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Haim Gaifman
Columbia University
  1. A Simpler and More Realistic Subjective Decision Theory.Haim Gaifman & Yang Liu - forthcoming - Synthese:1-37.
    In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...)
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  2. Vagueness, Tolerance and Contextual Logic.Haim Gaifman - 2010 - Synthese 174 (1):5 - 46.
    The goal of this paper is a comprehensive analysis of basic reasoning patterns that are characteristic of vague predicates. The analysis leads to rigorous reconstructions of the phenomena within formal systems. Two basic features are dealt with. One is tolerance: the insensitivity of predicates to small changes in the objects of predication (a one-increment of a walking distance is a walking distance). The other is the existence of borderline cases. The paper shows why these should be treated as different, though (...)
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  3.  21
    Context-Dependent Utilities.Haim Gaifman & Yang Liu - 2015 - In Wiebe Van Der Hoek, Wesley H. Holliday & Wen Fang Wang (eds.), Logic, Rationality, and Interaction. Springer. pp. 90-101.
    Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to consequences. (...)
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  4.  75
    Probabilities Over Rich Languages, Testing and Randomness.Haim Gaifman & Marc Snir - 1982 - Journal of Symbolic Logic 47 (3):495-548.
  5.  83
    Reasoning with Limited Resources and Assigning Probabilities to Arithmetical Statements.Haim Gaifman - 2004 - Synthese 140 (1-2):97 - 119.
    There are three sections in this paper. The first is a philosophical discussion of the general problem of reasoning under limited deductive capacity. The second sketches a rigorous way of assigning probabilities to statements in pure arithmetic; motivated by the preceding discussion, it can nonetheless be read separately. The third is a philosophical discussion that highlights the shifting contextual character of subjective probabilities and beliefs.
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  6.  86
    Pointers to Truth.Haim Gaifman - 1992 - Journal of Philosophy 89 (5):223-261.
    If we try to evaluate the sentence on line 1 we ¯nd ourselves going in an unending cycle. For this reason alone we may conclude that the sentence is not true. Moreover we are driven to this conclusion by an elementary argument: If the sentence is true then what it asserts is true, but what it asserts is that the sentence on line 1 is not true. Consequently the sentence on line 1 is not true. But when we write this (...)
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  7. What Gödel's Incompleteness Result Does and Does Not Show.Haim Gaifman - 2000 - Journal of Philosophy 97 (8):462 - 470.
    In a recent paper S. McCall adds another link to a chain of attempts to enlist Gödel’s incompleteness result as an argument for the thesis that human reasoning cannot be construed as being carried out by a computer.1 McCall’s paper is undermined by a technical oversight. My concern however is not with the technical point. The argument from Gödel’s result to the no-computer thesis can be made without following McCall’s route; it is then straighter and more forceful. Yet the argument (...)
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  8.  68
    Non-Standard Models in a Broader Perspective.Haim Gaifman - manuscript
    Non-standard models were introduced by Skolem, first for set theory, then for Peano arithmetic. In the former, Skolem found support for an anti-realist view of absolutely uncountable sets. But in the latter he saw evidence for the impossibility of capturing the intended interpretation by purely deductive methods. In the history of mathematics the concept of a nonstandard model is new. An analysis of some major innovations–the discovery of irrationals, the use of negative and complex numbers, the modern concept of function, (...)
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  9.  84
    Deceptive Updating and Minimal Information Methods.Haim Gaifman & Anubav Vasudevan - 2012 - Synthese 187 (1):147-178.
    The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method and argue that non-deceptiveness is a necessary condition for rational coherence. Infomin has been criticized on the grounds that there are no higher (...)
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  10.  16
    Models and Types of Peano's Arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
  11.  92
    On Ontology and Realism in Mathematics.Haim Gaifman - 2012 - Review of Symbolic Logic 5 (3):480-512.
  12. Pointers to Propositions.Haim Gaifman - manuscript
    The semantic paradoxes, whose paradigm is the Liar, played a crucial role at a crucial juncture in the development of modern logic. In his 1908 seminal paper, Russell outlined a system, soon to become that of the Principia Mathematicae, whose main goal was the solution of the logical paradoxes, both semantic and settheoretic. Russell did not distinguish between the two and his theory of types was designed to solve both kinds in the same uniform way. Set theoreticians, however, were content (...)
     
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  13.  34
    Subjective Probability, Natural Predicates and Hempel's Ravens.Haim Gaifman - 1979 - Erkenntnis 14 (2):105 - 147.
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  14.  3
    Pointers to Truth.Haim Gaifman - 1992 - Journal of Philosophy 89 (5):223.
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  15.  57
    Paradoxes of Infinity and Self-Applications, I.Haim Gaifman - 1983 - Erkenntnis 20 (2):131 - 155.
  16. Meeting of the Association for Symbolic Logic: Jerusalem, Israel, 1975.Haim Gaifman, Azriel Levy & Gert H. Müller - 1977 - Journal of Symbolic Logic 42 (1):140-142.
  17.  65
    Is the "Bottom-Up" Approach From the Theory of Meaning to Metaphysics Possible?Haim Gaifman - 1996 - Journal of Philosophy 93 (8):373-407.
    Dummett’s The Logical Foundations of Metaphysics (LFM) outlines an ambitious project that has been at the core of his work during the last forty years. The project is built around a particular conception of the theory of meaning (or philosophy of language), according to which such a theory should constitute the corner stone of philosophy and, in particular, provide answers to various metaphysical questions. The present paper is intended as a critical evaluation of some of the main features of that (...)
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  18. Operational Pointer Semantics: Solution to Self-Referential Puzzles I.Haim Gaifman - 1988 - In M. Y. Vardi (ed.), Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge. Morgan Kaufman.
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  19.  57
    Naming and Diagonalization, From Cantor to Gödel to Kleene.Haim Gaifman - 2006 - Logic Journal of the IGPL 14 (5):709-728.
    We trace self-reference phenomena to the possibility of naming functions by names that belong to the domain over which the functions are defined. A naming system is a structure of the form ,{ }), where D is a non-empty set; for every a∈ D, which is a name of a k-ary function, {a}: Dk → D is the function named by a, and type is the type of a, which tells us if a is a name and, if it is, (...)
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  20.  61
    Self-Reference and the Acyclicity of Rational Choice.Haim Gaifman - 1999 - Annals of Pure and Applied Logic 96 (1-3):117-140.
    Self-reference in semantics, which leads to well-known paradoxes, is a thoroughly researched subject. The phenomenon can appear also in decision theoretic situations. There is a structural analogy between the two and, more interestingly, an analogy between principles concerning truth and those concerning rationality. The former can serve as a guide for clarifying the latter. Both the analogies and the disanalogies are illuminating.
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  21.  42
    On Inductive Support and Some Recent Tricks.Haim Gaifman - 1985 - Erkenntnis 22 (1-3):5 - 21.
  22.  45
    A Reason for Theoretical Terms.Haim Gaifman, Daniel N. Osherson & Scott Weinstein - 1990 - Erkenntnis 32 (2):149 - 159.
    The presence of nonobservational vocabulary is shown to be necessary for wide application of a conservative principle of theory revision.
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  23.  74
    The Easy Way to Gödel's Proof and Related Matters.Haim Gaifman - unknown
    This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method [1891]. It renders the proof of the so–called fixed point theorem transparent. We also point out various historical details and make some observations on circularity and some comparisons with natural language. The sketch does not include the messy details of the arithmetization of the language, but the motive for arithmetization and what it should accomplish are made obvious. We suggest this as a way to (...)
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  24.  59
    Contextual Logic with Modalities for Time and Space.Haim Gaifman - 2008 - Review of Symbolic Logic 1 (4):433-458.
    Contextuality is trivially pervasive: all human experience takes place in endlessly changing environments and inexorably moving time frames. In order to have any meaning, the changing items must be placed within a more stable setting, a framework that is not subject to the same kind of contextual change. Total contextuality collapses into chaos, or becomes ineffable. While basic learning is highly contextual (one learns by example), what is learned transcends the examples used in the learning. Perhaps, in a similar manner, (...)
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  25.  28
    Ontology and Conceptual Frameworks: Part I.Haim Gaifman - 1975 - Erkenntnis 9 (3):329 - 353.
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  26.  29
    Ontology and Conceptual Frameworks Part II.Haim Gaifman - 1976 - Erkenntnis 10 (1):21 - 85.
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  27.  72
    Gödel's Incompleteness Results.Haim Gaifman - unknown
    This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method [1891]. It renders Gödel’s proof and its relation to the semantic paradoxes transparent. Some historical details, which are often ignored, are pointed out. We also make some observations on circularity and draw brief comparisons with natural language. The sketch does not include the messy details of the arithmetization of the language, but the motives for it are made obvious. We suggest this as a more (...)
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  28.  74
    Erratum To: Vagueness, Tolerance and Contextual Logic.Haim Gaifman - 2011 - Synthese 179 (3):501 - 502.
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  29.  15
    2001 Annual Meeting of the Association for Symbolic Logic.Joan Feigenbaum, Haim Gaifman, Jean-Yves Girard, C. Ward Henson, Denis Hirschfeldt, Carl G. Jockusch Jr, Saul Kripke, Salma Kuhlmann, John C. Mitchell & Ernest Schimmerling - 2001 - Bulletin of Symbolic Logic 7 (3):420-435.
  30.  73
    Some Thoughts and a Proposal in the Philosophy of Mathematics.Haim Gaifman - manuscript
    The paper outlines a project in the philosophy of mathematics based on a proposed view of the nature of mathematical reasoning. It also contains a brief evaluative overview of the discipline and some historical observations; here it points out and illustrates the division between the philosophical dimension, where questions of realism and the status of mathematics are treated, and the more descriptive and looser dimension of epistemic efficiency, which has to do with ways of organizing the mathematical material. The paper’s (...)
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  31.  62
    Formal Philosophy: Interviews.Haim Gaifman - manuscript
    Please send the completed questionnaire by October 1, 2005 either electronically to Vincent F. Hendricks (vincent@ruc.dk) or John Symons (jsymons@utep.edu) or mail (fax) to Vincent F. Hendricks, Dept. of Philosophy and Science Studies, Roskilde University, DK4000 Roskilde, Denmark, Fax: +45 4674 3012..
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  32.  2
    Is the "Bottom-Up" Approach From the Theory of Meaning to Metaphysics Possible?Haim Gaifman - 1996 - Journal of Philosophy 93 (8):373-407.
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  33.  20
    Review: Saul A. Kripke, An Extension of a Theorem of Gaifman-Hales-Solovay. [REVIEW]Haim Gaifman - 1969 - Journal of Symbolic Logic 34 (1):131-132.
  34.  9
    The Sure Thing Principle, Dilations, and Objective Probabilities.Haim Gaifman - 2013 - Journal of Applied Logic 11 (4):373-385.
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  35.  1
    Models and Types of Peano's Arithmetic.Haim Gaifman, Julia F. Knight, Fred G. Abramson & Leo A. Harrington - 1983 - Journal of Symbolic Logic 48 (2):484-485.
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  36.  6
    On Play by Means of Computing Machines .A Theory of Higher Order Probabilities.Knowledge and Efficient Computation.Realizability Semantics for Error-Tolerant Logics. [REVIEW]William J. Rapaport, Nimrod Megiddo, Avi Wigderson, Haim Gaifman, Silvio Micali, John C. Mitchell & Michael J. O'Donnell - 1988 - Journal of Symbolic Logic 53 (2):669.
  37.  10
    Of the Association for Symbolic Logic.Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman - 2006 - Bulletin of Symbolic Logic 12 (3-4):503.
  38.  4
    Kripke Saul A.. An Extension of a Theorem of Gaifman-Hales-Solovay. Fundamenta Mathematicae, Vol. 61 , Pp. 29–32.Haim Gaifman - 1969 - Journal of Symbolic Logic 34 (1):131-132.
  39.  4
    What Godel's Incompleteness Result Does and Does Not Show.Haim Gaifman - 2000 - Journal of Philosophy 97 (8):462.
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  40.  7
    The Hilton New York Hotel New York, NY December 27–29, 2005.Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman - 2006 - Bulletin of Symbolic Logic 12 (3).
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  41.  1
    2005–06 Winter Meeting of the Association for Symbolic Logic.Haim Gaifman - 2006 - Bulletin of Symbolic Logic 12 (3):503-516.
  42.  1
    On Play by Means of Computing Machines.Nimrod Megiddo, Avi Wigderson, Haim Gaifman, Silvio Micali, John C. Mitchell & Michael J. O'donnell - 1988 - Journal of Symbolic Logic 53 (2):669-670.
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  43. Extensions of Non-Standard Models of Number Theory.Andrew Adler & Haim Gaifman - 1975 - Journal of Symbolic Logic 40 (2):244-245.
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