Set Theory
Roles: set, element, membership, subset, complement, union, intersection, universal-set, empty-set, paradox
The mathematical study of collections and membership. As a source domain, set theory supplies the vocabulary of classification itself: what belongs, what is excluded, what overlaps. Its most productive metaphorical exports are its pathologies — the paradoxes that arise when classification is turned on itself. Russell’s paradox, the barber who shaves all those who don’t shave themselves, and Cantor’s diagonal argument all reveal that naive classification breaks under self-reference. When we ask “does this category include itself?” in governance, taxonomy, or software type systems, we are borrowing from set theory’s hard-won understanding of what happens when containment becomes recursive.