Nuel Belnap

Nuel D. Belnap Jr. (/ˈbɛlnæp/; born 1930) is an American logician and philosopher who has made contributions to the philosophy of logic, temporal logic, and structural proof theory. He taught at the University of Pittsburgh from 1963 until his retirement in 2011.


As an undergraduate, Belnap studied at University of Illinois where he obtained his BA. He recalled Max Fisch assigned Whitehead readings. After military service he attended Yale University and enjoyed metaphysics. His professors included Paul Weiss, Arthur Pap, Henry Maginau, Frederic Fitch, and Rulon Wells.

On a Fulbright Fellowship in 1958 he went to Louvain to study with Canon Robert Feys. Belnap domiciled in Brussels with wife and 2-year-old. Feys directed Belnap to read Wilhelm Ackermann's article on rigorous implication in the Journal of Symbolic Logic.[1]

Alan Ross Anderson and Belnap began to discuss relevant implication. In 1960 Anderson told Belnap to write up the work he had done on relevance logic, and this was Belnap's PhD dissertation. The dissertation was published through Omar Kayam Moore at Office of Naval Research, Group Psychology Branch. Belnap became an assistant professor at Yale. He recalled hiring Jon Barwise and John Wallace as research assistants.

Pittsburgh University wanted Wilfrid Sellars, and according to Belnap, "Jerry Sneewind and I hung on his coattails." Adolf Grunbaum and Nicholas Rescher were at Pitt. Vice chancellor Charlie Peake brought Alan Anderson to Pitt in 1965, where he worked until his death in 1973. Anderson and Belnap were co-authors of Entailment: The logic of relavance and necessity.[2][3] "The way we worked when we worked together was cheek by jaw. We just sat down and wrote sentences together."[4]

Belnap became full professor in 1966. Kurt Baier was department chairman. Belnap began to teach philosophy of social sciences, with students including Bas van Fraassen and Mike Dunn. In 1967 he became professor of sociology and in 1971 professor philosophy of science. Eventually he occupied the endowed chair named for Alan Ross Anderson. He recalled Rich Tomason, student of intelligent systems, pasing through Pitt.

Wary of consequences of contradictory stored data, Belnap proposed a four-valued logic to avoid run-away inferences such as (A & ~A) → B for an arbitrary statement B.[5] Known as the principle of explosion in classical logic, the four-valued logic provides a basis for paraconsistent logic to avoid this pathology of two-valued logic.

In 1976 Belnap and T. B. Steel Jr. published The Logic of Questions and Answers as a timely contribution to erotetics. Beyond propositional and sentential logic, they noted that the evolving databases make possible "dossier files on individuals" (page 146) leading to the "problem of privacy in record keeping." The book included a 45-page annotated bibliography of erotetics, sectioned by philosophy, linguistics, automatic question-answering, and pedagogy, compiled by Hubert Schleichert and Urs Egli.

On sabbatical, Belnap was visiting professor at University of California, Irvine and at Bloomington Indiana, in the falls of 77, 78, 79 with Mike Dunn. In 1982 at Stanford Center for Advanced Studies in the Behavioral Sciences, and in 1996 at Leipzig, Centrum für Höhere Studien with Heirich Wansing. He was a founding member of the Society for Exact Philosophy, which collaborated with Canadians such as Mario Bunge. Belnap has served as referee for many academic papers.[4]

He was elected a Fellow of the American Academy of Arts and Sciences in 2008.[6]

Selected works

  • 1975: (with Dorothy L. Grover & Joseph L. Camp) "The Prosentential Theory of Truth", Philosophical Studies 27(1): 73–125
  • 1993: (with Anil Gupta) The Revision Theory of Truth, MIT Press
  • 2001: (with Ming Xu and Michel Perloff) Facing the Future: agents and choices in our indeterministic world, Oxford University Press (ISBN 0195138783).

See also


  1. Wilhelm Ackermann (1956) Begrundung einer strengen implikation, Journal of Symbolic Logic 21: 113 to 128 via Project Euclid
  2. Anderson, A. R. and Belnap, N. D. (1979) Entailment: The Logic of Relevance and Necessity. Vol. 1., Princeton University Press.
  3. Anderson, A. R., Belnap, N. D., and Dunn, J. M. (1992) Entailment: The Logic of Relevance and Necessity. Vol. 2., Princeton University Press. ISBN 0-691-07339-2
  4. N. Belnap (2014) "Biographical Interview", pages 377 to 409 in Belnap on Indeterminism and Free Action, Thomas Müller editor, Springer books doi:10.1007/978-3-319-01754-9
  5. N. Belnap (1975) "How Computers Should Think", pages 30 to 56 in Contemporary Aspects of Philosophy, Gilbert Ryle editor, Oriel Press ISBN 0-85362-161-6
  6. "Book of Members, 1780-2010: Chapter B" (PDF). American Academy of Arts and Sciences. Retrieved May 30, 2011.
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