31 found
Sort by:
  1. Haim Gaifman, Formal Philosophy: Interviews.
    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..
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  2. Haim Gaifman, Gödel's Incompleteness Results.
    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 (...)
    No categories
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  3. Haim Gaifman, Naming and Diagonalization, From Cantor to G¨ Odel to Kleene.
    odel’s incompleteness results apply to formal theories for which syntactic constructs can be given names, in the same language, so that some basic syntactic operations are representable in the theory. It is now customary to derive these results from the fixed point theorem (also known as the reflection theorem), which asserts the existence of sentences that “speak about themselves”. Let T be the theory and, for each wff φ, let pφq be the term that serves as its name. Then the (...)
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  4. Haim Gaifman, Non-Standard Models in a Broader Perspective.
    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, (...)
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  5. Haim Gaifman, Pointers to Propositions.
    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 (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  6. Haim Gaifman, Some Thoughts and a Proposal in the Philosophy of Mathematics.
    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 (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  7. Haim Gaifman, The Easy Way to Gödel's Proof and Related Matters.
    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 (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  8. Haim Gaifman (2012). Deceptive Updating and Minimal Information Methods. 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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  9. Haim Gaifman (2012). On Ontology and Realism in Mathematics. Review of Symbolic Logic 5 (3):480-512.
    No categories
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  10. Haim Gaifman (2011). Erratum To: Vagueness, Tolerance and Contextual Logic. Synthese 179 (3):501 - 502.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  11. Haim Gaifman (2010). Vagueness, Tolerance and Contextual Logic. 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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  12. Haim Gaifman (2008). Contextual Logic with Modalities for Time and Space. 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, (...)
    Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  13. Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman (2006). Of the Association for Symbolic Logic. Bulletin of Symbolic Logic 12 (3-4):503.
    Direct download  
     
    My bibliography  
     
    Export citation  
  14. Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman (2006). The Hilton New York Hotel New York, NY December 27–29, 2005. Bulletin of Symbolic Logic 12 (3).
    Direct download  
     
    My bibliography  
     
    Export citation  
  15. Haim Gaifman (2004). Reasoning with Limited Resources and Assigning Probabilities to Arithmetical Statements. 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.
    No categories
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  16. 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). 2001 Annual Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 7 (3).
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  17. Haim Gaifman (2000). What Gödel's Incompleteness Result Does and Does Not Show. Journal of Philosophy 97 (8):462 - 470.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  18. Haim Gaifman (1999). Self-Reference and the Acyclicity of Rational Choice. 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.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  19. Haim Gaifman (1996). Is the "Bottom-Up" Approach From the Theory of Meaning to Metaphysics Possible? 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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  20. Haim Gaifman (1992). Pointers to Truth. 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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  21. Haim Gaifman, Daniel N. Osherson & Scott Weinstein (1990). A Reason for Theoretical Terms. 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.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  22. Haim Gaifman (1988). Operational Pointer Semantics: Solution to Self-Referential Puzzles I. In M. Y. Vardi (ed.), Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge. Morgan Kaufman.
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  23. Haim Gaifman (1985). On Inductive Support and Some Recent Tricks. Erkenntnis 22 (1-3):5 - 21.
    No categories
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  24. Haim Gaifman (1983). Paradoxes of Infinity and Self-Applications, I. Erkenntnis 20 (2):131 - 155.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  25. Haim Gaifman & Marc Snir (1982). Probabilities Over Rich Languages, Testing and Randomness. Journal of Symbolic Logic 47 (3):495-548.
  26. Haim Gaifman (1979). Subjective Probability, Natural Predicates and Hempel's Ravens. Erkenntnis 14 (2):105 - 147.
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  27. Haim Gaifman, Azriel Levy & Gert H. Müller (1977). Meeting of the Association for Symbolic Logic: Jerusalem, Israel, 1975. Journal of Symbolic Logic 42 (1):140-142.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  28. Haim Gaifman (1976). Models and Types of Peano's Arithmetic. Annals of Mathematical Logic 9 (3):223-306.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  29. Haim Gaifman (1976). Ontology and Conceptual Frameworks Part II. Erkenntnis 10 (1):21 - 85.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  30. Haim Gaifman (1975). Ontology and Conceptual Frameworks: Part I. Erkenntnis 9 (3):329 - 353.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  31. Haim Gaifman (1969). Review: Saul A. Kripke, An Extension of a Theorem of Gaifman-Hales-Solovay. [REVIEW] Journal of Symbolic Logic 34 (1):131-132.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation