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

Abstract

This paper experimentally investigates presupposition projection from the scope of
the quantifiers every and at least one, as triggered by the factive verb be aware and the iterative
adverb again. The first issue we are concerned with is whether presuppositions project
universally or existentially from quantified sentences. Different theoretical accounts endorse
opposing views here (e.g., Heim, 1983; Geurts, 1999; Beaver, 2001; Schlenker, 2008, 2009;
Fox, 2012), while recent experimental work (Chemla, 2009; Tiemann, 2014) suggests that
the force of the projected presupposition varies by quantifier. The second issue we look at
is how the descriptively observed readings arise—in particular, as a direct result output from
the 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 can
yield what looks like non-universal inferences in light of the overall, unrestricted domain, even
if the projection mechanism itself yields a universal presupposition. Finally, we test whether
the 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 different
patterns 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 overwhelmingly
giving rise to non-universal presuppositions. Our results also indicate the availability of
presupposition-less readings for both triggers in the task at hand, apparently more prevalent
than domain restriction. Thereby, we present novel evidence that helps to pinpoint which of the
theoretical options can be substantiated experimentally.
Keywords: Presupposition projection, quantifiers, domain restriction, entailment.