**Nuel**** Belnap**

**(Some) papers
and publications**

Downloadable
papers:

**Papers are
downloadable in pdf format.**

**
Portable Document Format (get free Acrobat Reader from ****www.adobe.com)**

**2. “A modification of Ackermann’s ‘rigorous implication’”
**[by A. R. Anderson and NDB] (abstract), *Journal
of symbolic logic,* vol. 23 (1958), pp. 457-458.

**4.“Modalities in Ackermann’s ‘rigorous implication’”
**[by A. R. Anderson and NDB], *Journal** of symbolic logic*, vol. 24 (1959), pp.
107-111.

**5.“Pure rigorous implication as a ‘Sequenzen-kalkul’”
**(abstract), *Journal
of symbolic logic,* vol. 24 (1959), pp. 282-283.

**6.“A proof of the Loewenheim-Skolem
theorem**” [by A. R. Anderson and NDB]
(abstract), *Journal of symbolic logic*,
vol. 24 (1959), pp. 285-286.

**9.
Book note: Axiomatic set theory** (New York, 1960) by P. Suppes, *Review of metaphysics,* vol. 14
(1960-61), p. 175.

**11.“Tautological entailments” **(abstract), *Journal of symbolic
logic*, vol. 24 (1959), p. 316.

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

**13. “A simple proof of Goedel’s
completeness theorem”** [by A. R. Anderson and NDB] (abstract), *Journal of symbolic logic*, vol. 24
(1959), pp. 320-321.

**15. Book note: Leviathan: a simulation of behavioral systems,
to operate dynamically on a digital computer*** *(Santa Monica, 1959) by Beatrice K. Rome and Sydney C. Rome, *Review of metaphysics,* vol. 15
(1961-62), p. 195.

**18.
Review of “Existential
presuppositions and existential commitments”** (*Journal of philosophy*, 1959) by J. Hintikka, Journal of symbolic logic, vol. 25 (1960), p.
88.

**19. Review of “Nondesignating
singular terms” **(Philosophical review, 1959) by H. Leblanc and T. Hailperin, *Journal of
symbolic logic*, vol. 25 (1960), pp. 87-88.

**20. Review of “Towards a theory of definite descriptions”** (*Analysis*, 1959) by J. J. Hintikka, *Journal of
symbolic logic*, vol. 25 (1960), pp. 88-89.

**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.

**26. “First
degree formulas” (abstract),** *Journal** of symbolic logic,* vol. 25 (1960), pp. 388-389.

**27.“First degree entailments”** [by A. R.
Anderson and NDB], *Mathematische** annalen,* vol.
149 (1963), pp.
302-319.A slightly revised version of item 10.

**28. Review
of Computers and common sense**

**30.“The pure calculus of entailment”** [by A. R.
Anderson and NDB], *Journal of symbolic
logic,* vol. 27 (1962), pp. 19-52.

**32. Review of Natural deduction** (Wadsworth, 1962)
by John M. Anderson and Henry W. Johnstone, Jr., *American mathematical monthly*, 1963.

**35. “On
not strengthening intuitionistic logic”** [by NDB, H.
Leblanc and R. H. Thomason], *Notre Dame
journal of formal logic*, vol. 4 (1963), pp. 313-320.

**36.“On not strengthening intuitionistic logic”** [by NDB, H.
Leblanc and R. H. Thomason] (abstract), read at December 1963 meeting of the
Association for Symbolic Logic, *Journal
of symbolic logic,* vol. 28 (1963), p. 297.

**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.

**44.“Intensionally complemented distributive lattices”** [by NDB and Joel Spencer], *Portugaliae** Mathematica*, vol. 25 (1966), pp. 99-104.

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

**46.“Special cases of the decision problem for entailment and
relevant implication,”** *Journal
of symbolic logic*, vol. 32 (1967), pp. 431-432. Abstract of a paper read at
the 1967 meeting of the Association for Symbolic Logic.

**47.“Homomorphisms of intentionally complemented distributive
lattices”** [by J. Michael Dunn and NDB] (abstract), *Journal of symbolic logic*, vol. 32 (1967), p. 446.

**50.“Homomorphisms of intensionally
complemented distributive lattices”** [by J. M. Dunn
and NDB], *Mathematische** annalen*, vol.
176 (1968), pp. 28-38.

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

**55.“Every functionally complete m-valued logic has a
Post-complete axiomatization”** [by NDB and
Storrs McCall], *Notre Dame journal of
formal logic*, vol. 11 (1970), p. 106

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

**57. Review of “A propositional logic with subjunctive
conditionals”** (*Journal of symbolic
logic,* 1962) by R. B. Angell, Journal of symbolic logic, vol. 35 (1970),
pp. 464-465.

**58.“S-P interrogatives,”** *Journal of philosophical logic*, vol. 1
(1972), pp. 331-346.

**63.“A prosentential theory of truth”** [by D. L. Grover,
J. L. Camp, Jr. and NDB], *Philosophical
Studies, vol*. 27 (1975), pp.
73-125.

**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.

**78.“A consecution calculus for positive relevant implication
with necessity”** [by NDB, Anil Gupta, and J. Michael Dunn], *Journal** of philosophical logic*, vol. 9 (1980),
pp. 343-362. (By error the title appeared as “A consecutive…
.”)

**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.

**92.“Display logic”** (abstract), *Journal of symbolic logic*, vol. 48
(1983), p. 907.

**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.

**104. “Linear logic
displayed,”** *Notre Dame journal of
formal logic,* vol. 31 (1990) pp. 14-25.

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

**107. “In the realm of agents”** [by NDB and M. Perloff], *DEON ‘91:First
International Workshop on Deontic Logic in Computer Science*, J.-J. Ch. Meyer and R. J. Wieringa
(eds.), Amsterdam, pp. 107-126.

**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.

**117.“The deliberative stit: a study
of action, omission, ability, and obligation”** [by John F. Horty and NDB], *Journal
of Philosophical Logic*, vol. 24 (1995), no. 6, pp. 583-644

**119.“Reply to Robert Koons”** [by A. Gupta and
NDB], *Notre Dame journal of formal logic*, vol. 35 no. 4
(1995), pp. 632-636.

**121.“Branching space-time analysis of the GHZ theorem”** [by Laszlo Szabo and NDB], *Foundations
of Physics*, vol. 26, no. 8, (1996), pp.989-1002.

**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

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

**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.

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

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

**148.
****"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*