Set Theorist Argues His Empty Apartment Is Actually Furnished

A set theorist facing eviction for violating his lease's furnished-apartment clause has argued that his apartment is, in fact, furnished, on the grounds that the empty set is a subset of every set, including the set of all possible furnishings. Dr. Zermelo Frankel, 39, a visiting researcher at the Institute for Advanced Study, rents a one-bedroom apartment that his landlord describes as "containing nothing" and that Frankel describes as "containing the empty collection, which is a legitimate and well-defined configuration of furniture." "The lease requires that the apartment be furnished," Frankel explained during a preliminary hearing. "It does not specify a minimum cardinality for the set of furnishings. The empty set satisfies the requirement vacuously. Every element of the empty set is a piece of furniture, because there are no elements to contradict this claim." The landlord, Mr. Anthony Realist, testified that the apartment contains no bed, no chairs, no tables, and no appliances. Frankel sleeps in a sleeping bag on the floor and eats meals at the university cafeteria. "He has a sleeping bag," Realist noted. "But he says it's not furniture, it's 'a topological covering.' I don't know what that means but I know it's not a bed." Frankel's legal defense rests on the distinction between "furnished" as a predicate requiring at least one piece of furniture and "furnished" as a state that is vacuously true in the absence of any counter-evidence. His attorney, who reportedly spent three hours on the phone with a logician before the hearing, has described the case as "surprisingly defensible." The judge has requested that both parties submit definitions of "furniture" by next Friday. Frankel has offered to provide a formal axiomatic definition. The landlord has offered to provide a photograph of an empty room.