Well, I guess what I'm technically doing is building a non-standard model of set theory in which my beer mugs are some kind of inaccessible sets that are not members of each other. And yes, that doesn't let me study the mugs themselves in any useful way, since I'm not interested in which mugs are members of which other mugs - but it does let me play around with sets of beer mugs and get comfortable with set theory. And it makes it feel like a simple theory if the entities it studies are just opaque "things".