Professor Belnap, a leading figure in logic and philosophical logic who spent most of his career at the University of Pittsburgh, where he was emeritus, died yesterday. His former student and colleague, Anil Gupta, kindly shared the obituary, posted below the fold:
Nuel Dinsmore Belnap, Jr., Alan Ross Anderson Distinguished Professor Emeritus of Philosophy at the University of Pittsburgh, was born on 1 May 1930 in Chicago, Illinois, and died on 12 June 2024 in Whitefield, New Hampshire. Belnap majored in Philosophy at the University of Illinois at Urbana-Champaign, and after a two-year stint in the US Air Force, went to Yale for his graduate studies. Belnap completed his Ph.D in 1960; his advisor was Alan Ross Anderson, and his dissertation was on Relevance Logic. Belnap’s dissertation work with Anderson was the beginning of their long and fruitful collaboration on Relevance Logic.
Belnap was appointed Assistant Professor at Yale in 1960 and was later part of the Exodus from Yale Philosophy. He moved to the University of Pittsburgh in 1963. Anderson made the same move in 1965, enabling the collaboration of the two to continue. Belnap remained at Pittsburgh till his retirement in 2011. In 2020, he moved to Whitefield, New Hampshire, to be near his daughter, Mary Jo Greene.
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).
A different kind of contribution deserves notice, one that illustrates Belnap’s generous nature. In the late 1960s, an Italian physicist, Aldo Bressan, who was thinking about the logical foundations of classical mechanics, worked up a novel and powerful system of higher-order modal logic. Bressan had trouble gaining the attention of the logic community, in part because his typescript was, frankly, a mess. Belnap took time away from his own research and poured hours of work helping Bressan. He went through Bressan’s typescript with a fine-toothed comb and helped bring it into publishable form. Bressan’s A General Interpreted Modal Calculus was published by Yale University Press in 1972. Helping others was second nature to Belnap.
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.
Belnap’s many honors include fellowships from Guggenheim Foundation, 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 a Fellow of the American Academy of Arts and Sciences.
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.
Belnap’s doctoral students include J. Michael Dunn, Mitch Green, Dorothy Grover, Anil Gupta, Glen Helman, Jeff Horty, Kohei Kishida, Virginia Klenk, Michael Kremer, Philip Kremer, Ruth Manor, Robert Meyer, Alasdair Urquhart, Matt Weiner, and Ming Xu.
Belnap had many interests and hobbies. He loved building electronic gadgets, and when computers came on the scene, working up programs for them. He built a program for designing mathematical fonts and downloading them into Epson printers—a program he made freely available and that was a great help to several of his colleagues and students.
Belnap loved photography, motorcycles, and Scottish Terriers. And he loved spending time at the family cottage in Marinette, Wisconsin, where the extended Belnap family would gather in the summers. Belnap spent nearly every summer since birth at this cottage.
Belnap is survived by his three sons, Nuel Belnap, III, Christopher Belnap (spouse: Florence), and Tyler Belnap (Paula); by daughter Mary Jo Greene (Chris); and by ten grandchildren and one great-grandchild.
Comments are open for remembrances from those who knew Professor Belnap or for those who wish to comment on the significance of his work.
