Search results for 'Metamathematics' (try it on Scholar)

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  1. Stephen Cole Kleene (1952). Introduction to Metamathematics. North Holland.score: 15.0
  2. A. I. Malʹt͡sev (1971). The Metamathematics of Algebraic Systems, Collected Papers: 1936-1967. Amsterdam,North-Holland Pub. Co..score: 15.0
     
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  3. Helena Rasiowa (1963). The Mathematics of Metamathematics. Warszawa, Państwowe Wydawn. Naukowe.score: 15.0
     
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  4. Tim Button (2011). The Metamathematics of Putnam's Model-Theoretic Arguments. Erkenntnis 74 (3):321-349.score: 12.0
    Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely immune to metamathematical challenges.
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  5. Judson Webb (1968). Metamathematics and the Philosophy of Mind. Philosophy of Science 35 (June):156-78.score: 12.0
    The metamathematical theorems of Gödel and Church are frequently applied to the philosophy of mind, typically as rational evidence against mechanism. Using methods of Post and Smullyan, these results are presented as purely mathematical theorems and various such applications are discussed critically. In particular, J. Lucas's use of Gödel's theorem to distinguish between conscious and unconscious beings is refuted, while more generally, attempts to extract philosophy from metamathematics are shown to involve only dramatizations of the constructivity problem in foundations. (...)
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  6. Jeremy Avigad, “Clarifying the Nature of the Infinite”: The Development of Metamathematics and Proof Theory.score: 12.0
    We discuss the development of metamathematics in the Hilbert school, and Hilbert’s proof-theoretic program in particular. We place this program in a broader historical and philosophical context, especially with respect to nineteenth century developments in mathematics and logic. Finally, we show how these considerations help frame our understanding of metamathematics and proof theory today.
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  7. Raymond M. Smullyan (1993). Recursion Theory for Metamathematics. Oxford University Press.score: 12.0
    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.
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  8. Karl-Georg Niebergall (1999). Nonmonotonicity in (the Metamathematics of) Arithmetic. Erkenntnis 50 (2-3):309-332.score: 12.0
    This paper is an attempt to bring together two separated areas of research: classical mathematics and metamathematics on the one side, non-monotonic reasoning on the other. This is done by simulating nonmonotonic logic through antitonic theory extensions. In the first half, the specific extension procedure proposed here is motivated informally, partly in comparison with some well-known non-monotonic formalisms. Operators V and, more generally, U are obtained which have some plausibility when viewed as giving nonmonotonic theory extensions. In the second (...)
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  9. Jean-Roch Beausoleil (1989). The Metamathematics-Popperian Epistemology Connection and its Relation to the Logic of Turing's Programme. British Journal for the Philosophy of Science 40 (3):307-322.score: 12.0
    Turing's programme, the idea that intelligence can be modelled computationally, is set in the context of a parallel between certain elements from metamathematics and Popper's schema for the evolution of knowledge. The parallel is developed at both the formal level, where it hinges on the recursive structuring of Popper's schema, and at the contentual level, where a few key issues common to both epistemology and metamathematics are briefly discussed. In light of this connection Popper's principle of transference, akin (...)
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  10. Matthias Wille (2011). 'Metamathematics' in Transition. History and Philosophy of Logic 32 (4):333 - 358.score: 12.0
    In this paper, we trace the conceptual history of the term ?metamathematics? in the nineteenth century. It is well known that Hilbert introduced the term for his proof-theoretic enterprise in about 1922. But he was verifiably inspired by an earlier usage of the phrase in the 1870s. After outlining Hilbert's understanding of the term, we will explore the lines of inducement and elucidate the different meanings of ?metamathematics? in the final decades of the nineteenth century. Finally, we will (...)
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  11. P. Clote (1989). The Metamathematics of Scattered Linear Orderings. Archive for Mathematical Logic 29 (1):9-20.score: 12.0
    Pursuing the proof-theoretic program of Friedman and Simpson, we begin the study of the metamathematics of countable linear orderings by proving two main results. Over the weak base system consisting of arithmetic comprehension, II 1 1 -CA0 is equivalent to Hausdorff's theorem concerning the canonical decomposition of countable linear orderings into a sum over a dense or singleton set of scattered linear orderings. Over the same base system, ATR0 is equivalent to a version of the Continuum Hypothesis for linear (...)
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  12. N. Shankar (1994). Metamathematics, Machines, and Gödel's Proof. Cambridge University Press.score: 12.0
    The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Gödel's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated (...)
     
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  13. Jeremy Avigad (2009). The Metamathematics of Ergodic Theory. Annals of Pure and Applied Logic 157 (2):64-76.score: 10.0
    The metamathematical tradition, tracing back to Hilbert, employs syntactic modeling to study the methods of contemporary mathematics. A central goal has been, in particular, to explore the extent to which infinitary methods can be understood in computational or otherwise explicit terms. Ergodic theory provides rich opportunities for such analysis. Although the field has its origins in seventeenth century dynamics and nineteenth century statistical mechanics, it employs infinitary, nonconstructive, and structural methods that are characteristically modern. At the same time, computational concerns (...)
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  14. Alfred Tarski (1956). Logic, Semantics, Metamathematics. Oxford, Clarendon Press.score: 9.0
    I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...
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  15. Richard Routley (1979). Dialectical Logic, Semantics and Metamathematics. Erkenntnis 14 (3):301 - 331.score: 9.0
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  16. Hourya Sinaceur (2001). Alfred Tarski: Semantic Shift, Heuristic Shift in Metamathematics. Synthese 126 (1-2):49 - 65.score: 9.0
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  17. Solomon Feferman with with R. L. Vaught, Arithmetization of Metamathematics in a General Setting.score: 9.0
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  18. John R. Lucas (1971). Metamathematics and the Philosophy of Mind: A Rejoinder. Philosophy of Science 38 (2):310-13.score: 9.0
  19. Harold T. Hodes (1984). Book Review. Mechanism, Mentalism and Metamathematics. J Webb. [REVIEW] Journal of Philosophy 81 (8):456-64.score: 9.0
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  20. Sarah Voss (1995). What Number is God?: Metaphors, Metaphysics, Metamathematics, and the Nature of Things. State University of New York Press.score: 9.0
    CHAPTER Meta-View BRIDGES When I was a child, I lived in an area renowned for its many wooden covered bridges. Sometimes my family would take a Sunday drive ...
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  21. W. J. Blok & Don Pigozzi (1988). Alfred Tarski's Work on General Metamathematics. Journal of Symbolic Logic 53 (1):36-50.score: 9.0
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  22. W. Hetper & Leon Chwistek (1938). New Foundation of Formal Metamathematics. Journal of Symbolic Logic 3 (1):1-36.score: 9.0
  23. G. Kreisel (1956). Review: Some Uses of Metamathematics. [REVIEW] British Journal for the Philosophy of Science 7 (26):161 - 173.score: 9.0
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  24. Harvey Friedman, Metamathematics of Ulm Theory.score: 9.0
    The classical Ulm theory provides a complete set of invariants for countable abelian p-groups, and hence also for countable torsion abelian groups. These invariants involve countable ordinals. One can read off many simple structural properties of such groups directly from the Ulm theory. We carry out a reverse mathematics analysis of several such properties. In many cases, we reverse to ATR0, thereby demonstrating a kind of necessary use of Ulm theory.
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  25. Matthias Schirn (2010). Consistency, Models, and Soundness. Axiomathes 20 (2-3):153-207.score: 9.0
    This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...)
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  26. David Charles McCarty (1991). Incompleteness in Intuitionistic Metamathematics. Notre Dame Journal of Formal Logic 32 (3):323-358.score: 9.0
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  27. Harvey Friedman, Metamathematics of Comparability.score: 9.0
    A number of comparability theorems have been investigated from the viewpoint of reverse mathematics. Among these are various comparability theorems between countable well orderings ([2],[8]), and between closed sets in metric spaces ([3],[5]). Here we investigate the reverse mathematics of a comparability theorem for countable metric spaces, countable linear orderings, and sets of rationals. The previous work on closed sets used a strengthened notion of continuous embedding. The usual weaker notion of continuous embedding is used here. As a byproduct, we (...)
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  28. Jan Mycielski (1995). New Set-Theoretic Axioms Derived From a Lean Metamathematics. Journal of Symbolic Logic 60 (1):191-198.score: 9.0
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  29. I. Grattan-Guinness (2011). Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics. [REVIEW] Logica Universalis 5 (1):21-73.score: 9.0
    A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: ‘omnipresent’ and ‘multipresent’ theories, and ‘ubiquitous’ notions that form dependent parts, or moments, of (...)
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  30. B. J. (1981). Mechanism, Mentalism and Metamathematics. Review of Metaphysics 35 (1):176-178.score: 9.0
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  31. Stewart Shapiro (1986). Review: Judson Chambers Webb, Mechanism, Mentalism, and Metamathematics. An Essay on Finitism. [REVIEW] Journal of Symbolic Logic 51 (2):472-476.score: 9.0
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  32. Péter Várdy (1994). On the Dialectics of Metamathematics. Graduate Faculty Philosophy Journal 17 (1-2):191-216.score: 9.0
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  33. Steven French (2007). Metamathematics and Mechanics. Metascience 16 (3):529-533.score: 9.0
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  34. Klaus Gloede (1977). The Metamathematics of Infinitary Set Theoretical Systems. Mathematical Logic Quarterly 23 (1‐6):19-44.score: 9.0
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  35. Douglas E. Miller (1981). The Metamathematics of Model Theory: Discovering Language in Action. Journal of Symbolic Logic 46 (3):490-498.score: 9.0
    We discuss the problem of defining the collection of first-order elementary classes in terms of the natural topological space of countable models.
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  36. Stanisław J. Surma (1968). Four Studies in Metamathematics. Studia Logica 23 (1):109-114.score: 9.0
  37. Alexander S. Kohanski (1973). Einstein's “Metamathematics”. Philosophia Mathematica (2):165-181.score: 9.0
  38. John T. Baldwin (2006). The Metamathematics of Random Graphs. Annals of Pure and Applied Logic 143 (1):20-28.score: 9.0
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  39. L. Chwistek & W. Hetper (1938). New Foundation of Formal Metamathematics. Journal of Symbolic Logic 3 (1):1 - 36.score: 9.0
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  40. Rod Downey (2002). Roman Murawski, Recursive Functions and Metamathematics. Studia Logica 70 (2):297-299.score: 9.0
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  41. José Sanmartín Esplugues (1971). Introduction to Model Theory and to the Metamathematics of Algebra. Teorema: Revista Internacional de Filosofía 1 (4):134-136.score: 9.0
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  42. Carol R. Karp (1964). Review: Abraham Robinson, Introduction to Model Theory and the Metamathematics of Algebra. [REVIEW] Journal of Symbolic Logic 29 (1):56-56.score: 9.0
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  43. Javier Legris (2005). On the Epistemological Justification of Hilbert's Metamathematics. Philosophia Scientiae 9 (2):225-238.score: 9.0
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  44. P. J. M. (1965). The Mathematics of Metamathematics. Review of Metaphysics 19 (1):157-157.score: 9.0
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  45. Steven Orey (1966). Review: S. Feferman, Arithmetization of Metamathematics in a General Setting. [REVIEW] Journal of Symbolic Logic 31 (2):269-270.score: 9.0
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  46. Francis Jeffry Pelletier (2000). Review: Petr Hájek, Metamathematics of Fuzzy Logic. [REVIEW] Bulletin of Symbolic Logic 6 (3):342-346.score: 9.0
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  47. W. V. Quine (1938). Review: L. Chwistek, W. Hetper, New Foundation of Formal Metamathematics. [REVIEW] Journal of Symbolic Logic 3 (3):120-121.score: 9.0
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  48. H. Rasiowa (1954). Review: Stephen Cole Kleene, Introduction to Metamathematics. [REVIEW] Journal of Symbolic Logic 19 (3):215-216.score: 9.0
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  49. Urszula Wybraniec-Skardowska (2004). Foundations for the Formalization of Metamathematics and Axiomatizations of Consequence Theories. Annals of Pure and Applied Logic 127 (1-3):243-266.score: 9.0
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  50. Alonzo Church (1952). Review: Crispin Kim-Bradley, Symbolic Logic and Metamathematics. [REVIEW] Journal of Symbolic Logic 17 (2):154-154.score: 9.0
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