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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.
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  2. 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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  3.  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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  4. Axioms for Actuality.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):27 - 34.
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  5. Some Theorems on the Expressive Limitations of Modal Languages.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):13 - 26.
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  6.  89
    On Modal Logics Which Enrich First-Order S5.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (4):423 - 454.
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  7. The Composition of Fregean Thoughts.Harold T. Hodes - 1982 - Philosophical Studies 41 (2):161 - 178.
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  8. 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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  9.  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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  10.  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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  11.  56
    Uniform Upper Bounds on Ideals of Turing Degrees.Harold T. Hodes - 1978 - Journal of Symbolic Logic 43 (3):601-612.
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  12.  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.
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  13. 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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  14.  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.
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  15. Corrections to "Where Do Sets Come From?".Harold T. Hodes - 1991 - Journal of Symbolic Logic 56 (4):1486.
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  16.  37
    Well-Behaved Modal Logics.Harold T. Hodes - 1984 - Journal of Symbolic Logic 49 (4):1393-1402.
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  17.  24
    Finite Level Borel Games and a Problem Concerning the Jump Hierarchy.Harold T. Hodes - 1984 - Journal of Symbolic Logic 49 (4):1301-1318.
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  18.  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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