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  1. Introduction to Metamathematics.H. Rasiowa - 1954 - Journal of Symbolic Logic 19 (3):215-216.
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  • Logical Consequence: A Defense of Tarski.Greg Ray - 1996 - Journal of Philosophical Logic 25 (6):617 - 677.
    In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant (...)
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  • On the Concept of Following Logically.Alfred Tarski - 2002 - History and Philosophy of Logic 23 (3):155-196.
    We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...)
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  • On a Fallacy Attributed to Tarski.Mario Gómez-Torrente - 1998 - History and Philosophy of Logic 19 (4):227-234.
    The purpose of this paper is to examine some passages of Tarski?s paper ?On the concept of logical consequence? and to show that some recent readings of those passages are wrong. John Etchemendy has claimed that in those passages Tarski gave an argument purporting to show that the notion of logical consequence defined by him (as opposed to some pretheoretic notion of logical consequence) possesses certain modal properties. Etchemendy further claims that the argument he attributes to Tarski is fallacious. Some (...)
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  • Did Tarski Commit "Tarski's Fallacy"?Gila Sher - 1996 - Journal of Symbolic Logic 61 (2):653-686.
  • On Tarski on Models.Timothy Bays - 2001 - Journal of Symbolic Logic 66 (4):1701-1726.
    This paper concerns Tarski’s use of the term “model” in his 1936 paper “On the Concept of Logical Consequence.” Against several of Tarski’s recent defenders, I argue that Tarski employed a non-standard conception of models in that paper. Against Tarski’s detractors, I argue that this non-standard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski’s ω-rule example.
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  • American Postulate Theorists and Alfred Tarski.Michael Scanlan - 2003 - History and Philosophy of Logic 24 (4):307-325.
    This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated axiomatic theories (...)
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  • Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):1-30.
    This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
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  • The Logical Syntax of Language.E. N. - 1937 - Journal of Philosophy 34 (11):303.
  • Logic, Semantics, Metamathematics.Atwell Turquette - 1958 - Philosophical Review 67 (1):113.
  • The Concept of Logical Consequence.Gary N. Curtis - 1994 - Noûs 28 (1):132-135.
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  • Bericht Über Untersuchungen Zur Allgemeinen Axiomatik.Rudolf Carnap - 1930 - Erkenntnis 1 (1):303-307.
  • Carnap, Completeness, and Categoricity:The Gabelbarkeitssatz OF 1928. [REVIEW]S. Awodey & A. W. Carus - 2001 - Erkenntnis 54 (2):145-172.
    In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...)
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  • Tarski Alfred. O Logice Matematycznej I Metodzie Dedukcyjnej . Bibljoteczka Matematyczna 3–5. Ksiażnica-Atlas, Lwów and Warsaw 1936, 167 Pp.Tarski Alfred. Einführung in Die Mathematische Logik Und in Die Methodologie der Mathematik. German Translation of the Preceding. Julius Springer, Vienna 1937, X+ 166 Pp. [REVIEW]Saunders MacLane - 1938 - Journal of Symbolic Logic 3 (1):51-52.
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  • Tarski and Geometry.L. W. Szczerba - 1986 - Journal of Symbolic Logic 51 (4):907-912.
  • Who Were the American Postulate Theorists?Michael Scanlan - 1991 - Journal of Symbolic Logic 56 (3):981-1002.
    Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.
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  • Alfred Tarski's Work in Model Theory.Robert L. Vaught - 1986 - Journal of Symbolic Logic 51 (4):869-882.
  • Tarski on Logical Consequence.Mario Gómez-Torrente - 1996 - Notre Dame Journal of Formal Logic 37 (1):125-151.
    This paper examines from a historical perspective Tarski's 1936 essay, "On the concept of logical consequence." I focus on two main aims. The primary aim is to show how Tarski's definition of logical consequence satisfies two desiderata he himself sets forth for it: (1) it must declare logically correct certain formalizations of the -rule and (2) it must allow for variation of the individual domain in the test for logical consequence. My arguments provide a refutation of some interpreters of Tarski, (...)
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  • Grundzüge der theoretischen Logik.D. Hilbert & W. Ackermann - 1928 - Annalen der Philosophie Und Philosophischen Kritik 7:157-157.
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  • Sur la méthode déductive.Alfred Tarski - 1937 - Travaux du IXe Congrès International de Philosophie 6:95-103.
    Le but principal de la communication est d’esquisser les traits essentiels de la méthode appliquée dans les sciences déductives.1. A quoi tend la méthode déductive? Termes primitifs et définis ; axiomes et théorèmes. Les sciences antérieures à une science donnée. La méthode déductive considérée comme propriété caractéristique des mathématiques.2. Liberté dans le choix des termes primitifs et des axiomes ; notion d’équivalence de deux systèmes de termes ou de propositions.Postulats d’indépendance des termes primitifs et des axiomes.3. Postulats de la formalisation (...)
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  • Sur la compatibilité Des axiomes: De l'arithmétique.Mario Pieri - 1906 - Revue de Métaphysique et de Morale 14 (2):196 - 207.
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  • On Mathematical Logic and the Deductive Method.Alfred Tarski - 1938 - Journal of Symbolic Logic 3 (1):51-52.
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  • Mathematical Thought From Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
     
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  • From Kant to Hilbert: A Source Book in the Foundations of Mathematics.William Bragg Ewald (ed.) - 1996 - Oxford University Press.
    This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...)
     
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