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Report on some ramified-type assignment systems and their model-theoretic semanticsIn Nicholas Griffin & Bernard Linsky (eds.), The Palgrave Centenary Companion to Principia Mathematica, Palgrave-macmillan. 2013.
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5Book reviews (review)History and Philosophy of Logic 14 (2): 221-263. 1993.Stewart Shapiro, Foundations without foundationalism: A case for second-order logic. Oxford: Clarendon Press, 1991. xvii + 277 pp. £35.00 A. Diaz, J, Echeverria and A. Ibarra, Structures in...
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350Where do sets come from?Journal of Symbolic Logic 56 (1): 150-175. 1991.A model-theoretic approach to the semantics of set-theoretic discourse.
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14Book Reviews (review)History and Philosophy of Logic 5 (2): 233-263. 1984.Albert Menne and Niels Öffenberger, Zur modernen Deutung der aristotelischen Logik. Band I:Über den Folgerungsbegriff in der aristotelischen Logik. Hildesheim and New York: Georg Olms Verlag, 1982. 220 pp. DM 48.Klaus Jacobi, Die Modalbegriffe in den logischen Schriften des Wilhelm von Shyreswood und in anderen Kompendien des 12. und 13. Jahrhunderts. Funktionsbestimmung und Gebrauch in der logischen Analyse. Leiden and KÖln: E.J. Brill, 1980. xiii + 528 pp. HFL 140.Nineteenth – Century Contrast…Read more
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221Cardinality logics. Part II: Definability in languages based on `exactly'Journal of Symbolic Logic 53 (3): 765-784. 1988.
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131Three Value Logics: An Introduction, A Comparison of Various Logical Lexica and Some Philosophical RemarksAnnals of Pure and Applied Logic 43 (2): 99-145. 1989.
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216Stewart Shapiro’s Philosophy of Mathematics (review)Philosophy and Phenomenological Research 65 (2). 2002.Two slogans define structuralism: contemporary mathematics studies structures; mathematical objects are places in those structures. Shapiro’s version of structuralism posits abstract objects of three sorts. A system is “a collection of objects with certain relations” between these objects. “An extended family is a system of people with blood and marital relationships.” A baseball defense, e.g., the Yankee’s defense in the first game of the 1999 World Series, is a also a system, “a collection of …Read more
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243Cut-conditions on sets of multiple-alternative inferencesMathematical Logic Quarterly 68 (1). 2022.I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships betwe…Read more
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404One-step Modal Logics, Intuitionistic and Classical, Part 1Journal of Philosophical Logic 50 (5): 837-872. 2021.This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 prese…Read more
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308One-Step Modal Logics, Intuitionistic and Classical, Part 2Journal of Philosophical Logic 50 (5): 873-910. 2021.Part 1 [Hodes, 2021] “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Part 1. For the sys…Read more
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130Jan von Plato and Sara Negri, Structural Proof Theory (review)Philosophical Review 115 (2): 255-258. 2006.
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70Book Review. Mechanism, Mentalism and Metamathematics. J Webb (review)Journal of Philosophy 81 (8): 456-64. 1984.
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46Meeting of the association for symbolic logic: New York 1979Journal of Symbolic Logic 46 (2): 427-434. 1981.
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280The Modal Theory Of Pure Identity And Some Related Decision ProblemsMathematical Logic Quarterly 30 (26-29): 415-423. 1984.Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke co…Read more
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302Individual-actualism and three-valued modal logics, part 1: Model-theoretic semanticsJournal of Philosophical Logic 15 (4). 1986.
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22Book Review. Principles of Intuitionism. Michael Dummett (review)Philosophical Review 91 (2): 253-62. 1982.
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14A Minimal Upper Bound on a Sequence of Turing Degrees Which Represents that SequencePacific Journal of Mathematics 108 (1): 115-119. 1983.
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231Where Do the Cardinal Numbers Come From?Synthese 84 (3): 347-407. 1990.This paper presents a model-theoretic semantics for discourse "about" natural numbers, one that captures what I call "the mathematical-object picture", but avoids what I can "the mathematical-object theory".
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61Review: Jaakko Hintikka, The Principles of Mathematics Revisited (review)Journal of Symbolic Logic 63 (4): 1615-1623. 1998.
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746Logicism and the ontological commitments of arithmeticJournal of Philosophy 81 (3): 123-149. 1984.
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51Book Review. Logic and Arithmetic, Volume I. D Bostock. (review)Journal of Philosophy 73 (6): 149-57. 1976.
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36Annual meeting of the Association for Symbolic Logic, New York City, December 1987Journal of Symbolic Logic 53 (4): 1287-1299. 1988.
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268Upper bounds on locally countable admissible initial segments of a Turing degree hierarchyJournal of Symbolic Logic 46 (4): 753-760. 1981.Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on results of Jensen and is detailed …Read more
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252Individual-actualism and three-valued modal logics, part 2: Natural-deduction formalizationsJournal of Philosophical Logic 16 (1). 1987.
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19Book Review. Reflections. Kurt Godel. (review)THe Journal for Symbolic Logic 54 (3): 1095-98. 1989.
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48Book Review. Abstract Objects. Bob Hale. (review)International Studies in Philosophy 24 (3): 146-48. 1992.