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I investigate the possibility that the apparent unique scope‐taking abilities of indefinites can be explained in terms of quantifier domain restriction, without departing from the classical view of indefinites as existential quantifiers over individuals whose scope is syntactically constrained in the same way as other quantifiers. The key idea is that when the domain of a quantifier is reduced to a singleton set, it becomes effectively scopeless. Indefinites, on this view, are freer than other quantifiers to make use of this option. I argue that alternative accounts which put the action in the semantics or the syntax of indefinites still need a pragmatic mechanism of quantifier domain restriction, so that to demonstrate the necessity for such approaches, one needs to explain why domain restriction down to singletons is not possible. There is an intuition that indefinites have specific readings in which they are referential and where the speaker can identify the referent, but the hearer cannot. In the final section of the paper, I try to make sense of that intuition in the context of a theory in which indefinites are apt to have singleton domains. I arrive at the conclusion that it is a symptom of a more general phenomenon whereby contextual parameters can be relativized to bearers of propositional attitudes.
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