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Harold T. Hodes [42]Harold Hodes [20]
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Harold Hodes
Cornell University
  1. Logicism and the Ontological Commitments of Arithmetic.Harold T. Hodes - 1984 - Journal of Philosophy 81 (3):123-149.
  2. Structural Proof Theory. [REVIEW]Harold T. Hodes - 2006 - Philosophical Review 115 (2):255-258.
  3. Why Ramify?Harold T. Hodes - 2015 - Notre Dame Journal of Formal Logic 56 (2):379-415.
    This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...)
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  4.  97
    One-Step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.
    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 presents (...)
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  5. Axioms for Actuality.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):27 - 34.
  6. Some Theorems on the Expressive Limitations of Modal Languages.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):13 - 26.
  7.  89
    On Modal Logics Which Enrich First-Order S5.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (4):423 - 454.
  8. Where Do the Natural Numbers Come From?Harold T. Hodes - 1990 - Synthese 84 (3):347-407.
  9. On The Sense and Reference of A Logical Constant.Harold Hodes - 2004 - Philosophical Quarterly 54 (214):134-165.
    Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...)
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  10. The Composition of Fregean Thoughts.Harold T. Hodes - 1982 - Philosophical Studies 41 (2):161 - 178.
  11. Ontological Commitments, Thick and Thin.Harold T. Hodes - 1990 - In George Boolos (ed.), Method, Reason and Language: Essays in Honor of Hilary Putnam. Cambridge University Press. pp. 235-260.
    Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role (...)
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  12.  56
    On the Sense and Reference of a Logical Constant.Harold Hodes - 2004 - Philosophical Quarterly 54 (214):134–165.
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  13.  20
    Three Value Logics: An Introduction, A Comparison of Various Logical Lexica and Some Philosophical Remarks.Harold Hodes - 1989 - Annals of Pure and Applied Logic 43 (2):99-145.
  14.  53
    Jumping Through the Transfinite: The Master Code Hierarchy of Turing Degrees.Harold T. Hodes - 1980 - Journal of Symbolic Logic 45 (2):204-220.
    Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.
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  15.  30
    One-Step Modal Logics, Intuitionistic and Classical, Part 2.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):873-910.
    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 systems associated with the intuitionistic counterparts (...)
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  16.  56
    Uniform Upper Bounds on Ideals of Turing Degrees.Harold T. Hodes - 1978 - Journal of Symbolic Logic 43 (3):601-612.
  17.  5
    Cut‐Conditions on Sets of Multiple‐Alternative Inferences.Harold T. Hodes - 2022 - Mathematical Logic Quarterly 68 (1):95-106.
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  18.  36
    Individual-Actualism and Three-Valued Modal Logics, Part 1: Model-Theoretic Semantics.Harold T. Hodes - 1986 - Journal of Philosophical Logic 15 (4):369 - 401.
  19.  37
    Mechanism, Mentalism and Metamathematics: An Essay on Finitism. [REVIEW]Harold T. Hodes - 1984 - Journal of Philosophy 81 (8):456-464.
  20. More About Uniform Upper Bounds on Ideals of Turing Degrees.Harold T. Hodes - 1983 - Journal of Symbolic Logic 48 (2):441-457.
    Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds on I (...)
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  21.  20
    Existence and Logic. [REVIEW]Harold Hodes & Milton Munitz - 1976 - Philosophical Review 85 (3):404.
  22.  39
    Individual-Actualism and Three-Valued Modal Logics, Part 2: Natural-Deduction Formalizations.Harold T. Hodes - 1987 - Journal of Philosophical Logic 16 (1):17 - 63.
  23. Corrections to "Where Do Sets Come From?".Harold T. Hodes - 1991 - Journal of Symbolic Logic 56 (4):1486.
  24.  53
    Intensional Mathematics. Stewart Shapiro. [REVIEW]Harold T. Hodes - 1989 - Philosophy of Science 56 (1):177-178.
  25.  19
    Book Review. Mechanism, Mentalism and Metamathematics. J Webb. [REVIEW]Harold T. Hodes - 1984 - Journal of Philosophy 81 (8):456-64.
  26.  47
    Stewart Shapiro’s Philosophy of Mathematics. [REVIEW]Harold Hodes - 2002 - Philosophy and Phenomenological Research 65 (2):467-475.
    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 people with on-field spatial and ‘defensive-role’ (...)
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  27.  79
    On Some Concepts Associated with Finite Cardinal Numbers.Harold T. Hodes - 2008 - Behavioral and Brain Sciences 31 (6):657-658.
    I catalog several concepts associated with finite cardinals, and then invoke them to interpret and evaluate several passages in Rips et al.'s target article. Like the literature it discusses, the article seems overly quick to ascribe the possession of certain concepts to children (and of set-theoretic concepts to non-mathematicians).
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  28.  21
    Jaakko Hintikka. The Principles of Mathematics Revisited. Cambridge University Press, Cambridge, New York, and Oakleigh, Victoria, 1996, Xii + 288 Pp. [REVIEW]Harold Hodes - 1998 - Journal of Symbolic Logic 63 (4):1615-1623.
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  29.  4
    Cardinality Logics, Part 1: Inclusions Between Languages Based on 'Exactly'.Harold Hodes - 1988 - Annals of Pure and Applied Logic 39 (3):199-238.
  30.  33
    The Modal Theory Of Pure Identity And Some Related Decision Problems.Harold Hodes - 1984 - Mathematical Logic Quarterly 30 (26-29):415-423.
    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 concerning formulae with two monadic predicates.
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  31.  37
    Where Do the Cardinal Numbers Come From?Harold T. Hodes - 1984 - Synthese 84:347-407.
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  32. Association for Symbolic Logic.Jon Barwise, Howard S. Becker, Chi Tat Chong, Herbert B. Enderton, Michael Hallett, C. Ward Henson, Harold Hodes, Neil Immerman, Phokion Kolaitis & Alistair Lachlan - 1998 - Bulletin of Symbolic Logic 4 (4):465-510.
  33. An Exact Pair for the Arithmetic Degrees Whose Join is Not a Weak Uniform Upper Bound.Harold T. Hodes - 1982 - Recursive Function Theory-Newsletters 28.
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  34. Book Review. Logic and Its Limits. P Shaw. [REVIEW]Harold T. Hodes - 1984 - History and Philosophy of Logic 5.
  35. Book Review. Language and Philosophical Problems. Soren Stenland. [REVIEW]Harold T. Hodes - 1993 - History and Philosophy of Logic:253-6.
  36.  42
    The Modal Theory of Pure Identity and Some Related Decision Problems.Harold T. Hodes - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (26‐29):415-423.
  37.  34
    Abstract Objects. [REVIEW]Harold T. Hodes - 1992 - International Studies in Philosophy 24 (3):146-148.
  38.  19
    Annual Meeting of the Association for Symbolic Logic, New York City, December 1987.Nicholas Goodman, Harold T. Hodes, Carl G. Jockusch & Kenneth McAloon - 1988 - Journal of Symbolic Logic 53 (4):1287-1299.
  39.  37
    Well-Behaved Modal Logics.Harold T. Hodes - 1984 - Journal of Symbolic Logic 49 (4):1393-1402.
  40.  24
    Finite Level Borel Games and a Problem Concerning the Jump Hierarchy.Harold T. Hodes - 1984 - Journal of Symbolic Logic 49 (4):1301-1318.
  41.  24
    Book Review. The Lambda-Calculus. H. P. Barendregt(. [REVIEW]Harold Hodes - 1988 - Philosophical Review 97 (1):132-7.
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  42.  35
    Meeting of the Association for Symbolic Logic: New York 1979.George Boolos, Sy Friedman & Harold Hodes - 1981 - Journal of Symbolic Logic 46 (2):427-434.
  43.  16
    Wang Hao. Reflections on Kurt Gödel. Bradford Books. The MIT Press, Cambridge, Mass., and London, 1987, Xxvi + 336 Pp. [REVIEW]Harold T. Hodes - 1989 - Journal of Symbolic Logic 54 (3):1095-1098.
  44.  27
    Book Review. Basic Set Theory. Azriel Levy. [REVIEW]Harold T. Hodes - 1981 - Philosophical Review 90 (2):298-300.
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  45.  19
    Review: Jaakko Hintikka, The Principles of Mathematics Revisited. [REVIEW]Harold Hodes - 1998 - Journal of Symbolic Logic 63 (4):1615-1623.
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  46.  31
    Stewart Shapiro’s Philosophy of Mathematics. [REVIEW]Harold Hodes - 2002 - Philosophy and Phenomenological Research 65 (2):467–475.
    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 people with on-field spatial and ‘defensive-role’ (...)
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  47.  43
    Ontological Reduction. [REVIEW]Harold Hodes - 1975 - Philosophical Review 84 (3):439.
  48.  6
    Book Review. Abstract Objects. Bob Hale. [REVIEW]Harold T. Hodes - 1992 - International Studies in Philosophy 24 (3):146-48.
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  49.  15
    Book Review. Principles of Intuitionism. Michael Dummett. [REVIEW]Harold T. Hodes - 1982 - Philosophical Review 91 (2):253-62.
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  50.  37
    Upper Bounds on Locally Countable Admissible Initial Segments of a Turing Degree Hierarchy.Harold T. Hodes - 1981 - Journal of Symbolic Logic 46 (4):753-760.
    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 (...)
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