Frege argued that a predicate was a functional expression and the reference of it a concept, which as a predicative function had one or more empty places and was thus incomplete. Frege’s view gives rise to what has been known as the paradox of the concept “horse.” In order to resolve this paradox, I argue for an opposite view which retains the point that a predicate is a function, i.e. that a predicative function is complete in a sense. Specifically speaking, a predicate performing the function of a predicate has at least one empty place and has no reference, while a predicate performing the function of a subject does not have any empty place but does have a reference. Frege not only regarded a concept with one or more empty places as the reference of a predicate but also took a set of objects without any empty place to be the extension of a concept with one or more empty places. Thus, it presents a complex relationship between the reference of a predicate and its corresponding extension, leading to disharmony in his theory. I argue that this is because there is a major defect in Frege’s theory of meaning, namely the neglect of common names. What he called extensions of concepts are actually extensions of common names, and the references of predicates and the extensions of common names have a substantial difference despite being closely related.