Some of the keys to understanding how Carnap positions himself with respect to theoretical entities after the mid-1950s are contained in his considerations related to abstract entities in “Empiricism, Semantics and Ontology” (Rev Int Philos 4:20–40, 1950[1956]). In this contribution, we defend that Carnap adopted an agnostic position in relation to the real existence (in a metaphysical sense) of both abstract entities and theoretical entities. We also aim to show that the ultimate reason for this agnosticism, in both cases, is Carnap’s rejection of external ontological questions as having no cognitive significance. In addition, we defend the idea that he would never have really succumbed to either an instrumentalist position or any sort of weak realism, such as structural realism, in opposition to some interpretations of Carnap’s work on the reference of theoretical terms. To demonstrate the validity of this latter stance of ours, we argue that: (i) the appeal to mathematical entities as referents of theoretical terms can only be understood in a deflationary way, and not in an instrumentalist manner (pace Lavers and Psillos); and (ii) Carnap’s use of the Ramsey sentence does not involve structural realism and the Newman objection does not apply to it (pace Psillos, Demopoulos and, perhaps, Friedman). In any case, even adopting a deflationist approach to theoretical entities, it sounds odd to consider them to be mathematical entities, as Carnap posited. As an alternative, we propose considering them as abstract artifacts.