Nuel Belnap, professor emeritus of philosophy at the University of Pittsburgh, well-known for his work on the philosophy of logic, has died.

Professor Belnap joined the University of Pittsburgh philosophy faculty in 1963 and retired in 2011. Prior to this he was an assistant professor at Yale University. He received his PhD from Yale in 1960 and his undergraduate degree in philosophy from the University of Illinois Urbana-Champaign.

Professor Belnap worked extensively on logic, truth, and time and agency. Anil Gupta, who was a doctoral student of Belnap’s and later his colleague at Pittsburgh, writes:

Belnap’s contributions to logic and philosophy are broad, deep, and elegant. He was a co-founder (or co-discoverer, depending on one’s philosophy) of the systems E and R of entailment logics, whose study has occupied several generations of logicians and philosophers. He isolated (with Michael Dunn) the truth-functional fragment of entailment logics—a fragment now known as the Belnap-Dunn logic—and provided a powerful motivation for it (in “How a Computer Should Think” and “A Useful Four-Valued Logic”). He was a pioneer in the study of the logic of questions and of the logic of agency in branching time. He generalized the notion of branching times to branching space-times to help us better understand physical as well as mental phenomena. He made an important contribution to proof theory with his Display Logic. He was a co-originator of the prosentential theory of truth, and he helped give birth to the revision theory of truth. (There is nothing odd here, for these two theories of truth are not competitors; they address different issues.) Belnap presented his research in numerous articles and in the following books: The Logic of Questions and Answers (co-authored with Thomas Steel, 1976), Entailment (vol. I, with Anderson, 1975; vol. II, with Anderson and J. M. Dunn, 1992), The Revision Theory of Truth (with A. Gupta, 1993), Facing the Future (with M. Perloff and M. Xu, 2001), and Branching Space-Times (with T. Müller and T. Placek, 2021).

Three volumes of essays have been published on Belnap’s work: Truth and Consequences (eds., J. M. Dunn and A. Gupta), New Essays on Belnap-Dunn Logic (eds., H. Omori and H. Wansing), and Nuel Belnap on Indeterminism and Free Action (ed., T. Müller). The last volume appeared in Springer’s Outstanding Contributions in Logic series.

You can read more about his work here and here.

Belnap received many honors, including fellowships from the Guggenheim Foundation, the National Science Foundation, and the National Endowment for the Humanities. He was a Fellow of the Center for Advanced Study in the Behavioral Sciences in 1982–1983 and received an Honorary Doctorate from Leipzig University in 2000. In 2008 he was elected as a Fellow of the
American Academy of Arts and Sciences.

Professor Gupta adds:

Belnap was an outstanding teacher and trained several generations of logicians and philosophers. He had a special talent for making vivid, and thus comprehensible, even the most abstract and complex concepts. What Belnap said once about Alan Anderson applies to him also: his presentations “pleased the sensibilities as well as the intellect.” Belnap was a generous teacher, quick to recognize even the smallest contributions of students. He made students feel that they too could contribute to this imposing enterprise that is logic and philosophy.

Professor Belnap died on June 12th, 2024 in Whitefield, New Hampshire.

(via Anil Gupta)