 is indeed a full Boolean algebra under the new operators (Pontow and Schubert 2006). This shows that, mathematically, mereology does indeed have all the resources to stand as a robust and yet nominalistically acceptable alternative to set theory, the real source of difference being the attitude towards the nature of singletons (as already emphasized by Leśniewski 1916 and eventually clarified in Lewis 1991). As already mentioned, however, from a philosophical perspective the Bottom axiom is by no means a favorite option. The null item would have to exist “nowhere and nowhen” (as Geach 1949: 522 put it), or perhaps “everywhere and everywhen” (as in Efird and Stoneham 2005), and that is hard to swallow. One may try to justify the gulp in various ways, perhaps by construing the null item as a non-existing individual (Bunge 1966), as a Meinongian object lacking all nuclear properties (Giraud 2013), as an Heideggerian nothing that nothings (Priest 2014a and 2014b: §6.13), or as the ultimate incarnation of divine omnipresent simplicity (Hudson 2006b, 2009). But few philosophers would be willing to go ahead and swallow for the sole purpose of neatening up the algebra. 