 Cantor called pluralities that are too large to be considered as a set inconsistent multiplicities (Cantor 1932). Today, Cantor’s inconsistent multiplicities are called proper classes. Some philosophers of mathematics hold that proper classes still constitute unities, and hence can be seen as a sort of collection. They are, in a Cantorian spirit, just collections that are too large to be sets. Nevertheless, there are problems with this view. Just as there can be no set of all sets, there can for diagonalization reasons also not be a proper class of all proper classes. So the proper class view seems compelled to recognize in addition a realm of super-proper classes, and so on. For this reason, Zermelo claimed that proper classes simply do not exist. This position is less strange than it looks at first sight. On close inspection, one sees that in ZFC one never needs to quantify over entities that are too large to be sets (although there exist systems of set theory that do quantify over proper classes). On this view, the set-theoretical universe is potentially infinite in an absolute sense of the word. It never exists as a completed whole, but is forever growing, and hence forever unfinished (Zermelo 1930). This way of speaking indicates that in our attempts to understand this notion of potential infinity, we are drawn to temporal metaphors. It is not surprising that these temporal metaphors cause some philosophers of mathematics acute discomfort. For this reason, contemporary philosophers of mathematics who are sympathetic to Zermelo’s potentialist interpretation of the set theoretic universe, tend to regard the modality involved in this interpretation as a non-temporal one: the nature of this modality is hotly debated (Linnebo 2013, Studd 2019).