep 'only' strong

As defined in Horn 1969 , only (p ) presupposes p . von Fintel & Iatridou ( 2007 ) note, however, that only (have to p ) may presuppose that p is possible , rather than necessary , and propose revising the analysis of only to weaken its contribution. Building on Ippolito 2007 , we show that this revision predicts interpretations which are too weak in data involving plurals and negation. A paradox thus arises: Horn’s only is too strong in some cases, but required in others. To resolve the paradox, we maintain Horn ’s only , but introduce an external source of weakening that is not always available: in von Fintel and Iatridou’s modal environment, the argument of only is weakened by a covert operator ( AT LEAST , Crnic 2011 ; Schwarz 2004 ) that is blocked in the problematic cases involving plurals and negation.