Keep 'only' strong

Luis Alonso-Ovalle, Aron Hirsch


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. 

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