 At the core of the problem lies the assumption that the set-theoretic paradoxes cast doubt upon the existence of a comprehensive domain of all objects. What they reveal, according to Dummett (1991, 1993), is the existence of indefinitely extensible concepts like set, ordinal, and object. For Dummett, the indefinite extensibility of set is incompatible with the existence of a comprehensive domain of all sets, since no matter what putative domain of all sets we isolate, we find that we can employ Russell’s reasoning to characterize further sets that lie beyond the putative domain of all sets with which we began. The set of all non-self-membered sets in the initial domain cannot, on pain of contradiction, be in that domain, which means that it must lie in a more comprehensive domain of all sets. If there is no domain of all sets, there is, the thought continues, no hope for a domain of all objects. One may respond to this line of argument by contesting Dummett’s diagnosis of the set-theoretic antinomies. Boolos (1993) suggests that we take Russell’s paradox, for example, to establish that not every condition determines a set. The moral of Russell’s paradox is that there is no set of all non-self-membered sets, not that it lies beyond the initial domain of quantification.