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46On Play by Means of Computing Machines .A Theory of Higher Order Probabilities.Knowledge and Efficient Computation.Realizability Semantics for Error-Tolerant Logics (review)Journal of Symbolic Logic 53 (2): 669. 1988.
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22An Extension of a Theorem of Gaifman-Hales-SolovayJournal of Symbolic Logic 34 (1): 131-132. 1969.
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68Saul A. Kripke. An extension of a theorem of Gaifman-Hales-Solovay. Fundamenta mathematicae, vol. 61 , pp. 29–32Journal of Symbolic Logic 34 (1): 131-132. 1969.
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519Context-dependent UtilitiesIn 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
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717A Simpler and More Realistic Subjective Decision TheorySynthese 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
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23Is the "Bottom-Up" Approach from the Theory of Meaning to Metaphysics Possible?Journal of Philosophy 93 (8): 373-407. 1996.
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104A reason for theoretical termsErkenntnis 32 (2). 1990.The presence of nonobservational vocabulary is shown to be necessary for wide application of a conservative principle of theory revision.
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73The 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
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143Probabilities over rich languages, testing and randomnessJournal of Symbolic Logic 47 (3): 495-548. 1982.
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68Non-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
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72This 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 s…Read more
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527What Godel's Incompleteness Result Does and Does Not ShowJournal of Philosophy 97 (8): 462. 2000.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 fails in an i…Read more
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164Reasoning with limited resources and assigning probabilities to arithmetical statementsSynthese 140 (1-2). 2004.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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217On ontology and realism in mathematicsReview of Symbolic Logic 5 (3): 480-512. 2012.The paper is concerned with the way in which “ontology” and “realism” are to be interpreted and applied so as to give us a deeper philosophical understanding of mathematical theories and practice. Rather than argue for or against some particular realistic position, I shall be concerned with possible coherent positions, their strengths and weaknesses. I shall also discuss related but different aspects of these problems. The terms in the title are the common thread that connects the various sectio…Read more
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74This 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 s…Read more
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61The 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
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212005–06 Winter Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 12 (3): 503-516. 2006.
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87Self-reference and the acyclicity of rational choiceAnnals 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.
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1Operational pointer semantics: Solution to self-referential puzzles IIn M. Y. Vardi (ed.), Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge, Morgan Kaufman. 1988.
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267Meeting of the association for symbolic logic: Jerusalem, Israel, 1975Journal of Symbolic Logic 42 (1): 140-142. 1977.
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83Contextual logic with modalities for time and spaceReview 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
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41The sure thing principle, dilations, and objective probabilitiesJournal of Applied Logic 11 (4): 373-385. 2013.
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189Pointers to truthJournal 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
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Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Philosophy of Probability |