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33and I CaPI e D, then I Pl e D for all similar assignments. (2) For all values of P and q, I CPCNPql e D. (3) For all values of the variables in a, if la( e U then INal e D. (4) The F,P are constant functions such that, for all values of P, ~ FIP~ = 1, I F, Pl = 2,..., I Fât I = m.
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27EQ and the First Order Functional CalculusZeitschrift fur mathematische Logik und Grundlagen der Mathematik 6 (7-14): 217-218. 1960.
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10Review: Jaakko Hintikka, Existential Presuppositions and Existential Commitments (review)Journal of Symbolic Logic 25 (1): 88-88. 1960.
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224Future Contingents and the Battle TomorrowReview of Metaphysics 64 (3): 581-602. 2011.Using Aristotle's well-known sea battle as our example, we offer a precise, intelligible analysis of future contingent assertions in the presence of indeterminism. After explaining our view of the problem, we present a picture of indeterminism in the context of a tree ofbranching histories. There follows a brief description ofthe semantic bases for our double-time-reference theory of future contingents. We then set out our account. Before concluding, we discuss some ramifications of, and alterna…Read more
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122Presentence, revision, truth, and paradox (review)Philosophy and Phenomenological Research 73 (3). 2006.Tim Maudiin’s Truth and Paradox (Maudlin 2004, cited here as T&P), a book that is richly endowed with interesting analyses and original theses, chooses to ignore both the prosentential theory of truth from Grover, Camp and Belnap 1975 and the revision theory in its book form, Gupta and Belnap 1993 (The Revision Theory of Truth, henceforth RTT).1 There is no discussion of either theory, nor even any mention of them in the list of references. I offer a pair of quotes chosen from among a number of …Read more
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47Relevant analytic tableauxStudia Logica 38 (2). 1979.Tableau formulations are given for the relevance logics E (Entailment), R (Relevant implication) and RM (Mingle). Proofs of equivalence to modus-ponens-based formulations are vialeft-handed Gentzen sequenzen-kalküle. The tableau formulations depend on a detailed analysis of the structure of tableau rules, leading to certain global requirements. Relevance is caught by the requirement that each node must be used; modality is caught by the requirement that only certain rules can cross a barrier. Op…Read more
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441Branching space-timeSynthese 92 (3). 1992.Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, an…Read more
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106Newtonian determinism to branching space-times indeterminism in two movesSynthese 188 (1): 5-21. 2012.“Branching space-times” (BST) is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its (more or less) relativistic theory of spatio-temporal relations; this ability is essential for the representation of local (in contrast with “gl…Read more
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32A Decision Procedure For the System E Ī of Entailment with NegationMathematical Logic Quarterly 11 (4): 277-289. 1965.
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1Facing the Future: Agents and Choices in Our Indeterminist WorldPhilosophical Quarterly 52 (209): 660-662. 2001.
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1Review: Rulon Wells, A Measure of Subjective Information (review)Journal of Symbolic Logic 30 (2): 244-245. 1965.
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13Every functionally complete $m$-valued logic has a Post-complete axiomatizationNotre Dame Journal of Formal Logic 11 (1): 106-106. 1970.
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24Following 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 cour…Read more
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50Permission is hereby granted until the end of December, 2009 to make single copies of this document as desired, and to make multiple copies for use by teachers or students in any course offered by any school.
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176The deliberative stit: A study of action, omission, ability, and obligation (review)Journal of Philosophical Logic 24 (6). 1995.
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8Backwards and Forwards in the Modal Logic of AgencyPhilosophy and Phenomenological Research 51 (4): 777-807. 1991.
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7Leblanc Hugues and Hailperin Theodore. Nondesignating singular terms. The philosophical review, vol. 68 , pp. 239–243Journal of Symbolic Logic 25 (1): 87-88. 1960.
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110Under Carnap’s Lamp: Flat Pre-semanticsStudia Logica 80 (1): 1-28. 2005.“Flat pre-semantics” lets each parameter of truth (etc.) be considered sepa-rately and equally, and without worrying about grammatical complications. This allows one to become a little clearer on a variety of philosophical-logical points, such as the use fulness of Carnapian tolerance and the deep relativity of truth. A more definite result of thinking in terms of flat pre-semantics lies in the articulation of some instructive ways of categorizing operations on meanings in purely logical terms i…Read more
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76A consecutive calculus for positive relevant implication with necessityJournal of Philosophical Logic 9 (4): 343-362. 1980.
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9Hintikka Jaakko. Existential presuppositions and existential commitments. The journal of philosophy, vol. 56 , pp. 125–137 (review)Journal of Symbolic Logic 25 (1): 88-88. 1960.
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42Truth by ascentDialectica 53 (3-4). 1999.This paper offers a lighthearted presentation of some of the chief ideas about truth that are shared by theories similar to those of Kripke, Herzberger, and Gupta. The problem is to explain the concept of truth for a language that contains its own truth predicate. The proposal of these theories is that one can unwind the tangles that threaten by invoking a transfinite series of stages of semantic reflection as one ascends the ordinals. The presentation emphasizes how each stage begins, to the ex…Read more
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109Entailment: The Logic of Relevance and Neccessity, Vol. IPrinceton University Press. 1975.In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in the…Read more
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75EPR-like “funny business” in the theory of branching space-timesIn T. Placek & J. Butterfield (eds.), Non-Locality and Modality, Kluwer Academic Publishers. pp. 293--315. 2002.
Pittsburgh, Pennsylvania, United States of America
Areas of Interest
Metaphysics |
Logic and Philosophy of Logic |