Understanding language requires the ability to compose the meanings of words into phrase and sentence meanings. Formal theories in semantics have framed the hypothesis that all instances of meaning composition, irrespective of the syntactic and semantic properties of the expressions involved, boil down to a unique formal operation, that is, the application of a function to an argument, a view known as "Frege's Conjecture." We test the processing consequences of this idea using event-related potentials (ERPs) and a novel experimental paradigm where composition versus noncomposition of words from the same grammatical category (nouns) are compared in two different syntactic environments: predication and modification. We found that noun composition in a modification context, where the noun follows an adjective, elicits a reduced N400 component, whereas noun composition in a predication context, where the noun follows a verb, produces an enhanced LAN component. These data challenge the uniqueness thesis, central to formal semantics, and support instead linguistic theories and processing models that posit different composition operations for predicates and modifiers.