In this article, we challenge Matushansky’s (Linguistics and Philosophy,21, 573–627, 2008) small clause treatment of proper names in naming constructions. While she is widely credited with establishing, based on cross-linguistic evidence, that names should be viewed as predicates in naming constructions, we present a counterexample from Polish that questions the universal interpretation of the small clause hypothesis (SCH). This leads us to advocate for an alternative analysis of proper names in naming constructions, wherein they are considered components of the argument (...) of a naming verb. We posit that this approach may have deflationist implications for predicativism concerning proper names, as it does not necessitate the existence of primitive name-predicates. We argue that there is no compelling positive evidence for the existence of predicative uses of names whose application conditions cannot be articulated using an equivalent phrase that quotes or mentions the name. Any apparent use of “Delia” as a predicate can be cast either (i) as not really a predicate, but rather an argument mentioning the name “Delia,” or (ii) as a genuine predicate, albeit one with an application condition defined by one of the well-established existing predicates, such as “individual called ‘Delia,’” where the name is mentioned. Predicative uses of names are thus dependent on the mention of names, and so there is a sense in which there are no primitive name-predicates. (shrink)