Nuel Belnap
(Some) papers and publications

Downloadable papers:
 

Papers are downloadable in pdf format.

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12.“A simple treatment of truth functions” [by A. R. Anderson and NDB], Journal of symbolic logic, vol. 24 (1959), pp. 301-302.

21.“Entailment and relevance,” Journal of symbolic logic, vol. 25 (1960), pp. 144-146.

22.“Enthymemes” [by A. R. Anderson and NDB], Journal of philosophy, vol. 58 (1961), pp. 713-723.

23.“Tautological entailments” [by A. R. Anderson and NDB], Philosophical Studies, vol. 13 (1962), pp. 9-24.

24.“Tonk, Plonk and Plink,” Analysis, vol. 22 (1961-62), pp. 130-134.

42.“Questions, answers, and presuppositions,” Journal of philosophy, vol. 63 (1966), pp. 609-611.Abstract of a paper read at the 1966 meeting of the Eastern Division of the American Philosophical Association.

45.“Intensional models for first degree formulas,” Journal of symbolic logic, vol. 32 (1967), pp. 1-22.

52.“The substitution interpretation of the quantifiers” [by J. M. Dunn and NDB], Noûs, vol. 2 (1968), pp. 177-185.

56.“Conditional assertion and restricted quantification,” Noûs, vol. 4 (1970), p. 1-13.

76.“Rescher’s hypothetical reasoning:an amendment,” The philosophy of Nicholas Rescher:discussion and replies, ed. E. Sosa, D. Reidel, 1979, pp. 19-28.

77.“Relevant analytic tableaux” [by M. A. McRobbie and NDB], Studia Logica, vol. 38 (1979), pp. 187-200.

87.“Display logic,” Journal of philosophical logic, vol. 11 (1982), pp. 375-417.

88.“Gupta’s rule of revision theory of truth,”Journal of philosophical logic, vol. 11 (1982), pp. 103-116.

95.“A note on extension, intension, and truth” [by A. Gupta and NDB], Journal of philosophy, vol. 84 (1987) pp. 168-174.

102. “Semantic holism” [by NDB and G. J. Massey], Studia logica, vol. 49 (1990) pp. 67-82.

103. “Declaratives are not enough,” Philosophical studies, vol. 59 (1990) pp. 1-30.

106. “Before refraining: concepts for agency,” Erkenntnis, vol. 34 (1991) pp. 137-169.

108. “Backwards and forwards in the modal logic of agency,” Philosophy and phenomenological research, vol. 51 (1991) pp. 777-807.

110. “Branching space-time,” Synthese, vol. 92 (1992) pp. 385-434.

111. “The way of the agent” [by NDB and M. Perloff], Studia logica, vol. 51 (1992) pp. 463-484.

114. “On rigorous definitions,” Philosophical studies, ed. Marian David, vol. 72 (1993) p. 115-146.

115. “Indeterminism and the thin red line” [by NDB and Mitchell Green], Philosophical perspectives, vol. 8, Logic and language, James Tomberlin (ed.), Ridgeview Publishing Co. (1994), pp. 365-388.

128.  “Concrete transitions,” in Actions, norms, values:discussions with George Henrik von Wright, George Meggle (ed.), Walter de Gruyter, 1997. (1999, pdf format)
 

Abstract:
Following von Wright, ``transitions'' are needed for understanding agency. I indicate how von Wright's account of transitions should be adapted to take account of objective indeterminism, using the idea of branching space-time. The essential point is the need to locate  transitions not merely in space-time, but concretely amid  the indeterministic, causally structured possibilities of our (only) world. (This is a ``postprint'' of Belnap 1999, as cited in the paper. The page numbers do not, of course, match those of the original.)
 

133.  EPR-like funny business in the theory of branching space-times Non-locality and Modality, T. Placek and J.
Butterfield (eds.), Kluwer Academic Publishers, 2002, pp. 293-315.(2002, pdf format.)

Abstract:
EPR-like phenomena are (presumably) indeterministic, but they furthermore suggest that our world involves seeming-strange ``funny business.'' Without invoking any heavy mathematics, the theory of branching space-times offers two apparently quite different ways in which EPR-like funny business goes beyond simple indeterminism. (1) The first is a modal version of a Bell-like correlation: There exist two space-like separated indeterministic initial events whose families of outcomes are nevertheless modally correlated. That is, although the occurrence of each outcome of each of the two space-like separated initial events is separately possible, some joint occurrence of their outcomes (one from each) is impossible. (2) The second sounds like superluminal causation: A certain initial event can bear a cause-like relation to a certain without being in the causal past of that outcome. The two accounts of EPR-like funny business are proved equivalent, a result that supports the claim of each as useful to mark the line between mere indeterminism and EPR-like funny business. (This is a ``postprint'' .  Numbers 135 and 139 below are closely related.)
 

134.   "Double time references:   Speech-act reports as modalities in an indeterministic setting"  in Advances in Modal Logic, F. Wolter, H. Wansing, M. De Rijke, and M. Zakharyaschev (eds.) , 2002.(2001, pdf format)

Abstract:
The background is a theory that describes agents and their choices in the branching-time represention of indeterminism, and that describes a language appropriate for use in such a setting.  The problem of this paper is to clarify the meaning, in the context of indeterminism, of speech acts such as promising, ordering, advising, asserting, and betting.  Such speech acts often have sentence that serves as a "declarative core," whose truth-conditional semantics in branching time contributes to the meaning of the speech act.  Direct-discourse reports of such speech acts can be treated as a kind of "modal" connective, e.g. "a1 promised a2 to make 'A' true." A key feature of the contribution of the declarative core is made in terms of its (now) being definitely settled at a later moment (in the branching tree) that the declarative core of the speech act was true (then) at the moment of the speech act.  That is the "double time reference" that needs clarification.
 

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

Abstract:
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.)

Abstract:
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.
 

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

Abstract:
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.
 

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

Abstract:
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.
 

139.  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)
 

140.  "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.)

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

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

144.  “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

145.  "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.

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

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)