Arguments challenging the existence of free will frequently share a common structure, relying on variants of a principle we call Closure, according to which having no choice about a truth is preserved under entailment. We show that, under plausible assumptions, Closure is valid if and only if the ‘no choice’ operator is intensional. By framing the debate in terms of the intensionality of this operator, this paper illuminates previously underappreciated constraints on defenses of Closure-based arguments against the existence of free will.