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Profile: Harold Hodes (Cornell University)
  1. Harold T. Hodes (2008). On Some Concepts Associated with Finite Cardinal Numbers. 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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  2. Harold T. Hodes (2006). Structural Proof Theory. Philosophical Review 115 (2):255-258.
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  3. Harold T. Hodes (2004). On The Sense and Reference of A Logical Constant. 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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  4. Harold T. Hodes (2002). Book Review. Philosophy of Mathematics: Structure and Ontology. Stewart Shapiro. [REVIEW] Philosophy and Phenomenological Research 65 (2):467-475.
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  5. Harold T. Hodes (2002). Review of S. Shapiro, Philosophy of Mathematics: Structure and Ontology. [REVIEW] Philosophy and Phenomenological Research 65 (2):467 - 475.
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  6. Harold T. Hodes (2002). Stewart Shapiro's Philosophy of Mathematics. [REVIEW] Philosophy and Phenomenological Research 65 (2):467–475.
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  7. Harold T. Hodes (1998). Book Review. The Principles of Mathematics Revisited. Jaakko Hintikka. [REVIEW] Journal of Symbolic Logic 63 (4):1615-23.
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  8. Harold T. Hodes (1993). Book Review. Language and Philosophical Problems. Soren Stenland. [REVIEW] History and Philosophy of Logic:253-6.
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  9. Harold T. Hodes (1992). Abstract Objects. International Studies in Philosophy 24 (3):146-148.
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  10. Harold T. Hodes (1992). Book Review. Abstract Objects. Bob Hale. [REVIEW] International Studies in Philosophy 24 (3):146-48.
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  11. Harold T. Hodes (1991). Corrections to "Where Do Sets Come From?&Quot;. Journal of Symbolic Logic 56 (4):1486.
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  12. Harold T. Hodes (1991). Where Do Sets Come From? Journal of Symbolic Logic 56 (1):150-175.
  13. Harold T. Hodes (1990). Ontological Commitments, Thick and Thin. In George Boolos (ed.), Method, Reason and Language: Essays in Honor of Hilary Putnam. Cambridge University Press.
    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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  14. Harold T. Hodes (1990). Where Do the Natural Numbers Come From? Synthese 84 (3):347-407.
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  15. Harold T. Hodes (1990). Where Do the Natural Numbers Come From? In Memory of Geoffrey Joseph. Synthese 84 (3):347 - 407.
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  16. Harold T. Hodes (1989). Book Review:Intensional Mathematics Stewart Shapiro. [REVIEW] Philosophy of Science 56 (1):177-.
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  17. Harold T. Hodes (1989). Book Review. Reflections. Kurt Godel. [REVIEW] THe Journal for Symbolic Logic 54 (3):1095-98.
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  18. Harold T. Hodes (1989). Review: Hao Wang, Reflections on Kurt Godel. [REVIEW] Journal of Symbolic Logic 54 (3):1095-1098.
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  19. Harold T. Hodes (1989). Three Value Logics: An Introduction, A Comparison of Various Logical Lexica and Some Philosophical Remarks. Annals of Pure and Applied Logic 43 (2):99-145.
  20. Nicholas Goodman, Harold T. Hodes, Carl G. Jockusch Jr & Kenneth McAloon (1988). Annual Meeting of the Association for Symbolic Logic, New York City, December 1987. Journal of Symbolic Logic 53 (4):1287 - 1299.
  21. Harold T. Hodes (1988). Book Review. The Lambda-Calculus. H. P. Barendregt(. [REVIEW] Philosophical Review 97 (1):132-7.
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  22. Harold T. Hodes (1988). Cardinality Logics. Part II: Definability in Languages Based on `Exactly'. Journal of Symbolic Logic 53 (3):765-784.
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  23. Harold T. Hodes (1988). Cardinality Logics, Part 1: Inclusions Between Languages Based on 'Exactly'. Annals of Pure and Applied Logic 39:199-238.
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  24. Harold T. Hodes (1987). Individual-Actualism and Three-Valued Modal Logics, Part 2: Natural-Deduction Formalizations. [REVIEW] Journal of Philosophical Logic 16 (1):17 - 63.
  25. Harold T. Hodes (1986). Individual-Actualism and Three-Valued Modal Logics, Part 1: Model-Theoretic Semantics. [REVIEW] Journal of Philosophical Logic 15 (4):369 - 401.
  26. Harold T. Hodes, Moral Explanation. Morality, Reason and Truth.
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  27. Harold T. Hodes (1984). Axioms for Actuality. Journal of Philosophical Logic 13 (1):27 - 34.
  28. Harold T. Hodes (1984). Book Review. Logic and Its Limits. P Shaw. [REVIEW] History and Philosophy of Logic 5.
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  29. Harold T. Hodes (1984). Book Review. Mechanism, Mentalism and Metamathematics. J Webb. [REVIEW] Journal of Philosophy 81 (8):456-64.
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  30. Harold T. Hodes (1984). Finite Level Borel Games and a Problem Concerning the Jump Hierarchy. Journal of Symbolic Logic 49 (4):1301-1318.
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  31. Harold T. Hodes (1984). Logicism and the Ontological Commitments of Arithmetic. Journal of Philosophy 81 (3):123-149.
  32. Harold T. Hodes (1984). On Modal Logics Which Enrich First-Order S. Journal of Philosophical Logic 13 (4):423 - 454.
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  33. Harold T. Hodes (1984). Some Theorems on the Expressive Limitations of Modal Languages. Journal of Philosophical Logic 13 (1):13 - 26.
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  34. Harold T. Hodes (1984). The Modal Theory of Pure Identity and Some Related Decision Problems. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (26‐29):415-423.
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  35. Harold T. Hodes (1984). Well-Behaved Modal Logics. Journal of Symbolic Logic 49 (4):1393-1402.
  36. Harold T. Hodes (1983). A Minimal Upper Bound on a Sequence of Turing Degrees Which Represents That Sequence. Pacific Journal of Mathematics 108 (1):115-119.
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  37. Harold T. Hodes (1983). More About Uniform Upper Bounds on Ideals of Turing Degrees. 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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  38. Harold T. Hodes (1982). An Exact Pair for the Arithmetic Degrees Whose Join is Not a Weak Uniform Upper Bound. Recursive Function Theory-Newsletters 28.
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  39. Harold T. Hodes (1982). Book Review. Principles of Intuitionism. Michael Dummett. [REVIEW] Philosophical Review 91 (2):253-62.
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  40. Harold T. Hodes (1982). Jumping to a Uniform Upper Bound. Proceedings of the American Mathematical Society 85 (4):600-602.
    A uniform upper bound on a class of Turing degrees is the Turing degree of a function which parametrizes the collection of all functions whose degree is in the given class. I prove that if a is a uniform upper bound on an ideal of degrees then a is the jump of a degree c with this additional property: there is a uniform bound b<a so that b V c < a.
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  41. Harold T. Hodes (1982). The Composition of Fregean Thoughts. Philosophical Studies 41 (2):161 - 178.
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  42. George Boolos, Sy Friedman & Harold T. Hodes (1981). Meeting of the Association for Symbolic Logic: New York 1979. Journal of Symbolic Logic 46 (2):427-434.
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  43. Harold T. Hodes (1981). Book Review. Basic Set Theory. Azriel Levy. [REVIEW] Philosophical Review 90 (2):298-300.
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  44. Harold T. Hodes (1981). Upper Bounds on Locally Countable Admissible Initial Segments of a Turing Degree Hierarchy. 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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  45. Harold T. Hodes (1980). Jumping Through the Transfinite: The Master Code Hierarchy of Turing Degrees. 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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  46. Harold T. Hodes (1978). Uniform Upper Bounds on Ideals of Turing Degrees. Journal of Symbolic Logic 43 (3):601-612.
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  47. Harold T. Hodes (1976). Book Review. Existence and Logic. Milton Munitz. [REVIEW] Philosophical Review 85 (3):404-08.
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  48. Harold T. Hodes (1976). Book Review. Logic and Arithmetic, Volume I. D Bostock. [REVIEW] Journal of Philosophy 73 (6):149-57.
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  49. Harold T. Hodes (1975). Book Review. Ontological Reduction. Reinhardt Grossman. [REVIEW] Philosophical Review 84 (3):439-444.
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  50. Harold T. Hodes, Harold Hodes: Bibliography.
    An Exact Pair for the Arithmetic Degrees whose join is not a Weak Uniform Upper Bound, in the Recursive Function Theory-Newsletters, No. 28, August-September 1982.
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