Nuel Dinsmore Belnap Jr., Alan Ross Anderson Distinguished Professor Emeritus of Philosophy, whose work shaped new areas of thinking in logic during a 46-year career at Pitt, died June 12, 2024.
Belnap was a fellow of both the Center for Advanced Study in the Behavioral Sciences and the American Academy of Arts and Sciences, and received grants from the Guggenheim Foundation, the National Science Foundation and the National Endowment for the Humanities. He also received an honorary doctorate from Leipzig University in 2000 and the medal “Plus ratio quam vis” in 2009 from Jagiellonian University in Kraków, Poland.
Anil Gupta, Belnap’s former graduate student and colleague and today the department’s Anderson Distinguished Professor, called Belnap “a giant in the field of philosophy,” whose “contributions to logic and philosophy are broad, deep and elegant,” in a written remembrance.
“He was the most important teacher for me here,” Gupta told the University Times. “The very first semester, I think my mind was made up: I would work with Belnap.
“He was a brilliant teacher. Such a model of intellectual integrity. He would never utter a falsehood even if it was embarrassing to him” to admit that he did not know the answer to a question. “He would credit students with even small observations they had made” when they contributed to commentary he offered to another philosopher. “He had just a quiet strength. A humble person, but brilliant.”
“He had a gentle sense of humor and he was completely reliable,” Gupta added. Even as a graduate student, Gupta and he would talk logic and play board games together. “He was completely trustworthy, generous. He had the great virtues.”
Even as a very senior professor, Gupta recalled of Belnap’s later years, “at department meetings he didn't throw his weight around. As a colleague, he would call me and try some ideas on me” and they would work them out together in Belnap’s office.
Born May 1, 1930 in Chicago, Belnap majored in -hilosophy at the University of Illinois—Urbana-Champaign, spent two years in the Air Force and then attended Yale for graduate studies. Under advisor Alan Ross Anderson, Belnap wrote his dissertation on relevance logic, which began their collaboration on the subject. Belnap completed his Ph.D. in 1960 and that year was appointed assistant professor at Yale. In 1963, after a year spent in Belgium on a Fulbright Fellowship, he joined Pitt, with Anderson following in 1965. Belnap retired in 2011.
In his written remembrance, Gupta detailed Belnap’s work:
“He was a co-founder (or co-discoverer, depending on one’s philosophy) of the systems E and R, 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. … Belnap presented his research in numerous articles and in the 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, 2022).
“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 to Logic series.
“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 equally to him: his presentations ‘pleased the sensibilities as well as the intellect.’”
He is survived by sons Nuel Belnap III, Christopher Belnap (Florence) and Tyler Belnap (Paula), and daughter Mary Jo Greene (Chris), all children from his first wife, Joan Gohde Belnap. He is also survived by his 10 grandchildren: Autumn, Matthew (Jess), Maggie, Tess, Penelope, Owen, Ethan, Jack, Sam and Caroline, his great granddaughter Olivia and many nieces and nephews.
Memorial contributions are suggested to the University of Pittsburgh in support of the Alan Ross Anderson Distinguished Professor of Philosophy, P.O. Box 640093, Pittsburgh, PA 15264-0093 (www.giveto.pitt.edu/alan_ross_anderson_philosophy_fund).
— Marty Levine