•  5
    A beginner's guide to mathematical logic
    Dover Publications. 2014.
    Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompletenes…Read more
  •  7
    At the turn of the century, there appeared two comprehensive mathematical systems, which were indeed so vast that it was taken for granted that all mathematics could be decided on the basis of them. However, in 1931, Kurt Gödel surprised the entire mathematical world with his epoch‐making paper which begins with the following startling words: The development of mathematics in the direction of greater precision has led to large areas of it being formalized, so that proofs can be carried out accor…Read more
  •  3
    More on propositional and first-order logic -- More on propositional logic -- More on first-order logic -- Recursion theory and metamathematics -- Some special topics -- Elementary formal systems and recursive enumerability -- Some recursion theory -- Doubling up -- Metamathematical applications -- Elements of combinatory logic -- Beginning combinatory logic -- Combinatorics galore -- Sages, oracles, and doublets -- Complete and partial systems -- Combinators, recursion, and the undecidable -- W…Read more
  •  10
    Theory of Formal Systems
    Princeton University Press. 1961.
    This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.
  •  1
    Methods of Logic
    Journal of Symbolic Logic 24 (3): 219-220. 1959.
  •  19
    Languages in Which Self Reference is Possible
    Journal of Symbolic Logic 24 (3): 228-228. 1959.
  •  8
    On Post's Canonical Systems
    Journal of Symbolic Logic 33 (4): 623-623. 1968.
  •  6
    Um dualista desafortunado
    Critica -. 2006.
  •  235
    Meeting of the association for symbolic logic
    with James K. Feibleman and R. L. Vaught
    Journal of Symbolic Logic 35 (2): 352-363. 1970.
  •  15
    Forever undecided: a puzzle guide to Gödel
    Oxford University Press. 1987.
    Collects a variety of mathematics and logic puzzles, some based on the theorems of the mathematician Kurt Godel
  •  6
    Creativity and Effective Inseparability
    Journal of Symbolic Logic 30 (3): 391-392. 1965.
  •  29
    Uniform Gentzen systems
    Journal of Symbolic Logic 33 (4): 549-559. 1968.
    Generally speaking, it appears correct to say that in a formulation of first order logic in which a large number of connectives are taken as primitive which allows us to have our cake and eat it too.
  •  53
    Analytic cut
    Journal of Symbolic Logic 33 (4): 560-564. 1968.
  •  7
    An entertaining series of logic problems and puzzles of increasing difficulty, and all relating important mathematical and logical concepts, includes mind-benders, paradoxes, metapuzzles, number exercises, and a mathematical novel.
  •  58
    Recursion theory for metamathematics
    Oxford University Press. 1993.
    This work is a sequel to the author's Godel's Incompleteness Theorems, though it can be read independently by anyone familiar with Godel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
  •  28
    Monadic Elementary Formal Systems
    Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (6): 81-83. 1961.
  •  15
    Elementary Formal Systems
    Journal of Symbolic Logic 34 (1): 117-117. 1969.
  •  42
    Analytic natural deduction
    Journal of Symbolic Logic 30 (2): 123-139. 1965.
  •  32
    The tao is silent
    HarperSanFrancisco. 1977.
    The Tao Is Silent Is Raymond Smullyan's beguiling and whimsical guide to the meaning and value of eastern philosophy to westerners. "To me," Writes Smullyan, "Taoism means a state of inner serenity combined with an intense aesthetic awareness. Neither alone is adequate; a purely passive serenity is kind of dull, and an anxiety-ridden awareness is not very appealing." This is more than a book on Chinese philosophy. It is a series of ideas inspired by Taoism that treats a wide variety of subjects …Read more
  •  91
    Some unifying fixed point principles
    Studia Logica 50 (1). 1991.
    This article is written for both the general mathematican and the specialist in mathematical logic. No prior knowledge of metamathematics, recursion theory or combinatory logic is presupposed, although this paper deals with quite general abstractions of standard results in those three areas. Our purpose is to show how some apparently diverse results in these areas can be derived from a common construction. In Section 1 we consider five classical fixed point arguments (or rather, generalizations …Read more
  •  28
    On post's canonical systems
    Journal of Symbolic Logic 27 (1): 55-57. 1962.
  •  220
    Gödel's incompleteness theorems
    Oxford University Press. 1992.
    Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinat…Read more
  •  86
    Chameleonic languages
    Synthese 60 (2). 1984.
  •  78
    Uniform self-reference
    Studia Logica 44 (4). 1985.
    Self-referential sentences have played a key role in Tarski's proof [9] of the non-definibility of arithmetic truth within arithmetic and Gödel's proof [2] of the incompleteness of Peano Arithmetic. In this article we consider some new methods of achieving self-reference in a uniform manner.
  •  6
    An epistemological nightmare
    In Douglas R. Hofstadter & Daniel C. Dennett (eds.), The Mind's I, Basic Books. 1981.