Interpreting presuppositions in the scope of quantifiers: "every" vs. "at least one"

This paper experimentally investigates presupposition projection from the scope ofthe quantifiers every and at least one, as triggered by the factive verb be aware and the iterativeadverb again. The first issue we are concerned with is whether presuppositions projectuniversally or existentially from quantified sentences. Different theoretical accounts endorseopposing views here (e.g., Heim, 1983; Geurts, 1999; Beaver, 2001; Schlenker, 2008, 2009;Fox, 2012), while recent experimental work (Chemla, 2009; Tiemann, 2014) suggests thatthe force of the projected presupposition varies by quantifier. The second issue we look atis how the descriptively observed readings arise—in particular, as a direct result output fromthe projection mechanism, or via additional, independent mechanisms such as domain restriction(e.g., Geurts and van Tiel, 2016): if the domain of the quantifier is restricted, this canyield what looks like non-universal inferences in light of the overall, unrestricted domain, evenif the projection mechanism itself yields a universal presupposition. Finally, we test whetherthe presupposed content also forms part of the entailed content, at least for certain triggers(Sudo, 2012; Klinedinst, 2016; Zehr and Schwarz, 2016). Our results yield clearly differentpatterns for every and at least one, with every giving rise to universal presuppositions, which,to a very limited extent, can be weakened by domain restriction, and at least one overwhelminglygiving rise to non-universal presuppositions. Our results also indicate the availability ofpresupposition-less readings for both triggers in the task at hand, apparently more prevalentthan domain restriction. Thereby, we present novel evidence that helps to pinpoint which of thetheoretical options can be substantiated experimentally.Keywords: Presupposition projection, quantifiers, domain restriction, entailment.