•  27
    On Play by Means of Computing Machines .A Theory of Higher Order Probabilities.Knowledge and Efficient Computation.Realizability Semantics for Error-Tolerant Logics (review)
    with William J. Rapaport, Nimrod Megiddo, Avi Wigderson, Silvio Micali, John C. Mitchell, and Michael J. O'Donnell
    Journal of Symbolic Logic 53 (2): 669. 1988.
  •  16
    An Extension of a Theorem of Gaifman-Hales-Solovay
    Journal of Symbolic Logic 34 (1): 131-132. 1969.
  •  470
    Context-dependent Utilities
    with Yang Liu
    In Wiebe Van Der Hoek, Wesley H. Holliday & Wen Fang Wang (eds.), Logic, Rationality, and Interaction, Springer. pp. 90-101. 2015.
    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 sta…Read more
  •  12
    Models and Types of Peano's Arithmetic
    with Julia F. Knight, Fred G. Abramson, and Leo A. Harrington
    Journal of Symbolic Logic 48 (2): 484-485. 1983.
  •  602
    A Simpler and More Realistic Subjective Decision Theory
    with Yang Liu
    Synthese 195 (10): 4205--4241. 2018.
    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 satisf…Read more
  •  61
    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 to tr…Read more
  •  40
    Ontology and conceptual frameworks part II
    Erkenntnis 10 (1). 1976.
  •  15
    Infinite Boolean Polynomials I
    with A. W. Hales
    Journal of Symbolic Logic 32 (1): 131-132. 1967.
  •  80
    Self-reference and the acyclicity of rational choice
    Annals of Pure and Applied Logic 96 (1-3): 117-140. 1999.
    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.
  •  257
    Meeting of the association for symbolic logic: Jerusalem, Israel, 1975
    with Azriel Levy and Gert H. Müller
    Journal of Symbolic Logic 42 (1): 140-142. 1977.
  •  80
    Contextual logic with modalities for time and space
    Review of Symbolic Logic 1 (4): 433-458. 2008.
    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. P…Read more
  •  179
    Pointers to truth
    Journal of Philosophy 89 (5): 223-261. 1992.
    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 true conclusion on line 2 we ¯nd ourselves repeating the very same sentence. It se…Read more
  •  47
    Ontology and Conceptual Frameworks: Part I
    Erkenntnis 9 (3). 1975.
  •  131
    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 th…Read more
  •  91
    Naming and Diagonalization, from Cantor to Gödel to Kleene
    Logic Journal of the IGPL 14 (5): 709-728. 2006.
    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, the arity of the named function. Under quite general conditions we get a fixed point theorem, whose special cas…Read more
  •  130
    Deceptive updating and minimal information methods
    Synthese 187 (1): 147-178. 2012.
    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 ar…Read more
  •  318
    Vagueness, tolerance and contextual logic
    Synthese 174 (1). 2010.
    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…Read more
  •  31
    Pointers to Truth
    Journal of Philosophy 89 (5): 223. 1992.
  •  16
  •  100
    A reason for theoretical terms
    with DanielN Osherson and Scott Weinstein
    Erkenntnis 32 (2). 1990.
    The presence of nonobservational vocabulary is shown to be necessary for wide application of a conservative principle of theory revision.
  •  73
    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 mathe…Read more
  •  68
    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…Read more