Nuel Belnap


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Pittsburgh, PA 15206
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Nuel D. Belnap, Jr. (born 1930) is an American logician and philosopher who has made many important contributions to the philosophy of logic, temporal logic, and structural proof theory. He has taught at the University of Pittsburgh since 1961 until his retirement in 2011; before that he was at Yale University. His best-known work is his collaboration with Alan Ross Anderson on relevance logic. He has also published books on the logic of questions and answers, with Thomas Steel, and the logic of agency, with Michael Perloff and Ming Xu. He has contributed to the foundations of two very distinct theories of truth: he was a co-author of The Prosentential Theory of Truth with Dorothy Grover and Joseph Camp, and of The Revision Theory of Truth with Anil Gupta. He is also co-author with Ming Xu and Michel Perloff of Facing the Future. He was elected a Fellow of the American Academy of Arts and Sciences in 2008

Select Publications

No-common-cause EPR-like funny business in branching space-times (in Philosophical Studies 2003, pdf format.)

There is “no EPR-like funny business” if (contrary to apparent fact) our world is as indeterministic as you wish, but is free from the EPR-like quantum mechanical phenomena such as is sometimes described in terms of superluminal causation or correlation between distant events. The theory of branching spacetimes can be used to sharpen the theoretical dichotomy between “EPR-like funny business” and “no EPR-like funny business”. Belnap (2002) offered two analyses of the dichotomy, and proved them equivalent. This essay adds two more, both connected with Reichenbach’s “principle of the common cause”, the principle that sends us hunting for a common-causal explanation of distant correlations. The two previous ideas of funny business and the two ideas introduced in this essay are proved to be all equivalent, which increases one’s confidence in the stability of (and helpfulness of) the BST analysis of the dichotomy between EPR-like funny business and its absence.

Branching histories approach to indeterminism and free will (a pre-print of 141B. “Branching Histories Approach to Indeterminism and Free Will,” Truth and Probability Essays in Honour of Hugues Leblanc. Bryson Brown and Francois Lepage, eds. 2005. pp. 197—211.)

An informal sketch is offered of some chief ideas of the (formal) ``branching histories'' theory of objective possibility, free will and indeterminism. Reference is made to ``branching time'' and to ``branching space-times,'' with emphasis on a theme that they share: Objective possibilities are in Our World, organized by
the relation of causal order.

"Agents in branching space-times," Journal of Sun Yatsen University, Social Science Edition, vol. 43, 2003, pp. 147--166.

The aim of this essay is to make some brief suggestions on the beginnings of a theory of agents and agency in branching space-times.  The thought is to combine the ideas of agency as developed against the relatively simple background of branching time with the richer notions of indeterminism as structured in the theory of branching space-times.  My plan is to say a little about agency in branching time and a little about branching space-times, and then ask how the two can be brought together.  At the end there is an appendix, extracted from Belnap, Perloff and Xu 2001 (Facing the future), listing in a convenient form all the main ideas about agents and their choices in branching time.

 "Some non-classical logics seen from a variety of perspectives,"Journal of Sun Yatsen University, Social Science Edition, vol. 43, 2003, pp. 167--179.

Logicians have worked with so many different logical systems that it is not possible even to estimate the number.  Of these, many are best seen as extensions of classical logic, including both those of interest to mathematics and those of interest to philosophy and computer science.  (Henceforth I will use the term "intelligent systems theory" for the common ground of philosophical logic and that part of computer science that concerns itself with activities plausibly taken to embody intelligence in some degree.) On the mathematical side are, of course, higher order logics, set theories, systems of arithmetic, and so forth.  On the intelligent systems side, useful extensions of classical logic include modal logic, deontic logic, epistemic logic, tense logic, indexical logic, and so forth.

This essay, however, does not deal with those logics; instead, it concerns itself with non-classical logics of interest to intelligent-systems theory.  There are doubtless hundreds of non-classical logics, and I consider only a few.  Chiefly I will talk about "relevance" logics and some close cousins.  Sometimes these are called "substructural logics" for reasons that will emerge.  Concerning these logics, I wish to emphasize the very large number of approaches to them that have proved enlightening and useful.

A theory of causation:  Causae causantes (originating causes) as inus conditions in branching space-times  (in British Journal of the Philosophy of Science. vol. 56, 2005, pp. 221-253)  

"Under Carnap's Lamp:  Flat Pre-Semantics,"  (in Philosophical Studies, vol. 80, No. 1, June 2005, pp. 1--28)

Branching space-time, postprint January, 2003 (2003, pdf format.)

"How Causal Probabilities Might Fit into Our Objectively Indeterministic World," w/ Matt Weiner (in Synthese, Volume 149, March 2006, pp. 1--36.)

Prosentence, Revision, Truth and Paradox, “Philosophy and Phenomenological Research”, Vol. LXXIII No. 3, November, 2006, pp. 705—712.

“Propensities and probabilities,” Studies in History and Philosophy of Modern Physics, Volume 38, 2007, pp.  593—625.  DOI:  10.1016/j.hpsb.2006.09.003

"Propensities and probabilities,"  (2010 corrected postprint of 144).

 "From Newtonian determinism to branching-space-time indeterminism," Logik, Begriffe, Prinzipien des Handelns (Logic, Concepts, Principles of Action).  Thomas Müller/ Albert Newen (eds.), mentis Verlag GmbII, 2007, pp. 13--31.

"From Newtonian determinism to branching-space-time indeterminism," revision of 145, forthcoming in Synthese.

"Funny business in branching space-times:  infinite modal correlations,"  w/ Thomas Mueller and Kohei Kishida (in Synthese (2008) 164:  pp. 141--159.

"Branching with Uncertain Semantics: Discussion Note on Saunders and Wallace, ‘Branching and Uncertainty’," [by NB and Thomas Mueller] Brit. J. Phil. Sci. (2010), pp. 1–16.

 Future Contingents and the Battle Tomorrow w/ Michael Perloff forthcoming in Review of Metaphysics.

Notes on the Art of Logic 2009 (2009, pdf format, Unpublished)

Notes on the Science of Logic 2009 (2009, pdf format, Unpublished)

 How a computer should think (from Entailment II)

 Facing the Future (Chapters 7 and 8)

Indeterminism is a modal notion:  branching spacetimes and Earman's pruning(Placek and Belnap 2010) Forthcoming Synthese

Phil 2505, S 2011, Indeterminism, BT, and BST.

Prolegomenon to norms in BST