Nuel Belnap (1930-2024)
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)
I’m so glad to see that Dr. Belnap lived such a long life. He worked with my father, Alan Ross Anderson. Nuel, (as I knew him), used to ride his scooter to Oakland and park it at our house, and then walk to the University. He was such a sweet person, and very kind to us children, back in the 60s and early 70s. His first wife, Joan, was one of my godmothers. I have a great affection for him.
Some scholars advocate for what they call “person-affecting” theories of population ethics. Those scholars may benefit from studying Professor Belnap’s work on branching space-time, indeterminism, and future contingents.
Nuel had a gentle and kind face, with warm but probing eyes, all of this reflecting accurately how he was in person. I was his assistant for a year at Pitt (thanks to holding the Alan Ross Anderson Fellowship in that year), and, although I honestly do not think of myself as having been especially helpful, Nuel was always appreciative and encouraging. During that year, I sought to bypass the graduate student translation requirement; Nuel told me, with that wry smile of his, that he would not have been doing what he was doing, if not for having being able to read Gentzen’s work.
Nuel Belnap was my dissertation director, way back in 1984-86. While I was in coursework in my first two years at Pitt, although I took a lot of logic, I did not actually take a course with Nuel, for various reasons. But after I was done with course work, Nuel basically saved my graduate student career. I spent about a year floundering around looking for a dissertation topic — I contemplated vast topics that I could not possibly conquer, such as the debate about metaphysical realism which Putnam and others had made prominent at that time, and was sinking into despair. Then I noted a course being offered by Nuel on Theories of Truth and the Liar Paradox, and decided to sit in. In the course of that term, I managed to prove something that I thought I could use in a dissertation, and I started to see ways to connect it to more philosophical things that I had already been thinking about, related to Brandom’s inferentialism. So I found a topic. But I also found a director, and finished in a couple more years. Later, Nuel also directed my brother Phil’s dissertation, in relevance logic.
Nuel was, as a director, just what I needed. He insisted that we meet every week, and that every week I have something to talk to him about. It didn’t need to be written but I needed to have new thoughts, and I needed to explain them to him and accept his feedback. Sometimes when I did have something written, he didn’t really have anything to say at all, other than “good stuff” or something like that, but that was partly because we had talked things through so much before I actually produced the writing. Anyway this proved to be extremely efficient and got me through, undiagnosed ADHD and all. He also accepted that all my drafts before the final version were handwritten. Of course we were still at the beginning of the use of printers rather than typewriters, and there were a lot of symbols in my thesis. But at the time, I worked better writing things by hand. Only later did I adapt to typing everything. (Eventually I bought a computer and a dot matrix printer and adapted a BASIC program of Nuel and Anil Gupta’s to set up a special font for logical characters. So Nuel helped me with that too.)
Nuel had a delightful but quirky sense of humor, that would often show up in his published work, either in footnotes or in asides. I remember in his paper “Display Logic” a theorem that had as “Proof”, “by diddling.”
I only saw Nuel occasionally after I graduated, but every time was a delight. He was always encouraging, even as my philosophical work moved further and further away from logic. I have not had much contact with him in the last 10 years, but I am glad that I was able to speak with him last year, thanks to Anil Gupta putting me in touch with his daughter. I had been meaning to call him again, and I’m sorry that I lost that chance.