This book argues that relational cognition, a form of social cognition, exhibits digital infinity as does language. Copies of elementary models are combined and recursively nested to form a potentially infinite number of complex models. Just as one posits proof-theoretic grammars in order to account for the digital infinity of language, one also should posit proof-theoretic grammars to account for the digital infinity of relational cognition. Objections to a proof-theoretic approach, often equally applicable both to language and to relational cognition, are considered and criticized. Such objections either posit overly complex alternatives or overlook the role of idealization in science. John Bolender is a Visiting Fellow at Princeton University, and Assistant Professor of Philosophy, Middle East Technical University, Ankara, Turkey.